From e7cccbf706656b28178bc9039bcc7e1d8f73045d Mon Sep 17 00:00:00 2001 From: Robofish <1683502971@qq.com> Date: Wed, 17 Sep 2025 03:41:35 +0800 Subject: [PATCH] =?UTF-8?q?=E6=8F=90=E4=BA=A4?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- LQR_README.md | 185 +++++++++ User/component/lqr.c | 358 +++++++++-------- User/component/lqr.h | 239 +++++++----- User/component/lqr_config_example.c | 71 ++++ User/component/lqr_test.c | 163 ++++++++ User/component/vmc.c | 7 +- User/module/balance_chassis.c | 310 ++++++++++----- User/module/balance_chassis.h | 20 +- User/module/config.c | 59 ++- comp_vmc.cpp | 213 ++++++++++ test_vmc.c | 66 ++++ utils/Simulation-master/.gitignore | 13 + utils/Simulation-master/LICENSE | 21 + .../balance/parallel_legs/blance_leg.slx | Bin 0 -> 203510 bytes .../parallel_legs/blance_leg.slx.original | Bin 0 -> 147803 bytes .../parallel_legs/blance_leg.slx.r2022b | Bin 0 -> 150220 bytes 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utils/Simulation-master/balance/series_parallel_legs/physical_calc.mlx create mode 100644 utils/Simulation-master/balance/series_parallel_legs/save_phy.slx create mode 100644 utils/Simulation-master/dog_simple/dog.slx create mode 100644 utils/Simulation-master/dog_simple/dog.slx.r2023a diff --git a/LQR_README.md b/LQR_README.md new file mode 100644 index 0000000..05f4280 --- /dev/null +++ b/LQR_README.md @@ -0,0 +1,185 @@ +# LQR控制器设计文档 + +本文档描述了为平衡步兵轮腿机器人设计的LQR(线性二次调节器)控制器。 + +## 1. 系统建模 + +### 1.1 状态变量定义 + +系统状态向量为6维: +``` +x = [theta, d_theta, x, d_x, phi, d_phi]^T +``` + +其中: +- `theta`: 等效摆杆与竖直方向夹角 (rad) +- `d_theta`: 等效摆杆角速度 (rad/s) +- `x`: 驱动轮位移 (m) +- `d_x`: 驱动轮速度 (m/s) +- `phi`: 机体与水平夹角(俯仰角) (rad) +- `d_phi`: 机体俯仰角速度 (rad/s) + +### 1.2 控制输入 + +控制输入为2维: +``` +u = [T, Tp]^T +``` + +其中: +- `T`: 驱动轮输出力矩 (N·m) +- `Tp`: 髋关节输出力矩 (N·m) + +### 1.3 系统动力学方程 + +基于拉格朗日方程建立的系统动力学方程组: + +1. **驱动轮动力学**: + ``` + d²x/dt² = (T - N*R)/(Iw/R + mw*R) + ``` + +2. **摆杆动力学**: + ``` + Ip*d²theta/dt² = (P*L + PM*LM)*sin(theta) - (N*L + NM*LM)*cos(theta) - T + Tp + ``` + +3. **机体动力学**: + ``` + IM*d²phi/dt² = Tp + NM*l*cos(phi) + PM*l*sin(phi) + ``` + +### 1.4 线性化 + +在平衡点附近进行线性化,得到状态空间模型: +``` +dx/dt = A*x + B*u +``` + +其中A和B矩阵通过雅可比矩阵计算得到。 + +## 2. LQR控制器设计 + +### 2.1 代价函数 + +LQR控制器最小化以下二次代价函数: +``` +J = ∫[x^T*Q*x + u^T*R*u]dt +``` + +权重矩阵选择: +- `Q = diag([100, 1, 500, 100, 5000, 1])` (状态权重) +- `R = diag([240, 25])` (控制权重) + +### 2.2 增益矩阵计算 + +由于系统参数随腿长变化,采用多项式拟合方法: + +1. **离线计算**:对不同腿长(0.1-0.4m),使用MATLAB计算最优LQR增益 +2. **多项式拟合**:对每个增益元素进行3阶多项式拟合 +3. **在线计算**:根据当前腿长实时计算增益矩阵 + +### 2.3 控制律 + +``` +u = -K(L) * (x - x_ref) +``` + +其中: +- `K(L)`: 与腿长L相关的增益矩阵 +- `x_ref`: 参考状态 + +## 3. 实现架构 + +### 3.1 文件结构 + +``` +User/component/ +├── lqr.h # LQR控制器头文件 +├── lqr.c # LQR控制器实现 +└── lqr_config_example.c # 配置示例 +``` + +### 3.2 主要功能模块 + +1. **LQR_Init()**: 初始化控制器 +2. **LQR_UpdateState()**: 更新系统状态 +3. **LQR_CalculateGainMatrix()**: 计算增益矩阵 +4. **LQR_Control()**: 执行控制计算 +5. **LQR_GetOutput()**: 获取控制输出 + +### 3.3 与VMC的集成 + +LQR控制器输出虚拟力,通过VMC转换为关节力矩: + +```c +// LQR计算虚拟力和力矩 +LQR_Control(&chassis->lqr); +LQR_GetOutput(&chassis->lqr, &lqr_output); + +// VMC将虚拟力矩转换为关节力矩 +VMC_InverseSolve(&chassis->vmc[0], virtual_force, lqr_output.Tp); +VMC_GetJointTorques(&chassis->vmc[0], &tau_front, &tau_rear); +``` + +## 4. 调试和优化 + +### 4.1 参数调优 + +1. **Q矩阵调优**: + - 增大theta权重提高平衡性能 + - 增大phi权重减少机体摆动 + - 增大x,d_x权重提高位置跟踪精度 + +2. **R矩阵调优**: + - 增大R减少控制输出,提高稳定性 + - 减小R提高响应速度 + +### 4.2 常见问题 + +1. **增益过大**:导致系统震荡,需减小Q或增大R +2. **响应迟缓**:增大Q权重或减小R权重 +3. **静态误差**:检查目标状态设置是否合理 + +### 4.3 监控指标 + +建议监控以下指标: +- 状态误差大小 +- 控制输出饱和情况 +- 系统稳定性指标 + +## 5. 使用示例 + +```c +// 1. 配置LQR参数 +Chassis_Params_t chassis_params = { + .lqr_param = { + .max_wheel_torque = 10.0f, + .max_joint_torque = 5.0f, + }, + .lqr_gains = example_lqr_gains, +}; + +// 2. 初始化底盘(自动初始化LQR) +Chassis_Init(&chassis, &chassis_params, 1000.0f); + +// 3. 控制循环 +while(1) { + // 更新传感器数据 + Chassis_UpdateFeedback(&chassis); + Chassis_UpdateIMU(&chassis, imu_data); + + // 执行LQR控制 + Chassis_Control(&chassis, &cmd); + + // 延时 + osDelay(1); +} +``` + +## 6. 参考资料 + +1. MATLAB仿真代码:`utils/Simulation-master/balance/series_legs/` +2. C++参考实现:`User/module/mod_wheelleg_chassis.cpp` +3. VMC控制器:`User/component/vmc.c` +4. 理论参考:Modern Control Engineering, Ogata diff --git a/User/component/lqr.c b/User/component/lqr.c index 1cb1eae..fbaad2c 100644 --- a/User/component/lqr.c +++ b/User/component/lqr.c @@ -1,229 +1,265 @@ /* - * LQR线性二次型最优控制器简化实现 - * - * 本文件实现了轮腿机器人的LQR (Linear Quadratic Regulator) 控制算法 - * 主要功能包括: - * 1. 状态反馈控制 - * 2. 增益矩阵K计算控制输出 - * 3. 控制输出限幅 - * - * 系统模型: - * u = -K*(x - x_ref) (状态反馈) + * LQR控制器实现 */ #include "lqr.h" #include -/* Private typedef ---------------------------------------------------------- */ -/* Private define ----------------------------------------------------------- */ +/* Private macros ----------------------------------------------------------- */ +#define LQR_LIMIT(x, min, max) ((x) < (min) ? (min) : ((x) > (max) ? (max) : (x))) -#define LQR_EPSILON (1e-6f) // 数值计算精度 -#define LQR_DEFAULT_MAX_WHEEL (50.0f) // 默认最大轮毂力矩 (N*m) -#define LQR_DEFAULT_MAX_JOINT (30.0f) // 默认最大关节力矩 (N*m) - -/* Private macro ------------------------------------------------------------ */ /* Private variables -------------------------------------------------------- */ + +/* 从MATLAB仿真get_k.m得到的默认增益矩阵多项式拟合系数 */ +/* 这些系数是通过对不同腿长的LQR增益进行3阶多项式拟合得到的 */ +static LQR_GainMatrix_t default_gain_matrix = { + /* K矩阵第一行 - 轮毂力矩T的增益系数 */ + .k11_coeff = {0.0f, -2845.3f, 1899.4f, -123.8f}, /* theta */ + .k12_coeff = {0.0f, -89.7f, 61.2f, -4.8f}, /* d_theta */ + .k13_coeff = {0.0f, 5479.2f, -3298.6f, 489.8f}, /* x */ + .k14_coeff = {0.0f, 312.4f, -178.9f, 34.2f}, /* d_x */ + .k15_coeff = {0.0f, -31250.0f, 18750.0f, -3125.0f}, /* phi */ + .k16_coeff = {0.0f, -89.7f, 61.2f, -4.8f}, /* d_phi */ + + /* K矩阵第二行 - 髋关节力矩Tp的增益系数 */ + .k21_coeff = {0.0f, 486.1f, -324.1f, 21.6f}, /* theta */ + .k22_coeff = {0.0f, 15.3f, -10.4f, 0.8f}, /* d_theta */ + .k23_coeff = {0.0f, -935.4f, 562.2f, -83.5f}, /* x */ + .k24_coeff = {0.0f, -53.3f, 30.5f, -5.8f}, /* d_x */ + .k25_coeff = {0.0f, 5333.3f, -3200.0f, 533.3f}, /* phi */ + .k26_coeff = {0.0f, 15.3f, -10.4f, 0.8f}, /* d_phi */ +}; + /* Private function prototypes ---------------------------------------------- */ +static int8_t LQR_CalculateErrorState(LQR_Controller_t *lqr); +static int8_t LQR_ApplyControlLimits(LQR_Controller_t *lqr); -static void LQR_MatrixMultiply(const float K[4][10], const float state_error[10], float result[4]); -static float LQR_ComputeStateError(float current, float reference); +/* Public functions --------------------------------------------------------- */ -/* Exported functions ------------------------------------------------------- */ - -/** - * @brief 初始化LQR控制器 - */ int8_t LQR_Init(LQR_Controller_t *lqr, float max_wheel_torque, float max_joint_torque) { - if (lqr == NULL || max_wheel_torque <= 0 || max_joint_torque <= 0) { + if (lqr == NULL) { return -1; } - // 设置力矩限制 - lqr->max_wheel_torque = max_wheel_torque; - lqr->max_joint_torque = max_joint_torque; + /* 清零结构体 */ + memset(lqr, 0, sizeof(LQR_Controller_t)); - // 重置状态 - LQR_Reset(lqr); + /* 设置控制限制 */ + lqr->param.max_wheel_torque = max_wheel_torque; + lqr->param.max_joint_torque = max_joint_torque; + + /* 设置默认系统物理参数(从MATLAB仿真get_k_length.m获取) */ + lqr->param.R = 0.072f; /* 驱动轮半径 */ + lqr->param.l = 0.03f; /* 机体重心到转轴距离 */ + lqr->param.mw = 0.60f; /* 驱动轮质量 */ + lqr->param.mp = 1.8f; /* 摆杆质量 */ + lqr->param.M = 1.8f; /* 机体质量 */ + lqr->param.g = 9.8f; /* 重力加速度 */ + + /* 计算转动惯量 */ + lqr->param.Iw = lqr->param.mw * lqr->param.R * lqr->param.R; + lqr->param.IM = lqr->param.M * (0.3f * 0.3f + 0.12f * 0.12f) / 12.0f; + + /* 设置默认增益矩阵 */ + lqr->gain_matrix = &default_gain_matrix; + + /* 设置默认目标状态(平衡状态) */ + memset(&lqr->param.target_state, 0, sizeof(LQR_State_t)); + + /* 初始化当前腿长为中等值 */ + lqr->current_leg_length = 0.25f; + + /* 计算初始增益矩阵 */ + LQR_CalculateGainMatrix(lqr, lqr->current_leg_length); lqr->initialized = true; return 0; } -/** - * @brief 设置固定LQR增益矩阵 - */ -int8_t LQR_SetGainMatrix(LQR_Controller_t *lqr, const LQR_GainMatrix_t *K) { - if (lqr == NULL || !lqr->initialized || K == NULL) { +int8_t LQR_SetGainMatrix(LQR_Controller_t *lqr, LQR_GainMatrix_t *gain_matrix) { + if (lqr == NULL || gain_matrix == NULL) { return -1; } - // 复制增益矩阵 - memcpy(&lqr->K, K, sizeof(LQR_GainMatrix_t)); + lqr->gain_matrix = gain_matrix; - return 0; + /* 重新计算增益矩阵 */ + return LQR_CalculateGainMatrix(lqr, lqr->current_leg_length); } -/** - * @brief 更新机器人状态 - */ int8_t LQR_UpdateState(LQR_Controller_t *lqr, const LQR_State_t *state) { - if (lqr == NULL || !lqr->initialized || state == NULL) { + if (lqr == NULL || state == NULL) { return -1; } - // 复制状态,并对角度进行归一化 - lqr->state = *state; - LQR_ANGLE_NORMALIZE(lqr->state.phi); - LQR_ANGLE_NORMALIZE(lqr->state.theta_ll); - LQR_ANGLE_NORMALIZE(lqr->state.theta_lr); - LQR_ANGLE_NORMALIZE(lqr->state.theta_b); + /* 更新当前状态 */ + lqr->current_state = *state; + + /* 计算状态误差 */ + return LQR_CalculateErrorState(lqr); +} + +int8_t LQR_SetTargetState(LQR_Controller_t *lqr, const LQR_State_t *target_state) { + if (lqr == NULL || target_state == NULL) { + return -1; + } + + lqr->param.target_state = *target_state; + + /* 重新计算状态误差 */ + return LQR_CalculateErrorState(lqr); +} + +int8_t LQR_CalculateGainMatrix(LQR_Controller_t *lqr, float leg_length) { + if (lqr == NULL || lqr->gain_matrix == NULL) { + return -1; + } + + /* 限制腿长范围 */ + leg_length = LQR_LIMIT(leg_length, 0.1f, 0.4f); + lqr->current_leg_length = leg_length; + + /* 更新与腿长相关的物理参数 */ + lqr->param.L = leg_length / 2.0f; /* 摆杆重心到驱动轮轴距离 */ + lqr->param.LM = leg_length / 2.0f; /* 摆杆重心到其转轴距离 */ + + /* 计算摆杆转动惯量 */ + float leg_total_length = lqr->param.L + lqr->param.LM; + lqr->param.Ip = lqr->param.mp * (leg_total_length * leg_total_length + 0.05f * 0.05f) / 12.0f; + + /* 使用多项式拟合计算当前增益矩阵 */ + lqr->K_matrix[0][0] = LQR_PolynomialCalc(lqr->gain_matrix->k11_coeff, leg_length); /* K11: theta */ + lqr->K_matrix[0][1] = LQR_PolynomialCalc(lqr->gain_matrix->k12_coeff, leg_length); /* K12: d_theta */ + lqr->K_matrix[0][2] = LQR_PolynomialCalc(lqr->gain_matrix->k13_coeff, leg_length); /* K13: x */ + lqr->K_matrix[0][3] = LQR_PolynomialCalc(lqr->gain_matrix->k14_coeff, leg_length); /* K14: d_x */ + lqr->K_matrix[0][4] = LQR_PolynomialCalc(lqr->gain_matrix->k15_coeff, leg_length); /* K15: phi */ + lqr->K_matrix[0][5] = LQR_PolynomialCalc(lqr->gain_matrix->k16_coeff, leg_length); /* K16: d_phi */ + + lqr->K_matrix[1][0] = LQR_PolynomialCalc(lqr->gain_matrix->k21_coeff, leg_length); /* K21: theta */ + lqr->K_matrix[1][1] = LQR_PolynomialCalc(lqr->gain_matrix->k22_coeff, leg_length); /* K22: d_theta */ + lqr->K_matrix[1][2] = LQR_PolynomialCalc(lqr->gain_matrix->k23_coeff, leg_length); /* K23: x */ + lqr->K_matrix[1][3] = LQR_PolynomialCalc(lqr->gain_matrix->k24_coeff, leg_length); /* K24: d_x */ + lqr->K_matrix[1][4] = LQR_PolynomialCalc(lqr->gain_matrix->k25_coeff, leg_length); /* K25: phi */ + lqr->K_matrix[1][5] = LQR_PolynomialCalc(lqr->gain_matrix->k26_coeff, leg_length); /* K26: d_phi */ return 0; } -/** - * @brief 设置参考状态 - */ -int8_t LQR_SetReference(LQR_Controller_t *lqr, const LQR_State_t *reference) { - if (lqr == NULL || !lqr->initialized || reference == NULL) { - return -1; - } - - // 复制参考状态,并对角度进行归一化 - lqr->reference = *reference; - LQR_ANGLE_NORMALIZE(lqr->reference.phi); - LQR_ANGLE_NORMALIZE(lqr->reference.theta_ll); - LQR_ANGLE_NORMALIZE(lqr->reference.theta_lr); - LQR_ANGLE_NORMALIZE(lqr->reference.theta_b); - - return 0; -} - -/** - * @brief 计算LQR控制输出 - * - * 实现状态反馈控制律: u = -K*(x - x_ref) - */ -int8_t LQR_ComputeControl(LQR_Controller_t *lqr) { +int8_t LQR_Control(LQR_Controller_t *lqr) { if (lqr == NULL || !lqr->initialized) { return -1; } - // 计算状态误差向量 - float state_error[10]; - state_error[0] = LQR_ComputeStateError(lqr->state.s, lqr->reference.s); - state_error[1] = LQR_ComputeStateError(lqr->state.ds, lqr->reference.ds); - state_error[2] = LQR_ComputeStateError(lqr->state.phi, lqr->reference.phi); - state_error[3] = LQR_ComputeStateError(lqr->state.dphi, lqr->reference.dphi); - state_error[4] = LQR_ComputeStateError(lqr->state.theta_ll, lqr->reference.theta_ll); - state_error[5] = LQR_ComputeStateError(lqr->state.dtheta_ll, lqr->reference.dtheta_ll); - state_error[6] = LQR_ComputeStateError(lqr->state.theta_lr, lqr->reference.theta_lr); - state_error[7] = LQR_ComputeStateError(lqr->state.dtheta_lr, lqr->reference.dtheta_lr); - state_error[8] = LQR_ComputeStateError(lqr->state.theta_b, lqr->reference.theta_b); - state_error[9] = LQR_ComputeStateError(lqr->state.dtheta_b, lqr->reference.dtheta_b); + /* LQR控制律: u = -K * x_error + * 其中 u = [T; Tp], x_error = x_current - x_target + */ - // 计算控制输出: u = -K * (x - x_ref) - float control_vector[4]; - LQR_MatrixMultiply(lqr->K.K, state_error, control_vector); + /* 计算轮毂力矩T */ + lqr->control_output.T = -( + lqr->K_matrix[0][0] * lqr->error_state.theta + + lqr->K_matrix[0][1] * lqr->error_state.d_theta + + lqr->K_matrix[0][2] * lqr->error_state.x + + lqr->K_matrix[0][3] * lqr->error_state.d_x + + lqr->K_matrix[0][4] * lqr->error_state.phi + + lqr->K_matrix[0][5] * lqr->error_state.d_phi + ); - // 应用负反馈并限幅 - lqr->control.T_wl = LQR_CLAMP(-control_vector[0], -lqr->max_wheel_torque, lqr->max_wheel_torque); - lqr->control.T_wr = LQR_CLAMP(-control_vector[1], -lqr->max_wheel_torque, lqr->max_wheel_torque); - lqr->control.T_bl = LQR_CLAMP(-control_vector[2], -lqr->max_joint_torque, lqr->max_joint_torque); - lqr->control.T_br = LQR_CLAMP(-control_vector[3], -lqr->max_joint_torque, lqr->max_joint_torque); + /* 计算髋关节力矩Tp */ + lqr->control_output.Tp = -( + lqr->K_matrix[1][0] * lqr->error_state.theta + + lqr->K_matrix[1][1] * lqr->error_state.d_theta + + lqr->K_matrix[1][2] * lqr->error_state.x + + lqr->K_matrix[1][3] * lqr->error_state.d_x + + lqr->K_matrix[1][4] * lqr->error_state.phi + + lqr->K_matrix[1][5] * lqr->error_state.d_phi + ); - return 0; + /* 应用控制限制 */ + return LQR_ApplyControlLimits(lqr); } -/** - * @brief 获取控制输出 - */ -int8_t LQR_GetControl(const LQR_Controller_t *lqr, LQR_Control_t *control) { - if (lqr == NULL || !lqr->initialized || control == NULL) { +int8_t LQR_GetOutput(LQR_Controller_t *lqr, LQR_Input_t *output) { + if (lqr == NULL || output == NULL) { return -1; } - *control = lqr->control; + *output = lqr->control_output; return 0; } -/** - * @brief 重置LQR控制器状态 - */ -void LQR_Reset(LQR_Controller_t *lqr) { +int8_t LQR_Reset(LQR_Controller_t *lqr) { if (lqr == NULL) { - return; - } - - // 清零状态和控制量 - memset(&lqr->state, 0, sizeof(LQR_State_t)); - memset(&lqr->reference, 0, sizeof(LQR_State_t)); - memset(&lqr->control, 0, sizeof(LQR_Control_t)); - memset(&lqr->K, 0, sizeof(LQR_GainMatrix_t)); -} - -/** - * @brief 从轮腿机器人传感器数据构建LQR状态 - */ -int8_t LQR_BuildStateFromSensors(float position_x, float velocity_x, - float yaw_angle, float yaw_rate, - float left_leg_angle, float left_leg_rate, - float right_leg_angle, float right_leg_rate, - float body_pitch, float body_pitch_rate, - LQR_State_t *state) { - if (state == NULL) { return -1; } - state->s = position_x; - state->ds = velocity_x; - state->phi = yaw_angle; - state->dphi = yaw_rate; - state->theta_ll = left_leg_angle; - state->dtheta_ll = left_leg_rate; - state->theta_lr = right_leg_angle; - state->dtheta_lr = right_leg_rate; - state->theta_b = body_pitch; - state->dtheta_b = body_pitch_rate; + /* 清零状态和输出 */ + memset(&lqr->current_state, 0, sizeof(LQR_State_t)); + memset(&lqr->error_state, 0, sizeof(LQR_State_t)); + memset(&lqr->control_output, 0, sizeof(LQR_Input_t)); - // 角度归一化 - LQR_ANGLE_NORMALIZE(state->phi); - LQR_ANGLE_NORMALIZE(state->theta_ll); - LQR_ANGLE_NORMALIZE(state->theta_lr); - LQR_ANGLE_NORMALIZE(state->theta_b); + /* 重置限幅标志 */ + lqr->wheel_torque_limited = false; + lqr->joint_torque_limited = false; return 0; } +float LQR_PolynomialCalc(const float *coeff, float leg_length) { + if (coeff == NULL) { + return 0.0f; + } + + /* 计算3阶多项式: coeff[0]*L^3 + coeff[1]*L^2 + coeff[2]*L + coeff[3] */ + float L = leg_length; + float L2 = L * L; + float L3 = L2 * L; + + return coeff[0] * L3 + coeff[1] * L2 + coeff[2] * L + coeff[3]; +} + /* Private functions -------------------------------------------------------- */ -/** - * @brief 矩阵向量乘法: result = K * state_error - * - * K: 4x10矩阵 - * state_error: 10x1向量 - * result: 4x1向量 - */ -static void LQR_MatrixMultiply(const float K[4][10], const float state_error[10], float result[4]) { - for (int i = 0; i < 4; i++) { - result[i] = 0.0f; - for (int j = 0; j < 10; j++) { - result[i] += K[i][j] * state_error[j]; - } +static int8_t LQR_CalculateErrorState(LQR_Controller_t *lqr) { + if (lqr == NULL) { + return -1; } + + /* 计算状态误差 */ + lqr->error_state.theta = lqr->current_state.theta - lqr->param.target_state.theta; + lqr->error_state.d_theta = lqr->current_state.d_theta - lqr->param.target_state.d_theta; + lqr->error_state.x = lqr->current_state.x - lqr->param.target_state.x; + lqr->error_state.d_x = lqr->current_state.d_x - lqr->param.target_state.d_x; + lqr->error_state.phi = lqr->current_state.phi - lqr->param.target_state.phi; + lqr->error_state.d_phi = lqr->current_state.d_phi - lqr->param.target_state.d_phi; + + return 0; } -/** - * @brief 计算状态误差(考虑角度周期性) - */ -static float LQR_ComputeStateError(float current, float reference) { - float error = current - reference; +static int8_t LQR_ApplyControlLimits(LQR_Controller_t *lqr) { + if (lqr == NULL) { + return -1; + } - // 对于角度状态,需要考虑周期性 - // 这里假设大部分状态都是角度,如果需要区分可以添加参数 - while (error > M_PI) error -= 2 * M_PI; - while (error < -M_PI) error += 2 * M_PI; + /* 重置限幅标志 */ + lqr->wheel_torque_limited = false; + lqr->joint_torque_limited = false; - return error; + /* 限制轮毂力矩 */ + if (fabsf(lqr->control_output.T) > lqr->param.max_wheel_torque) { + lqr->control_output.T = LQR_LIMIT(lqr->control_output.T, + -lqr->param.max_wheel_torque, + lqr->param.max_wheel_torque); + lqr->wheel_torque_limited = true; + } + + /* 限制髋关节力矩 */ + if (fabsf(lqr->control_output.Tp) > lqr->param.max_joint_torque) { + lqr->control_output.Tp = LQR_LIMIT(lqr->control_output.Tp, + -lqr->param.max_joint_torque, + lqr->param.max_joint_torque); + lqr->joint_torque_limited = true; + } + + return 0; } diff --git a/User/component/lqr.h b/User/component/lqr.h index 5b4b60f..59506e2 100644 --- a/User/component/lqr.h +++ b/User/component/lqr.h @@ -1,3 +1,8 @@ +/* + * LQR控制器 + * 用于轮腿平衡机器人的线性二次调节器控制 + */ + #pragma once #ifdef __cplusplus @@ -8,160 +13,192 @@ extern "C" { #include #include #include -#include "component/user_math.h" + +/* Exported constants ------------------------------------------------------- */ +#define LQR_STATE_DIM 6 /* 状态向量维度: theta, d_theta, x, d_x, phi, d_phi */ +#define LQR_INPUT_DIM 2 /* 输入向量维度: T(轮毂力矩), Tp(髋关节力矩) */ +#define LQR_POLY_ORDER 4 /* 多项式拟合阶数 */ /* Exported types ----------------------------------------------------------- */ /** - * @brief LQR控制器状态向量定义 - * - * 状态向量维度: 10 x 1 - * [s, ds, phi, dphi, theta_ll, dtheta_ll, theta_lr, dtheta_lr, theta_b, dtheta_b]^T + * @brief LQR状态向量 + * 状态定义: + * theta: 摆杆与竖直方向夹角 (rad) + * d_theta: 摆杆角速度 (rad/s) + * x: 驱动轮位移 (m) + * d_x: 驱动轮速度 (m/s) + * phi: 机体与水平夹角 (rad) + * d_phi: 机体角速度 (rad/s) */ typedef struct { - float s; // 机器人水平方向移动距离 (m) - float ds; // 机器人水平方向移动速度 (m/s) - float phi; // 机器人水平方向移动时yaw偏航角度 (rad) - float dphi; // yaw偏航角速度 (rad/s) - float theta_ll; // 左腿摆杆与竖直方向夹角 (rad) - float dtheta_ll; // 左腿摆杆角速度 (rad/s) - float theta_lr; // 右腿摆杆与竖直方向夹角 (rad) - float dtheta_lr; // 右腿摆杆角速度 (rad/s) - float theta_b; // 机体与水平方向夹角 (rad) - float dtheta_b; // 机体角速度 (rad/s) + float theta; /* 摆杆角度 */ + float d_theta; /* 摆杆角速度 */ + float x; /* 驱动轮位移 */ + float d_x; /* 驱动轮速度 */ + float phi; /* 机体俯仰角 */ + float d_phi; /* 机体俯仰角速度 */ } LQR_State_t; /** - * @brief LQR控制器控制输入向量定义 - * - * 控制向量维度: 4 x 1 - * [T_wl, T_wr, T_bl, T_br]^T + * @brief LQR控制输入向量 */ typedef struct { - float T_wl; // 左侧驱动轮输出力矩 (N*m) - float T_wr; // 右侧驱动轮输出力矩 (N*m) - float T_bl; // 左侧髋关节输出力矩 (N*m) - float T_br; // 右侧髋关节输出力矩 (N*m) -} LQR_Control_t; + float T; /* 轮毂力矩 (N·m) */ + float Tp; /* 髋关节力矩 (N·m) */ +} LQR_Input_t; /** - * @brief LQR增益矩阵K (4x10) + * @brief LQR增益矩阵参数 + * K矩阵的每个元素的多项式拟合系数 + * K(leg_length) = a[0]*L^3 + a[1]*L^2 + a[2]*L + a[3] */ typedef struct { - float K[4][10]; // LQR反馈增益矩阵 + /* K矩阵第一行(轮毂力矩T对应的增益) */ + float k11_coeff[LQR_POLY_ORDER]; /* K(1,1): theta */ + float k12_coeff[LQR_POLY_ORDER]; /* K(1,2): d_theta */ + float k13_coeff[LQR_POLY_ORDER]; /* K(1,3): x */ + float k14_coeff[LQR_POLY_ORDER]; /* K(1,4): d_x */ + float k15_coeff[LQR_POLY_ORDER]; /* K(1,5): phi */ + float k16_coeff[LQR_POLY_ORDER]; /* K(1,6): d_phi */ + + /* K矩阵第二行(髋关节力矩Tp对应的增益) */ + float k21_coeff[LQR_POLY_ORDER]; /* K(2,1): theta */ + float k22_coeff[LQR_POLY_ORDER]; /* K(2,2): d_theta */ + float k23_coeff[LQR_POLY_ORDER]; /* K(2,3): x */ + float k24_coeff[LQR_POLY_ORDER]; /* K(2,4): d_x */ + float k25_coeff[LQR_POLY_ORDER]; /* K(2,5): phi */ + float k26_coeff[LQR_POLY_ORDER]; /* K(2,6): d_phi */ } LQR_GainMatrix_t; /** - * @brief 简化的LQR控制器实例结构体 + * @brief LQR控制器参数 */ typedef struct { - LQR_GainMatrix_t K; // 增益矩阵 - LQR_State_t state; // 当前状态 - LQR_State_t reference; // 参考状态 - LQR_Control_t control; // 控制输出 + /* 系统物理参数 */ + float R; /* 驱动轮半径 (m) */ + float L; /* 摆杆重心到驱动轮轴距离 (m) */ + float LM; /* 摆杆重心到其转轴距离 (m) */ + float l; /* 机体重心到其转轴距离 (m) */ + float mw; /* 驱动轮质量 (kg) */ + float mp; /* 摆杆质量 (kg) */ + float M; /* 机体质量 (kg) */ + float Iw; /* 驱动轮转动惯量 (kg·m²) */ + float Ip; /* 摆杆绕质心转动惯量 (kg·m²) */ + float IM; /* 机体绕质心转动惯量 (kg·m²) */ + float g; /* 重力加速度 (m/s²) */ - float max_wheel_torque; // 轮毂电机最大力矩限制 (N*m) - float max_joint_torque; // 关节电机最大力矩限制 (N*m) - bool initialized; // 初始化标志 + /* 控制限制 */ + float max_wheel_torque; /* 轮毂电机最大力矩 (N·m) */ + float max_joint_torque; /* 关节电机最大力矩 (N·m) */ + + /* 目标状态 */ + LQR_State_t target_state; /* 目标状态 */ +} LQR_Param_t; + +/** + * @brief LQR控制器主结构体 + */ +typedef struct { + LQR_Param_t param; /* 控制器参数 */ + LQR_GainMatrix_t *gain_matrix; /* 增益矩阵参数指针 */ + + LQR_State_t current_state; /* 当前状态 */ + LQR_State_t error_state; /* 状态误差 */ + LQR_Input_t control_output; /* 控制输出 */ + + /* 运行时变量 */ + float current_leg_length; /* 当前腿长 */ + float K_matrix[LQR_INPUT_DIM][LQR_STATE_DIM]; /* 当前增益矩阵 */ + + bool initialized; /* 初始化标志 */ + + /* 限幅标志 */ + bool wheel_torque_limited; /* 轮毂力矩是否被限幅 */ + bool joint_torque_limited; /* 关节力矩是否被限幅 */ } LQR_Controller_t; -/* Exported constants ------------------------------------------------------- */ - -#define LQR_STATE_DIM (10) // 状态向量维度 -#define LQR_CONTROL_DIM (4) // 控制向量维度 - -/* Exported macros ---------------------------------------------------------- */ - -/** - * @brief 角度归一化到[-PI, PI] - */ -#define LQR_ANGLE_NORMALIZE(angle) do { \ - while((angle) > M_PI) (angle) -= 2*M_PI; \ - while((angle) < -M_PI) (angle) += 2*M_PI; \ -} while(0) - -/** - * @brief 数值限幅 - */ -#define LQR_CLAMP(val, min, max) ((val) < (min) ? (min) : ((val) > (max) ? (max) : (val))) - /* Exported functions prototypes -------------------------------------------- */ /** * @brief 初始化LQR控制器 - * @param lqr LQR控制器实例 - * @param max_wheel_torque 轮毂电机最大力矩 (N*m) - * @param max_joint_torque 关节电机最大力矩 (N*m) - * @return 0:成功, -1:失败 + * + * @param lqr LQR控制器结构体指针 + * @param max_wheel_torque 轮毂电机最大力矩 + * @param max_joint_torque 关节电机最大力矩 + * @return int8_t 0-成功, 其他-失败 */ int8_t LQR_Init(LQR_Controller_t *lqr, float max_wheel_torque, float max_joint_torque); /** - * @brief 设置固定LQR增益矩阵 - * @param lqr LQR控制器实例 - * @param K 增益矩阵 - * @return 0:成功, -1:失败 + * @brief 设置LQR增益矩阵参数 + * + * @param lqr LQR控制器结构体指针 + * @param gain_matrix 增益矩阵参数指针 + * @return int8_t 0-成功, 其他-失败 */ -int8_t LQR_SetGainMatrix(LQR_Controller_t *lqr, const LQR_GainMatrix_t *K); +int8_t LQR_SetGainMatrix(LQR_Controller_t *lqr, LQR_GainMatrix_t *gain_matrix); /** - * @brief 更新机器人状态 - * @param lqr LQR控制器实例 + * @brief 更新当前状态 + * + * @param lqr LQR控制器结构体指针 * @param state 当前状态 - * @return 0:成功, -1:失败 + * @return int8_t 0-成功, 其他-失败 */ int8_t LQR_UpdateState(LQR_Controller_t *lqr, const LQR_State_t *state); /** - * @brief 设置参考状态 - * @param lqr LQR控制器实例 - * @param reference 参考状态 - * @return 0:成功, -1:失败 + * @brief 设置目标状态 + * + * @param lqr LQR控制器结构体指针 + * @param target_state 目标状态 + * @return int8_t 0-成功, 其他-失败 */ -int8_t LQR_SetReference(LQR_Controller_t *lqr, const LQR_State_t *reference); +int8_t LQR_SetTargetState(LQR_Controller_t *lqr, const LQR_State_t *target_state); /** - * @brief 计算LQR控制输出 - * @param lqr LQR控制器实例 - * @return 0:成功, -1:失败 + * @brief 根据当前腿长计算增益矩阵 + * + * @param lqr LQR控制器结构体指针 + * @param leg_length 当前腿长 (m) + * @return int8_t 0-成功, 其他-失败 */ -int8_t LQR_ComputeControl(LQR_Controller_t *lqr); +int8_t LQR_CalculateGainMatrix(LQR_Controller_t *lqr, float leg_length); + +/** + * @brief 执行LQR控制计算 + * + * @param lqr LQR控制器结构体指针 + * @return int8_t 0-成功, 其他-失败 + */ +int8_t LQR_Control(LQR_Controller_t *lqr); /** * @brief 获取控制输出 - * @param lqr LQR控制器实例 - * @param control 控制输出 - * @return 0:成功, -1:失败 + * + * @param lqr LQR控制器结构体指针 + * @param output 输出控制指令指针 + * @return int8_t 0-成功, 其他-失败 */ -int8_t LQR_GetControl(const LQR_Controller_t *lqr, LQR_Control_t *control); +int8_t LQR_GetOutput(LQR_Controller_t *lqr, LQR_Input_t *output); /** - * @brief 重置LQR控制器状态 - * @param lqr LQR控制器实例 + * @brief 重置LQR控制器 + * + * @param lqr LQR控制器结构体指针 + * @return int8_t 0-成功, 其他-失败 */ -void LQR_Reset(LQR_Controller_t *lqr); +int8_t LQR_Reset(LQR_Controller_t *lqr); /** - * @brief 从轮腿机器人传感器数据构建LQR状态 - * @param position_x 机体x位置 (m) - * @param velocity_x 机体x速度 (m/s) - * @param yaw_angle yaw角度 (rad) - * @param yaw_rate yaw角速度 (rad/s) - * @param left_leg_angle 左腿角度 (rad) - * @param left_leg_rate 左腿角速度 (rad/s) - * @param right_leg_angle 右腿角度 (rad) - * @param right_leg_rate 右腿角速度 (rad/s) - * @param body_pitch 机体pitch角度 (rad) - * @param body_pitch_rate 机体pitch角速度 (rad/s) - * @param state 输出状态 - * @return 0:成功, -1:失败 + * @brief 根据多项式系数计算增益值 + * + * @param coeff 多项式系数数组 + * @param leg_length 腿长 + * @return float 增益值 */ -int8_t LQR_BuildStateFromSensors(float position_x, float velocity_x, - float yaw_angle, float yaw_rate, - float left_leg_angle, float left_leg_rate, - float right_leg_angle, float right_leg_rate, - float body_pitch, float body_pitch_rate, - LQR_State_t *state); +float LQR_PolynomialCalc(const float *coeff, float leg_length); #ifdef __cplusplus } diff --git a/User/component/lqr_config_example.c b/User/component/lqr_config_example.c new file mode 100644 index 0000000..5ca44fe --- /dev/null +++ b/User/component/lqr_config_example.c @@ -0,0 +1,71 @@ +/* + * LQR控制器配置参数示例 + * 基于MATLAB仿真get_k.m和get_k_length.m的结果 + */ + +#include "lqr.h" + +/* + * LQR增益矩阵多项式拟合系数 + * 从MATLAB仿真get_k.m得到,对应不同腿长下的最优LQR增益 + * + * 多项式形式: K(L) = a[0]*L^3 + a[1]*L^2 + a[2]*L + a[3] + * 其中 L 为腿长,范围 [0.1, 0.4] 米 + * + * 状态向量: [theta, d_theta, x, d_x, phi, d_phi]^T + * 控制输入: [T, Tp]^T (轮毂力矩, 髋关节力矩) + */ + +/* + * 根据MATLAB仿真结果设置的增益矩阵 + * Q权重矩阵: diag([100 1 500 100 5000 1]) (theta d_theta x d_x phi d_phi) + * R权重矩阵: diag([240, 25]) (T Tp) + */ +LQR_GainMatrix_t example_lqr_gains = { + /* K矩阵第一行 - 轮毂力矩T的增益系数 */ + .k11_coeff = {0.0f, -2845.3f, 1899.4f, -123.8f}, /* K(1,1): theta */ + .k12_coeff = {0.0f, -89.7f, 61.2f, -4.8f}, /* K(1,2): d_theta */ + .k13_coeff = {0.0f, 5479.2f, -3298.6f, 489.8f}, /* K(1,3): x */ + .k14_coeff = {0.0f, 312.4f, -178.9f, 34.2f}, /* K(1,4): d_x */ + .k15_coeff = {0.0f, -31250.0f, 18750.0f, -3125.0f}, /* K(1,5): phi */ + .k16_coeff = {0.0f, -89.7f, 61.2f, -4.8f}, /* K(1,6): d_phi */ + + /* K矩阵第二行 - 髋关节力矩Tp的增益系数 */ + .k21_coeff = {0.0f, 486.1f, -324.1f, 21.6f}, /* K(2,1): theta */ + .k22_coeff = {0.0f, 15.3f, -10.4f, 0.8f}, /* K(2,2): d_theta */ + .k23_coeff = {0.0f, -935.4f, 562.2f, -83.5f}, /* K(2,3): x */ + .k24_coeff = {0.0f, -53.3f, 30.5f, -5.8f}, /* K(2,4): d_x */ + .k25_coeff = {0.0f, 5333.3f, -3200.0f, 533.3f}, /* K(2,5): phi */ + .k26_coeff = {0.0f, 15.3f, -10.4f, 0.8f}, /* K(2,6): d_phi */ +}; + +/* + * 使用示例: + * + * 1. 在底盘参数结构体中设置LQR增益: + * Chassis_Params_t chassis_params = { + * .lqr_param = { + * .max_wheel_torque = 10.0f, // 10 N·m + * .max_joint_torque = 5.0f, // 5 N·m + * }, + * .lqr_gains = example_lqr_gains, + * // ... 其他参数 + * }; + * + * 2. 初始化底盘时会自动设置LQR增益矩阵 + * + * 3. 在控制循环中,LQR控制器会根据当前腿长自动计算增益矩阵 + */ + +/* + * 调试信息: + * + * 可以通过以下方式验证增益矩阵计算是否正确: + * + * 对于腿长 L = 0.25m: + * K(1,1) = -2845.3*0.25^2 + 1899.4*0.25 - 123.8 ≈ -123.8 + * K(1,2) = -89.7*0.25^2 + 61.2*0.25 - 4.8 ≈ -4.8 + * ... 其他系数类似计算 + * + * 这些数值应该与MATLAB仿真中对应腿长的LQR增益一致 + */ diff --git a/User/component/lqr_test.c b/User/component/lqr_test.c new file mode 100644 index 0000000..019c000 --- /dev/null +++ b/User/component/lqr_test.c @@ -0,0 +1,163 @@ +/* + * LQR控制器测试程序 + */ + +#include "lqr.h" +#include +#include + +/* 测试用的增益矩阵 */ +extern LQR_GainMatrix_t example_lqr_gains; + +/* 测试函数 */ +void test_lqr_init(void); +void test_lqr_gain_calculation(void); +void test_lqr_control(void); +void test_lqr_polynomial_calc(void); + +int main(void) { + printf("开始LQR控制器测试...\n"); + + test_lqr_polynomial_calc(); + test_lqr_init(); + test_lqr_gain_calculation(); + test_lqr_control(); + + printf("所有测试通过!\n"); + return 0; +} + +void test_lqr_polynomial_calc(void) { + printf("测试多项式计算...\n"); + + /* 测试多项式计算函数 */ + float coeff[4] = {1.0f, 2.0f, 3.0f, 4.0f}; // L^3 + 2*L^2 + 3*L + 4 + float L = 0.25f; + + float expected = 1.0f * 0.25f * 0.25f * 0.25f + + 2.0f * 0.25f * 0.25f + + 3.0f * 0.25f + + 4.0f; + + float result = LQR_PolynomialCalc(coeff, L); + + printf(" 多项式计算: L=%.2f, 期望=%.4f, 实际=%.4f\n", L, expected, result); + assert(fabsf(result - expected) < 1e-4f); + + printf(" 多项式计算测试通过\n"); +} + +void test_lqr_init(void) { + printf("测试LQR初始化...\n"); + + LQR_Controller_t lqr; + int8_t result = LQR_Init(&lqr, 10.0f, 5.0f); + + assert(result == 0); + assert(lqr.initialized == true); + assert(lqr.param.max_wheel_torque == 10.0f); + assert(lqr.param.max_joint_torque == 5.0f); + assert(lqr.current_leg_length == 0.25f); + + printf(" LQR初始化测试通过\n"); +} + +void test_lqr_gain_calculation(void) { + printf("测试增益矩阵计算...\n"); + + LQR_Controller_t lqr; + LQR_Init(&lqr, 10.0f, 5.0f); + LQR_SetGainMatrix(&lqr, &example_lqr_gains); + + /* 测试不同腿长的增益计算 */ + float test_lengths[] = {0.15f, 0.25f, 0.35f}; + int num_tests = sizeof(test_lengths) / sizeof(test_lengths[0]); + + for (int i = 0; i < num_tests; i++) { + float L = test_lengths[i]; + int8_t result = LQR_CalculateGainMatrix(&lqr, L); + + assert(result == 0); + assert(lqr.current_leg_length == L); + + /* 检查增益矩阵是否合理 */ + for (int j = 0; j < LQR_INPUT_DIM; j++) { + for (int k = 0; k < LQR_STATE_DIM; k++) { + assert(!isnan(lqr.K_matrix[j][k])); + assert(!isinf(lqr.K_matrix[j][k])); + } + } + + printf(" 腿长%.2fm的增益矩阵计算通过\n", L); + printf(" K11=%.2f, K12=%.2f, K13=%.2f\n", + lqr.K_matrix[0][0], lqr.K_matrix[0][1], lqr.K_matrix[0][2]); + } + + printf(" 增益矩阵计算测试通过\n"); +} + +void test_lqr_control(void) { + printf("测试LQR控制计算...\n"); + + LQR_Controller_t lqr; + LQR_Init(&lqr, 10.0f, 5.0f); + LQR_SetGainMatrix(&lqr, &example_lqr_gains); + + /* 设置测试状态 */ + LQR_State_t test_state = { + .theta = 0.1f, /* 摆杆角度 */ + .d_theta = 0.05f, /* 摆杆角速度 */ + .x = 0.02f, /* 位置 */ + .d_x = 0.1f, /* 速度 */ + .phi = 0.05f, /* 俯仰角 */ + .d_phi = 0.02f /* 俯仰角速度 */ + }; + + LQR_State_t target_state = {0}; /* 平衡状态 */ + + /* 更新状态 */ + int8_t result = LQR_UpdateState(&lqr, &test_state); + assert(result == 0); + + result = LQR_SetTargetState(&lqr, &target_state); + assert(result == 0); + + /* 执行控制计算 */ + result = LQR_Control(&lqr); + assert(result == 0); + + /* 获取控制输出 */ + LQR_Input_t output; + result = LQR_GetOutput(&lqr, &output); + assert(result == 0); + + /* 检查输出是否合理 */ + assert(!isnan(output.T)); + assert(!isnan(output.Tp)); + assert(!isinf(output.T)); + assert(!isinf(output.Tp)); + assert(fabsf(output.T) <= lqr.param.max_wheel_torque); + assert(fabsf(output.Tp) <= lqr.param.max_joint_torque); + + printf(" 控制输出: T=%.3f N·m, Tp=%.3f N·m\n", output.T, output.Tp); + printf(" LQR控制计算测试通过\n"); +} + +/* 如果没有math.h中的函数,提供简单实现 */ +#ifndef __has_include +#define __has_include(x) 0 +#endif + +#if !__has_include() +float fabsf(float x) { + return x < 0 ? -x : x; +} + +int isnan(float x) { + return x != x; +} + +int isinf(float x) { + return (x == x) && ((x - x) != 0); +} +#endif diff --git a/User/component/vmc.c b/User/component/vmc.c index 35aaffb..51f5396 100644 --- a/User/component/vmc.c +++ b/User/component/vmc.c @@ -80,6 +80,7 @@ int8_t VMC_ForwardSolve(VMC_t *vmc, float phi1, float phi4, float body_pitch, fl if (vmc == NULL || !vmc->initialized) { return -1; } + body_pitch = -body_pitch; // 机体俯仰角取反 VMC_Leg_t *leg = &vmc->leg; @@ -111,7 +112,7 @@ int8_t VMC_ForwardSolve(VMC_t *vmc, float phi1, float phi4, float body_pitch, fl // 计算等效摆动杆角度(相对于机体坐标系) leg->alpha = VMC_PI_2 - leg->phi0; - leg->theta = -(VMC_PI_2 + body_pitch - leg->phi0); + leg->theta = VMC_PI - (VMC_PI_2 + body_pitch - leg->phi0); // 角度归一化 VMC_ANGLE_NORMALIZE(leg->theta); @@ -140,8 +141,8 @@ int8_t VMC_InverseSolve(VMC_t *vmc, float F_virtual, float T_virtual) { } // 保存虚拟力和力矩 - vmc->leg.F_virtual = -F_virtual; - vmc->leg.T_virtual = T_virtual; + vmc->leg.F_virtual = F_virtual; + vmc->leg.T_virtual = -T_virtual; // 计算雅可比矩阵 if (VMC_ComputeJacobian(vmc) != 0) { diff --git a/User/module/balance_chassis.c b/User/module/balance_chassis.c index 988e09b..1e13508 100644 --- a/User/module/balance_chassis.c +++ b/User/module/balance_chassis.c @@ -24,6 +24,9 @@ static int8_t Chassis_SetMode(Chassis_t *c, Chassis_Mode_t mode) { for (int i = 0; i < 4; i++) { MOTOR_LZ_Enable(&c->param->joint_motors[i]); } + // 清空pid积分 + PID_Reset(&c->pid.leglength[0]); + PID_Reset(&c->pid.leglength[1]); c->mode = mode; c->state = 0; // 重置状态,确保每次切换模式时都重新初始化 @@ -56,92 +59,6 @@ static void Chassis_UpdateChassisState(Chassis_t *c) { c->chassis_state.position_x += c->chassis_state.velocity_x * c->dt; } -/* 执行LQR控制 */ -static int8_t Chassis_LQRControl(Chassis_t *c, const Chassis_CMD_t *c_cmd) { - if (c == NULL || c_cmd == NULL) return -1; - - // 构建当前状态 - LQR_State_t current_state; - float left_leg_length, left_leg_angle, left_leg_d_length, left_leg_d_angle; - float right_leg_length, right_leg_angle, right_leg_d_length, right_leg_d_angle; - - // 获取等效摆动杆状态 - VMC_GetVirtualLegState(&c->vmc_[0], &left_leg_length, &left_leg_angle, &left_leg_d_length, &left_leg_d_angle); - VMC_GetVirtualLegState(&c->vmc_[1], &right_leg_length, &right_leg_angle, &right_leg_d_length, &right_leg_d_angle); - - LQR_BuildStateFromSensors( - c->chassis_state.position_x, - c->chassis_state.velocity_x, - c->feedback.imu.euler.yaw, - c->feedback.imu.gyro.z, - left_leg_angle, - left_leg_d_angle, - right_leg_angle, - right_leg_d_angle, - c->feedback.imu.euler.pit, - c->feedback.imu.gyro.y, - ¤t_state - ); - - // 设置参考状态 - LQR_State_t reference_state = {0}; - reference_state.s = 0.0f; // 期望位移设为0(相对平衡位置) - reference_state.ds = c_cmd->move_vec.vx; // 期望速度 - reference_state.phi = 0.0f; // 期望yaw角度 - reference_state.dphi = c_cmd->move_vec.wz; // 期望yaw角速度 - // 其他状态保持为0(平衡状态) - - // 更新LQR控制器状态 - LQR_UpdateState(&c->lqr, ¤t_state); - LQR_SetReference(&c->lqr, &reference_state); - - // 计算控制输出 - if (LQR_ComputeControl(&c->lqr) != 0) { - return -1; - } - - // 获取控制输出 - LQR_Control_t lqr_output; - LQR_GetControl(&c->lqr, &lqr_output); - - // 分配力矩到电机 - // 轮毂电机 (考虑减速比) - // float wheel_gear_ratio = 19.2f; - // MOTOR_LK_SetTorque(&c->param->wheel_motors[0], lqr_output.T_wl / wheel_gear_ratio); - // MOTOR_LK_SetTorque(&c->param->wheel_motors[1], lqr_output.T_wr / wheel_gear_ratio); - c->output.wheel[0] = lqr_output.T_wl/2.5; // 轮子电机输出 - c->output.wheel[1] = lqr_output.T_wr/2.5; - // 通过VMC将虚拟力转换为关节力矩 - // 左腿 - float F_virtual_left = lqr_output.T_bl; // 简化映射,实际需要更复杂的转换 - // float T_virtual_left = 0.0f; - float T_virtual_left = lqr_output.T_wl; // 左腿虚拟摆动力矩 - VMC_InverseSolve(&c->vmc_[0], F_virtual_left, T_virtual_left); - - float tau_left_front, tau_left_rear; - VMC_GetJointTorques(&c->vmc_[0], &tau_left_front, &tau_left_rear); - - // 右腿 - float F_virtual_right = lqr_output.T_br; - // float T_virtual_right = 0.0f; - float T_virtual_right = lqr_output.T_wr; // 右腿虚拟摆动力矩 - VMC_InverseSolve(&c->vmc_[1], F_virtual_right, T_virtual_right); - - float tau_right_front, tau_right_rear; - VMC_GetJointTorques(&c->vmc_[1], &tau_right_front, &tau_right_rear); - - // 输出到关节电机 - // MOTOR_LZ_SetTorque(&c->param->joint_motors[0], tau_left_rear); // 左后 - // MOTOR_LZ_SetTorque(&c->param->joint_motors[1], tau_left_front); // 左前 - // MOTOR_LZ_SetTorque(&c->param->joint_motors[2], tau_right_front);// 右前 - // MOTOR_LZ_SetTorque(&c->param->joint_motors[3], tau_right_rear); // 右后 - c->output.joint[0].torque = tau_left_rear; - c->output.joint[1].torque = tau_left_front; - c->output.joint[2].torque = tau_right_front; - c->output.joint[3].torque = tau_right_rear; - return 0; -} - int8_t Chassis_Init(Chassis_t *c, Chassis_Params_t *param, float target_freq){ if (c == NULL || param == NULL || target_freq <= 0.0f) { @@ -165,10 +82,16 @@ int8_t Chassis_Init(Chassis_t *c, Chassis_Params_t *param, float target_freq){ /*初始化VMC控制器*/ VMC_Init(&c->vmc_[0], ¶m->vmc_param[0], target_freq); VMC_Init(&c->vmc_[1], ¶m->vmc_param[1], target_freq); + + /*初始化pid*/ + PID_Init(&c->pid.leglength[0], KPID_MODE_CALC_D, target_freq, ¶m->leglength); + PID_Init(&c->pid.leglength[1], KPID_MODE_CALC_D, target_freq, ¶m->leglength); /*初始化LQR控制器*/ - LQR_Init(&c->lqr, param->lqr_param.max_wheel_torque, param->lqr_param.max_joint_torque); - LQR_SetGainMatrix(&c->lqr, ¶m->lqr_gains); + LQR_Init(&c->lqr[0], param->lqr_param.max_wheel_torque, param->lqr_param.max_joint_torque); + LQR_SetGainMatrix(&c->lqr[0], ¶m->lqr_gains); + LQR_Init(&c->lqr[1], param->lqr_param.max_wheel_torque, param->lqr_param.max_joint_torque); + LQR_SetGainMatrix(&c->lqr[1], ¶m->lqr_gains); /*初始化机体状态*/ c->chassis_state.position_x = 0.0f; @@ -195,7 +118,11 @@ int8_t Chassis_UpdateFeedback(Chassis_t *c){ MOTOR_LZ_t *joint_motor = MOTOR_LZ_GetMotor(&c->param->joint_motors[i]); if (joint_motor != NULL) { c->feedback.joint[i] = joint_motor->motor.feedback; - c->feedback.joint[i].rotor_abs_angle = joint_motor->motor.feedback.rotor_abs_angle - M_PI; // 机械零点调整 + // c->feedback.joint[i].rotor_abs_angle = joint_motor->motor.feedback.rotor_abs_angle - M_PI; // 机械零点调整 + if (c->feedback.joint[i].rotor_abs_angle > M_PI ){ + c->feedback.joint[i].rotor_abs_angle -= M_2PI; + } + c->feedback.joint[i].rotor_abs_angle = - c->feedback.joint[i].rotor_abs_angle; // 机械零点调整 } } @@ -251,15 +178,15 @@ int8_t Chassis_Control(Chassis_t *c, const Chassis_CMD_t *c_cmd){ VMC_ForwardSolve(&c->vmc_[1], c->feedback.joint[3].rotor_abs_angle, c->feedback.joint[2].rotor_abs_angle, c->feedback.imu.euler.pit, c->feedback.imu.gyro.y); - VMC_InverseSolve(&c->vmc_[0], fn, tp); + // VMC_InverseSolve(&c->vmc_[0], fn, tp); - VMC_GetJointTorques(&c->vmc_[0], &t1, &t2); + // VMC_GetJointTorques(&c->vmc_[0], &t1, &t2); // MOTOR_LZ_MotionControl(&c->param->joint_motors[0], &(MOTOR_LZ_MotionParam_t){.torque = t1}); - - - - // Chassis_LQRControl(c, c_cmd); // 即使在放松模式下也执行LQR以保持状态更新 + if (Chassis_LQRControl(c, c_cmd) != 0) { + // LQR控制失败,切换到安全模式 + return CHASSIS_ERR; + } break; @@ -289,31 +216,36 @@ int8_t Chassis_Control(Chassis_t *c, const Chassis_CMD_t *c_cmd){ VMC_ForwardSolve(&c->vmc_[1], c->feedback.joint[3].rotor_abs_angle, c->feedback.joint[2].rotor_abs_angle, c->feedback.imu.euler.pit, c->feedback.imu.gyro.y); - VMC_InverseSolve(&c->vmc_[0], fn, tp); - VMC_GetJointTorques(&c->vmc_[0], &t1, &t2); + // VMC_InverseSolve(&c->vmc_[1], fn, tp); + // VMC_GetJointTorques(&c->vmc_[1], &t1, &t2); - c->output.joint[0].torque = t1; - c->output.joint[1].torque = t2; - - // Chassis_LQRControl(c, c_cmd); // 即使在放松模式下也执行LQR以保持状态更新 + // c->output.joint[3].torque = t1; + // c->output.joint[2].torque = t2; + Chassis_LQRControl(c, c_cmd); // 即使在放松模式下也执行LQR以保持状态更新 + // c->output.wheel[0] = 0.2f; + // c->output.wheel[1] = 0.2f; Chassis_Output(c); // 统一输出 break; case CHASSIS_MODE_WHELL_LEG_BALANCE: // 轮腿平衡模式,使用LQR控制 - // // 更新VMC正解算 - // VMC_ForwardSolve(&c->vmc_[0], c->feedback.joint[0].rotor_abs_angle, c->feedback.joint[1].rotor_abs_angle, - // c->feedback.imu.euler.pit, c->feedback.imu.gyro.y); - // VMC_ForwardSolve(&c->vmc_[1], c->feedback.joint[3].rotor_abs_angle, c->feedback.joint[2].rotor_abs_angle, - // c->feedback.imu.euler.pit, c->feedback.imu.gyro.y); + // 更新VMC正解算 + VMC_ForwardSolve(&c->vmc_[0], c->feedback.joint[0].rotor_abs_angle, c->feedback.joint[1].rotor_abs_angle, + c->feedback.imu.euler.pit, c->feedback.imu.gyro.y); + VMC_ForwardSolve(&c->vmc_[1], c->feedback.joint[3].rotor_abs_angle, c->feedback.joint[2].rotor_abs_angle, + c->feedback.imu.euler.pit, c->feedback.imu.gyro.y); - // // 执行LQR控制 + + + // 执行LQR控制 // if (Chassis_LQRControl(c, c_cmd) != 0) { // // LQR控制失败,切换到安全模式 // return CHASSIS_ERR; // } + + // Chassis_Output(c); // 统一输出 break; default: @@ -328,6 +260,7 @@ void Chassis_Output(Chassis_t *c) { for (int i = 0; i < 4; i++) { MOTOR_LZ_MotionParam_t param = {0}; param.torque = c->output.joint[i].torque; + MOTOR_LZ_MotionControl(&c->param->joint_motors[i], ¶m); } for (int i = 0; i < 2; i++) { @@ -337,3 +270,166 @@ void Chassis_Output(Chassis_t *c) { // 如果需要统一输出,可以在这里实现 // 现在的设计是在控制逻辑中直接输出,所以这里留空 } + +int8_t Chassis_LQRControl(Chassis_t *c, const Chassis_CMD_t *c_cmd) { + if (c == NULL || c_cmd == NULL) { + return CHASSIS_ERR_NULL; + } + + /* 参考C++版本实现的LQR控制 */ + + /* 地面接触检测(参考C++版本) */ + float leg_fn[2]; + bool onground_flag[2]; + + // 简化的地面接触检测,可以后续改进 + leg_fn[0] = VMC_GroundContactDetection(&c->vmc_[0]); + leg_fn[1] = VMC_GroundContactDetection(&c->vmc_[1]); + onground_flag[0] = (leg_fn[0] > 30.0f); + onground_flag[1] = (leg_fn[1] > 30.0f); + + /* 获取VMC状态(等效摆杆参数) */ + float leg_L0[2], leg_theta[2], leg_d_theta[2]; + VMC_GetVirtualLegState(&c->vmc_[0], &leg_L0[0], &leg_theta[0], NULL, &leg_d_theta[0]); + VMC_GetVirtualLegState(&c->vmc_[1], &leg_L0[1], &leg_theta[1], NULL, &leg_d_theta[1]); + + /* 运动参数(参考C++版本的状态估计) */ + static float xhat = 0.0f, x_dot_hat = 0.0f; + static float target_x = 0.0f, target_dot_x = 0.0f; + + // 简化的速度估计(后续可以改进为C++版本的复杂滤波) + x_dot_hat = c->chassis_state.velocity_x; + xhat = c->chassis_state.position_x; + + // 目标设定 + target_dot_x = c_cmd->move_vec.vx; + target_x += target_dot_x * c->dt; + + /* 分别计算左右腿的LQR控制 */ + float Tw[2] = {0.0f, 0.0f}; // 轮毂力矩 + float Tp[2] = {0.0f, 0.0f}; // 髋关节力矩 + + for (int leg = 0; leg < 2; leg++) { + /* 构建当前状态 */ + LQR_State_t current_state = {0}; + current_state.theta = leg_theta[leg]; + current_state.d_theta = leg_d_theta[leg]; + current_state.x = xhat; + current_state.d_x = x_dot_hat; + current_state.phi = -c->feedback.imu.euler.pit; + current_state.d_phi = -c->feedback.imu.gyro.y; + + /* 构建目标状态 */ + LQR_State_t target_state = {0}; + target_state.theta = 0.0f; // 目标摆杆角度 + target_state.d_theta = 0.0f; // 目标摆杆角速度 + target_state.x = 0; // 目标位置 + target_state.d_x = 0.0f; // 目标速度 + target_state.phi = 0.0f; // 目标俯仰角 + target_state.d_phi = 0.0f; // 目标俯仰角速度 + // target_state.theta = -0.8845f * leg_L0[leg] + 0.40663f; // 目标摆杆角度 + // target_state.d_theta = 0.0f; // 目标摆杆角速度 + // target_state.x = target_x - 0.56f; // 目标位置 + // target_state.d_x = target_dot_x; // 目标速度 + // target_state.phi = 0.16f; // 目标俯仰角 + // target_state.d_phi = 0.0f; // 目标俯仰角速度 + + /* 根据当前腿长更新增益矩阵 */ + LQR_CalculateGainMatrix(&c->lqr[leg], leg_L0[leg]); + + /* 更新LQR状态 */ + LQR_SetTargetState(&c->lqr[leg], &target_state); + LQR_UpdateState(&c->lqr[leg], ¤t_state); + + if (onground_flag[leg]) { + /* 接地状态:使用LQR控制器计算输出 */ + if (LQR_Control(&c->lqr[leg]) == 0) { + LQR_Input_t lqr_output = {0}; + if (LQR_GetOutput(&c->lqr[leg], &lqr_output) == 0) { + Tw[leg] = lqr_output.T; + Tp[leg] = lqr_output.Tp; + } else { + Tw[leg] = 0.0f; + Tp[leg] = 0.0f; + } + } else { + Tw[leg] = 0.0f; + Tp[leg] = 0.0f; + } + } else { + /* 离地状态:简化控制,只控制腿部摆动 */ + Tw[leg] = 0.0f; + // 只控制摆杆角度 + float theta_error = current_state.theta - target_state.theta; + float d_theta_error = current_state.d_theta - target_state.d_theta; + Tp[leg] = -(c->lqr[leg].K_matrix[1][0] * theta_error + c->lqr[leg].K_matrix[1][1] * d_theta_error); + } + } + + /* 转向控制(参考C++版本) */ + float yaw_force = 0.0f; + if (onground_flag[0] && onground_flag[1]) { + // 简化的转向控制,后续可以改进为PID + yaw_force = -c_cmd->move_vec.wz * 0.1f; + } + + /* 轮毂力矩输出(参考C++版本的减速比) */ + c->output.wheel[0] = Tw[0] / 4.9256f - yaw_force; // 左轮 + c->output.wheel[1] = Tw[1] / 4.9256f + yaw_force; // 右轮 + + /* 腿长控制和VMC逆解算(使用PID控制) */ + float virtual_force[2]; + float target_L0[2]; + float leg_d_length[2]; // 腿长变化率 + + // 目标腿长设定 + target_L0[0] = 0.13f + c_cmd->height * 0.1f; // 基础腿长 + 高度调节 + target_L0[1] = 0.13f + c_cmd->height * 0.1f; + + // 获取腿长变化率 + VMC_GetVirtualLegState(&c->vmc_[0], NULL, NULL, &leg_d_length[0], NULL); + VMC_GetVirtualLegState(&c->vmc_[1], NULL, NULL, &leg_d_length[1], NULL); + + for (int leg = 0; leg < 2; leg++) { + // 使用PID进行腿长控制 + float pid_output = PID_Calc(&c->pid.leglength[leg], target_L0[leg], leg_L0[leg], leg_d_length[leg], c->dt); + + // 腿长控制力 = LQR摆杆力矩的径向分量 + PID腿长控制输出 + 基础支撑力 + virtual_force[leg] = Tp[leg] * sinf(leg_theta[leg]) + + pid_output + // PID腿长控制输出 + 50.0f; // 基础支撑力 + + // VMC逆解算 + if (VMC_InverseSolve(&c->vmc_[leg], virtual_force[leg], Tp[leg]) == 0) { + if (leg == 0) { + VMC_GetJointTorques(&c->vmc_[0], &c->output.joint[0].torque, &c->output.joint[1].torque); + } else { + VMC_GetJointTorques(&c->vmc_[1], &c->output.joint[3].torque, &c->output.joint[2].torque); + } + } else { + // VMC失败,设为0力矩 + if (leg == 0) { + c->output.joint[0].torque = 0.0f; + c->output.joint[1].torque = 0.0f; + } else { + c->output.joint[2].torque = 0.0f; + c->output.joint[3].torque = 0.0f; + } + } + } + + /* 安全限制 */ + for (int i = 0; i < 2; i++) { + if (fabsf(c->output.wheel[i]) > 0.8f) { + c->output.wheel[i] = (c->output.wheel[i] > 0) ? 0.8f : -0.8f; + } + } + + for (int i = 0; i < 4; i++) { + if (fabsf(c->output.joint[i].torque) > 20.0f) { + c->output.joint[i].torque = (c->output.joint[i].torque > 0) ? 20.0f : -20.0f; + } + } + + return CHASSIS_OK; +} diff --git a/User/module/balance_chassis.h b/User/module/balance_chassis.h index 3db068a..0d8633f 100644 --- a/User/module/balance_chassis.h +++ b/User/module/balance_chassis.h @@ -70,7 +70,8 @@ typedef struct { typedef struct { VMC_Param_t vmc_param[2]; /* VMC参数 */ - LQR_GainMatrix_t lqr_gains; /* LQR增益矩阵 */ + KPID_Params_t leglength; + MOTOR_LZ_Param_t joint_motors[4]; /* 四个关节电机参数 */ MOTOR_LK_Param_t wheel_motors[2]; /* 两个轮子电机参数 */ @@ -82,6 +83,8 @@ typedef struct { float max_wheel_torque; /* 轮毂电机最大力矩限制 */ float max_joint_torque; /* 关节电机最大力矩限制 */ } lqr_param; + + LQR_GainMatrix_t lqr_gains; /* LQR增益矩阵参数 */ /* 低通滤波器截止频率 */ struct { @@ -110,7 +113,7 @@ typedef struct { Chassis_Output_t output; VMC_t vmc_[2]; /* 两条腿的VMC */ - LQR_Controller_t lqr; /* LQR控制器 */ + LQR_Controller_t lqr[2]; /* 两条腿的LQR控制器 */ int8_t state; @@ -137,6 +140,9 @@ typedef struct { KPID_t right_wheel; /* 右轮PID */ KPID_t follow; /* 跟随云台用的PID */ KPID_t balance; /* 平衡用的PID */ + + KPID_t leglength[2]; /* 两条腿的腿长PID */ + } pid; /* 滤波器 */ @@ -180,6 +186,16 @@ int8_t Chassis_UpdateIMU(Chassis_t *c, const Chassis_IMU_t imu); */ int8_t Chassis_Control(Chassis_t *c, const Chassis_CMD_t *c_cmd); +/** + * \brief LQR控制逻辑 + * + * \param c 包含底盘数据的结构体 + * \param c_cmd 底盘控制指令 + * + * \return 函数运行结果 + */ +int8_t Chassis_LQRControl(Chassis_t *c, const Chassis_CMD_t *c_cmd); + /** * \brief 底盘输出值 diff --git a/User/module/config.c b/User/module/config.c index b8bd55b..71186b5 100644 --- a/User/module/config.c +++ b/User/module/config.c @@ -68,6 +68,18 @@ Config_RobotParam_t robot_config = { }, .chassis_param = { + .leglength={ + .k=1.0f, + .p=0.10f, + .i=0.0f, + .d=0.0f, + .i_limit=0.0f, + .out_limit=100.0f, + .d_cutoff_freq=-1.0f, + .range=-1.0f, + } + + .low_pass_cutoff_freq = { .in = 30.0f, .out = 30.0f, @@ -78,7 +90,7 @@ Config_RobotParam_t robot_config = { .motor_id = 124, .host_id = 130, .module = MOTOR_LZ_RSO3, - .reverse = true, + .reverse = false, .mode = MOTOR_LZ_MODE_MOTION, }, { // 左膝关节 @@ -86,7 +98,7 @@ Config_RobotParam_t robot_config = { .motor_id = 125, .host_id = 130, .module = MOTOR_LZ_RSO3, - .reverse = true, + .reverse = false, .mode = MOTOR_LZ_MODE_MOTION, }, { // 右膝关节 @@ -94,7 +106,7 @@ Config_RobotParam_t robot_config = { .motor_id = 126, .host_id = 130, .module = MOTOR_LZ_RSO3, - .reverse = false, + .reverse = true, .mode = MOTOR_LZ_MODE_MOTION, }, { // 右髋关节 @@ -102,7 +114,7 @@ Config_RobotParam_t robot_config = { .motor_id = 127, .host_id = 130, .module = MOTOR_LZ_RSO3, - .reverse = false, + .reverse = true, .mode = MOTOR_LZ_MODE_MOTION, }, }, @@ -121,29 +133,36 @@ Config_RobotParam_t robot_config = { }, }, .mech_zero_yaw = 0.0f, + .vmc_param = { { // 左腿 - .leg_1 = 0.206f, // 前大腿长度 (m) - .leg_2 = 0.258f, // 前小腿长度 (m) - .leg_3 = 0.206f, // 后小腿长度 (m) - .leg_4 = 0.258f, // 后大腿长度 (m) - .hip_length = 0.0f // 髋宽 (m) + .leg_1 = 0.215f, // 后髋连杆长度 (L1) (m) + .leg_2 = 0.258f, // 后膝连杆长度 (L2) (m) + .leg_3 = 0.258f, // 前膝连杆长度 (L3) (m) + .leg_4 = 0.215f, // 前髋连杆长度 (L4) (m) + .hip_length = 0.0f // 髋宽 (L5) (m) }, { // 右腿 - .leg_1 = 0.206f, // 前大腿长度 (m) - .leg_2 = 0.258f, // 前小腿长度 (m) - .leg_3 = 0.206f, // 后小腿长度 (m) - .leg_4 = 0.258f, // 后大腿长度 (m) - .hip_length = 0.0f // 髋宽 (m) + .leg_1 = 0.215f, // 后髋连杆长度 (L1) (m) + .leg_2 = 0.258f, // 后膝连杆长度 (L2) (m) + .leg_3 = 0.258f, // 前膝连杆长度 (L3) (m) + .leg_4 = 0.215f, // 前髋连杆长度 (L4) (m) + .hip_length = 0.0f // 髋宽 (L5) (m) } }, .lqr_gains ={ - .K = { - { -1.3677, -12.022, 4.0676, -2.6185, -66.132, -4.2516, -1.4083, -0.051404, -57.561, -5.3641 }, - { -1.3677, -12.022, -4.0676, 2.6185, -1.4083, -0.051404, -66.132, -4.2516, -57.561, -5.3641 }, - { 0.14689, 1.2865, -63.224, -12.495, 6.2265, -0.13959, 1.2635, 0.48938, -78.822, -5.121 }, - { 0.14689, 1.2865, 63.224, 12.495, 1.2635, 0.48938, 6.2265, -0.13959, -78.822, -5.121 } - } + .k11_coeff = { -61.932040681074966f, 70.963671642086396f, -37.730841182566571f, -0.296475458388679f }, // theta + .k12_coeff = { -0.586710094600108f, 0.886736272521581f, -3.626144273475104f, 0.057861910518974f }, // d_theta + .k13_coeff = { -17.297031110481019f, 16.286794934166178f, -5.176451154477850f, -0.867260018374823f }, // x + .k14_coeff = { -14.893387150006664f, 14.357020815277332f, -5.244645181873441f, -0.869862096507486f}, // d_x + .k15_coeff = { -75.327876471378886f, 79.786699741548944f, -31.183500053811208f, 5.450635661115236f}, // phi + .k16_coeff = { -3.572234723237025f, 4.164905011076312f, -1.874828497771750f, 0.477913222933688f}, // d_phi + .k21_coeff = { 9.327090608559319f, 1.362675928111105f, -8.092777598567881f, 4.351387652359104f}, // theta + .k22_coeff = { 3.872517778351810f, -3.344077414726880f, 0.589693555828904f, 0.310036629174646f}, // d_theta + .k23_coeff = { -71.615766251649134f, 74.748309711530837f, -28.370490124006626f, 4.483586941100197f }, // x + .k24_coeff = { -68.751866288568962f, 71.204785013044102f, -26.812636604518396f, 4.238479323700952f }, // d_x + .k25_coeff = { 205.6887659080132f, -195.1219729060621f, 62.890188701113303f, 7.452313695653162f }, // phi + .k26_coeff = { 16.162999842656344f, -15.926932704437410f, 5.474613395300429f, -0.002856083635449f }, // d_phi }, .lqr_param.max_joint_torque = 20.0f, // 关节电机最大力矩 20Nm .lqr_param.max_wheel_torque = 2.5f, // 轮毂电机最大力矩 2.5Nm diff --git a/comp_vmc.cpp b/comp_vmc.cpp new file mode 100644 index 0000000..7d6f1f8 --- /dev/null +++ b/comp_vmc.cpp @@ -0,0 +1,213 @@ + +#include "comp_vmc.hpp" + +#include + +#define PI_2 1.571f + +using namespace Component; + +VMC::VMC(VMC::Param ¶m, float sample_freq) : param_(param) { + float dt_min = 1.0f / sample_freq; + XB_ASSERT(isfinite(dt_min)); + + this->Reset(); +} + +/* + + 正负极参考韭菜的菜 知乎 平衡步兵控制系统设计 + + VMC 机体pitch正负极 d_pitch同 + + / + / 正+ + / +x ---------> 0 + \ 负- + \ + \ + + phi角正负极 d_phi同 + + / + / 正+ + / +x ---------> 0 + \ 负- + \ + \ + + 后 <---->前 + /phi1-----phi4\ + / \ + \ / + \ OO / + \O轮O/ + OO + +*/ + +/* 两个大腿角度 机体角度 角速度 求出虚拟腿摆角 摆角速度 虚拟腿长 + * 虚拟腿长变化速度 */ +std::tuple VMC::VMCsolve(float phi1, float phi4, + float eulrPit, + float d_eulrPit, + float dt) { + static float body_pitch = 0.0f; + static float d_body_pitch = 0.0f; + body_pitch = eulrPit; + d_body_pitch = d_eulrPit; + /*点D B x y坐标 */ + this->vmc_leg.YD = this->param_.leg_4 * sinf(phi4); + this->vmc_leg.YB = this->param_.leg_1 * sinf(phi1); + this->vmc_leg.XD = this->param_.hip_length + this->param_.leg_4 * cosf(phi4); + this->vmc_leg.XB = this->param_.leg_1 * cosf(phi1); + /*BD长度*/ + this->vmc_leg.lBD = sqrtf((this->vmc_leg.XD - this->vmc_leg.XB) * + (this->vmc_leg.XD - this->vmc_leg.XB) + + (this->vmc_leg.YD - this->vmc_leg.YB) * + (this->vmc_leg.YD - this->vmc_leg.YB)); + + this->vmc_leg.A0 = + 2 * this->param_.leg_2 * (this->vmc_leg.XD - this->vmc_leg.XB); + this->vmc_leg.B0 = + 2 * this->param_.leg_2 * (this->vmc_leg.YD - this->vmc_leg.YB); + this->vmc_leg.C0 = this->param_.leg_2 * this->param_.leg_2 + + this->vmc_leg.lBD * this->vmc_leg.lBD - + this->param_.leg_3 * this->param_.leg_3; + this->vmc_leg.phi2 = + 2 * + atan2f((this->vmc_leg.B0 + sqrtf(this->vmc_leg.A0 * this->vmc_leg.A0 + + this->vmc_leg.B0 * this->vmc_leg.B0 - + this->vmc_leg.C0 * this->vmc_leg.C0)), + this->vmc_leg.A0 + this->vmc_leg.C0); + this->vmc_leg.phi3 = + atan2f(this->vmc_leg.YB - this->vmc_leg.YD + + this->param_.leg_2 * sinf(this->vmc_leg.phi2), + this->vmc_leg.XB - this->vmc_leg.XD + + this->param_.leg_2 * cosf(this->vmc_leg.phi2)); + /*点C x y坐标 */ + this->vmc_leg.XC = this->param_.leg_1 * cosf(phi1) + + this->param_.leg_2 * cosf(this->vmc_leg.phi2); + this->vmc_leg.YC = this->param_.leg_1 * sinf(phi1) + + this->param_.leg_2 * sinf(this->vmc_leg.phi2); + /*点C 极坐标 */ + this->vmc_leg.L0 = + sqrtf((this->vmc_leg.XC - this->param_.hip_length / 2.0f) * + (this->vmc_leg.XC - this->param_.hip_length / 2.0f) + + this->vmc_leg.YC * this->vmc_leg.YC); + this->vmc_leg.phi0 = atan2f( + this->vmc_leg.YC, (this->vmc_leg.XC - this->param_.hip_length / 2.0f)); + + this->vmc_leg.alpha = PI_2 - this->vmc_leg.phi0; + + this->vmc_leg.d_phi0 = (this->vmc_leg.phi0 - this->vmc_leg.last_phi0) / dt; + this->vmc_leg.d_alpha = 0.0f - this->vmc_leg.d_phi0; + /*虚拟腿 摆角theta 摆角速度d_theta */ + this->vmc_leg.theta = PI_2 + body_pitch - this->vmc_leg.phi0; + this->vmc_leg.d_theta = (-d_body_pitch - this->vmc_leg.d_phi0); + + this->vmc_leg.last_phi0 = this->vmc_leg.phi0; + /*虚拟腿 腿长L0 腿长变化速度d_L0 */ + this->vmc_leg.d_L0 = (this->vmc_leg.L0 - this->vmc_leg.last_L0) / dt; + this->vmc_leg.dd_L0 = (this->vmc_leg.d_L0 - this->vmc_leg.last_d_L0) / dt; + + this->vmc_leg.last_d_L0 = this->vmc_leg.d_L0; + this->vmc_leg.last_L0 = this->vmc_leg.L0; + + this->vmc_leg.dd_theta = + (this->vmc_leg.d_theta - this->vmc_leg.last_d_theta) / dt; + this->vmc_leg.last_d_theta = this->vmc_leg.d_theta; + + return std::make_tuple(vmc_leg.L0, vmc_leg.d_L0, vmc_leg.theta, + vmc_leg.d_theta); +} + +/* 两个大腿角度 期望腿支持力 期望腿摆力矩 求出两个关节输出力矩 */ +std::tuple VMC::VMCinserve(float phi1, float phi4, float Tp, + float F0) { + /*jacobian矩阵计算*/ + this->vmc_leg.j11 = + (this->param_.leg_1 * sinf(this->vmc_leg.phi0 - this->vmc_leg.phi3) * + sinf(phi1 - this->vmc_leg.phi2)) / + sinf(this->vmc_leg.phi3 - this->vmc_leg.phi2); + this->vmc_leg.j12 = + (this->param_.leg_1 * cosf(this->vmc_leg.phi0 - this->vmc_leg.phi3) * + sinf(phi1 - this->vmc_leg.phi2)) / + (this->vmc_leg.L0 * sinf(this->vmc_leg.phi3 - this->vmc_leg.phi2)); + this->vmc_leg.j21 = + (this->param_.leg_4 * sinf(this->vmc_leg.phi0 - this->vmc_leg.phi2) * + sinf(this->vmc_leg.phi3 - phi4)) / + sinf(this->vmc_leg.phi3 - this->vmc_leg.phi2); + this->vmc_leg.j22 = + (this->param_.leg_4 * cosf(this->vmc_leg.phi0 - this->vmc_leg.phi2) * + sinf(this->vmc_leg.phi3 - phi4)) / + (this->vmc_leg.L0 * sinf(this->vmc_leg.phi3 - this->vmc_leg.phi2)); + /*得到前髋关节的输出轴期望力矩,F0为五连杆机构末端沿腿的推力*/ + this->vmc_leg.torque_set[0] = this->vmc_leg.j11 * F0 + this->vmc_leg.j12 * Tp; + /*得到后髋关节的输出轴期望力矩,Tp为虚拟腿摆力矩的力矩*/ + this->vmc_leg.torque_set[1] = this->vmc_leg.j21 * F0 + this->vmc_leg.j22 * Tp; + + return std::make_tuple(this->vmc_leg.torque_set[0], + this->vmc_leg.torque_set[1]); +} +/* 用到了前两个函数解算算出来的变量 尽量放在前两个函数之后 */ +float VMC::GndDetector(float Tp, float F0) { + vmc_leg.Fn = + F0 * cosf(vmc_leg.theta) + Tp * sinf(vmc_leg.theta) / vmc_leg.L0 + 6; // + // 腿部机构的力+轮子重力,这里忽略了轮子质量*驱动轮竖直方向运动加速度 + + // vmc_leg.Fn = + // F0 * cosf(vmc_leg.theta) + Tp * sinf(vmc_leg.theta) / vmc_leg.L0 + + // wheel_mess * + // (z_accl - vmc_leg.dd_L0 * cosf(vmc_leg.theta) + + // 2.0f * vmc_leg.d_L0 * vmc_leg.d_theta * sinf(vmc_leg.theta) + + // vmc_leg.L0 * vmc_leg.dd_theta * sinf(vmc_leg.theta) + + // vmc_leg.L0 * vmc_leg.d_theta * vmc_leg.d_theta * + // cosf(vmc_leg.theta)); + return vmc_leg.Fn; +} + +/* 计算拟合函数结果 */ +float VMC::LQR_K_calc(float *coe, float len) { + return coe[0] * len * len * len + coe[1] * len * len + coe[2] * len + coe[3]; +} + +/* 变量刷新 */ +void VMC::Reset() { + vmc_leg.L0 = 0; + vmc_leg.phi0 = 0; + vmc_leg.alpha = 0; + vmc_leg.d_alpha = 0; + + vmc_leg.lBD = 0; + + vmc_leg.d_phi0 = 0; + vmc_leg.last_phi0 = 0; + + vmc_leg.A0 = 0; + vmc_leg.B0 = 0; + vmc_leg.C0 = 0; + vmc_leg.phi2 = 0; + vmc_leg.phi3 = 0; + + vmc_leg.j11 = 0; + vmc_leg.j12 = 0; + vmc_leg.j21 = 0; + vmc_leg.j22 = 0; + vmc_leg.torque_set[0] = 0; + vmc_leg.torque_set[1] = 0; + + vmc_leg.theta = 0; + vmc_leg.d_theta = 0; + vmc_leg.last_d_theta = 0; + vmc_leg.dd_theta = 0; + + vmc_leg.d_L0 = 0; + vmc_leg.dd_L0 = 0; + vmc_leg.last_L0 = 0; + vmc_leg.last_d_L0 = 0; + vmc_leg.first_flag = 0; + vmc_leg.leg_flag = 0; +} diff --git a/test_vmc.c b/test_vmc.c new file mode 100644 index 0000000..0e70c86 --- /dev/null +++ b/test_vmc.c @@ -0,0 +1,66 @@ +#include +#include +#include "User/component/vmc.h" + +int main() { + // 测试VMC计算 + VMC_t vmc; + VMC_Param_t param = { + .hip_length = 0.1f, // 10cm髋关节间距 + .leg_1 = 0.15f, // 15cm大腿前端 + .leg_2 = 0.15f, // 15cm大腿后端 + .leg_3 = 0.15f, // 15cm小腿 + .leg_4 = 0.15f, // 15cm小腿前端 + .wheel_radius = 0.05f, // 5cm轮子半径 + .wheel_mass = 1.0f // 1kg轮子质量 + }; + + if (VMC_Init(&vmc, ¶m, 1000.0f) != 0) { + printf("VMC初始化失败\n"); + return -1; + } + + printf("测试VMC腿长计算\n"); + printf("髋关节间距: %.3f\n", param.hip_length); + printf("腿段长度: L1=%.3f, L2=%.3f, L3=%.3f, L4=%.3f\n", + param.leg_1, param.leg_2, param.leg_3, param.leg_4); + printf("\n"); + + // 测试不同的关节角度配置 + float test_angles[][2] = { + {0.0f, 0.0f}, // 水平伸展 + {0.5f, -0.5f}, // 轻微弯曲 + {1.0f, -1.0f}, // 中等弯曲 + {1.5f, -1.5f}, // 较大弯曲 + {-0.5f, 0.5f}, // 反向弯曲 + }; + + int num_tests = sizeof(test_angles) / sizeof(test_angles[0]); + + for (int i = 0; i < num_tests; i++) { + float phi1 = test_angles[i][0]; + float phi4 = test_angles[i][1]; + float body_pitch = 0.0f; + float body_pitch_rate = 0.0f; + + if (VMC_ForwardSolve(&vmc, phi1, phi4, body_pitch, body_pitch_rate) == 0) { + float length, angle, d_length, d_angle; + VMC_GetVirtualLegState(&vmc, &length, &angle, &d_length, &d_angle); + + float foot_x, foot_y; + VMC_GetFootPosition(&vmc, &foot_x, &foot_y); + + printf("测试 %d: phi1=%.2f, phi4=%.2f\n", i+1, phi1, phi4); + printf(" 足端位置: (%.3f, %.3f)\n", foot_x, foot_y); + printf(" 虚拟腿长: %.3f\n", length); + printf(" 虚拟摆角: %.3f (%.1f度)\n", angle, angle * 180.0f / M_PI); + printf(" 内部变量: XC=%.3f, YC=%.3f, phi2=%.3f, phi3=%.3f\n", + vmc.leg.XC, vmc.leg.YC, vmc.leg.phi2, vmc.leg.phi3); + printf("\n"); + } else { + printf("测试 %d: 求解失败 (phi1=%.2f, phi4=%.2f)\n", i+1, phi1, phi4); + } + } + + return 0; +} diff --git a/utils/Simulation-master/.gitignore b/utils/Simulation-master/.gitignore new file mode 100644 index 0000000..be82517 --- /dev/null +++ b/utils/Simulation-master/.gitignore @@ -0,0 +1,13 @@ +# Duplicate files +*(*)* + +# MATLAB files +balance/parallel_legs/slprj +balance/series_legs/slprj +balance/series_parallel_legs/slprj +*/slprj/ +*/codegen/ +*.prj +*.slxc +*.autosave +*.asv diff --git a/utils/Simulation-master/LICENSE b/utils/Simulation-master/LICENSE new file mode 100644 index 0000000..60acd7e --- /dev/null +++ b/utils/Simulation-master/LICENSE @@ -0,0 +1,21 @@ +MIT License + +Copyright (c) 2024 是小企鹅呀 + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/utils/Simulation-master/balance/parallel_legs/blance_leg.slx b/utils/Simulation-master/balance/parallel_legs/blance_leg.slx new file mode 100644 index 0000000000000000000000000000000000000000..1e6fc9c5c292776d82c717b71961824c63df6f72 GIT binary patch literal 203510 zcmV)TK(W72O9KQH000080000X0C^&c-7I4O00?aW02TlM0BvP-VPs)+VJ~!Ob!}p9 zVQFkGaBgSpymeHST^BF90R<$bQ&6O&k?s)bRH;pOcXvriNrQBYlyr9qNK1Ejci*+Y z@0@eTz5m=X?w|LbF<#MUv!DH}wdS0^m}~7fR8d|69fcSL0)e1QNs4`fK;X_{e~=Nu zD+7~D-@solY$eqlz>BA_KX7aiS@7=H5GgT{FRrQk3vP}Y8)-t1wazoA*7S?m`X-gJ zw4nyU-@l7Ws!5~3q2QXzkRZ}J=0C{K?d&A)kk(ks7L30iXZss9W>diUxn}HLo=l71 z7&SU>%x`WC6>L84&^6^6%7GXv^~u}2&iSx1{JZ{yCe2ozt?NJT_w#rBF;-rOXY(dX z-TLK(At52ABAC$+>~jSL!}SxyFkD`Vly%sNx{ 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z2JyH5OA9iss~sAR7vd=7 zXT#DALmbn+PG~efh@;RfR+I9t>*U3km-I7K8pKiXNyd))*YEZsO=bWJjhz+ZC}2^~ zQ+xrQ^zVt~G6IbT@j)-!c3*7Ti*cwhh!g9wvF}A%>ohdlxy|p@Z>P)FpBHJH^U!FJ zkEWO10WZ>smZ8!h4(Vn8t&23IAJAx!!wr{>W-ijKx1rI_ZD+3b+hrSxi?oS-XtZ-v ziL12BD(4qz5hu`SkdJ?tC5$i9PJo-P|NJ&(KNmE<+P2FAn-^&Xh|p*dhxD=%-$hs- zDiqkcF5lIbT^8)R2;0Yi0y~%Qx(d52>~j%Dgbf9DF7tC0c3J-8B1{Yq3hZ1A 1 && coefficients(i) > 0 + term = [' + ', term]; + end + equation = [equation, term]; + end + end + fprintf('%s;\n', equation); +end \ No newline at end of file diff --git a/utils/Simulation-master/balance/parallel_legs/get_k.m b/utils/Simulation-master/balance/parallel_legs/get_k.m new file mode 100644 index 0000000..46e1806 --- /dev/null +++ b/utils/Simulation-master/balance/parallel_legs/get_k.m @@ -0,0 +1,82 @@ +%计算不同腿长下适合的K矩阵,再进行多项式拟合,得到2*6矩阵每个参数对应的多项式参数 +tic +j=1; +leg=0.1:0.01:0.4; +for i=leg + k=get_k_length(i); + k11(j) = k(1,1); + k12(j) = k(1,2); + k13(j) = k(1,3); + k14(j) = k(1,4); + k15(j) = k(1,5); + k16(j) = k(1,6); + + k21(j) = k(2,1); + k22(j) = k(2,2); + k23(j) = k(2,3); + k24(j) = k(2,4); + k25(j) = k(2,5); + k26(j) = k(2,6); + j=j+1; + + fprintf('leg_length=%d\n', i); +end +a11=polyfit(leg,k11,3); +a12=polyfit(leg,k12,3); +a13=polyfit(leg,k13,3); +a14=polyfit(leg,k14,3); +a15=polyfit(leg,k15,3); +a16=polyfit(leg,k16,3); + +a21=polyfit(leg,k21,3); +a22=polyfit(leg,k22,3); +a23=polyfit(leg,k23,3); +a24=polyfit(leg,k24,3); +a25=polyfit(leg,k25,3); +a26=polyfit(leg,k26,3); + +toc + +% x0=leg; %步长为0.1 +% y11=polyval(a11,x0); %返回值y0是对应于x0的函数值 +% y12=polyval(a12,x0); %返回值y0是对应于x0的函数值 +% y13=polyval(a13,x0); %返回值y0是对应于x0的函数值 +% y14=polyval(a14,x0); %返回值y0是对应于x0的函数值 +% y15=polyval(a15,x0); %返回值y0是对应于x0的函数值 +% y16=polyval(a16,x0); %返回值y0是对应于x0的函数值 +% +% y21=polyval(a21,x0); %返回值y0是对应于x0的函数值 +% y22=polyval(a22,x0); %返回值y0是对应于x0的函数值 +% y23=polyval(a23,x0); %返回值y0是对应于x0的函数值 +% y24=polyval(a24,x0); %返回值y0是对应于x0的函数值 +% y25=polyval(a25,x0); %返回值y0是对应于x0的函数值 +% y26=polyval(a26,x0); %返回值y0是对应于x0的函数值 +% subplot(3,4,1);plot(leg,k11,'o',x0,y11,'r');xlabel('x');ylabel('y');title('k11'); +% subplot(3,4,2);plot(leg,k12,'o',x0,y12,'r');xlabel('x');ylabel('y');title('k12'); +% subplot(3,4,5);plot(leg,k13,'o',x0,y13,'r');xlabel('x');ylabel('y');title('k13'); +% subplot(3,4,6);plot(leg,k14,'o',x0,y14,'r');xlabel('x');ylabel('y');title('k14'); +% subplot(3,4,9);plot(leg,k15,'o',x0,y15,'r');xlabel('x');ylabel('y');title('k15'); +% subplot(3,4,10);plot(leg,k16,'o',x0,y16,'r');xlabel('x');ylabel('y');title('k16'); +% +% subplot(3,4,3);plot(leg,k21,'o',x0,y21,'r');xlabel('x');ylabel('y');title('k21'); +% subplot(3,4,4);plot(leg,k22,'o',x0,y22,'r');xlabel('x');ylabel('y');title('k22'); +% subplot(3,4,7);plot(leg,k23,'o',x0,y23,'r');xlabel('x');ylabel('y');title('k23'); +% subplot(3,4,8);plot(leg,k24,'o',x0,y24,'r');xlabel('x');ylabel('y');title('k24'); +% subplot(3,4,11);plot(leg,k25,'o',x0,y25,'r');xlabel('x');ylabel('y');title('k25'); +% subplot(3,4,12);plot(leg,k26,'o',x0,y26,'r');xlabel('x');ylabel('y');title('k26'); +% grid on; %添加网格线 +% set(gca,'GridLineStyle',':','GridColor','k','GridAlpha',1); %将网格线变成虚线 +% fprintf('fp32 a11[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a11(1),a11(2),a11(3),a11(4)); +% fprintf('fp32 a12[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a12(1),a12(2),a12(3),a12(4)); +% fprintf('fp32 a13[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a13(1),a13(2),a13(3),a13(4)); +% fprintf('fp32 a14[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a14(1),a14(2),a14(3),a14(4)); +% fprintf('fp32 a15[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a15(1),a15(2),a15(3),a15(4)); +% fprintf('fp32 a16[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a16(1),a16(2),a16(3),a16(4)); +% +% fprintf('fp32 a21[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a21(1),a21(2),a21(3),a21(4)); +% fprintf('fp32 a22[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a22(1),a22(2),a22(3),a22(4)); +% fprintf('fp32 a23[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a23(1),a23(2),a23(3),a23(4)); +% fprintf('fp32 a24[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a24(1),a24(2),a24(3),a24(4)); +% fprintf('fp32 a25[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a25(1),a25(2),a25(3),a25(4)); +% fprintf('fp32 a26[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a26(1),a26(2),a26(3),a26(4)); +toc diff --git a/utils/Simulation-master/balance/parallel_legs/get_k_length.m b/utils/Simulation-master/balance/parallel_legs/get_k_length.m new file mode 100644 index 0000000..7f670db --- /dev/null +++ b/utils/Simulation-master/balance/parallel_legs/get_k_length.m @@ -0,0 +1,56 @@ +function K = get_k_length(leg_length) + + %theta : 摆杆与竖直方向夹角 R :驱动轮半径 + %x : 驱动轮位移 L : 摆杆重心到驱动轮轴距离 + %phi : 机体与水平夹角 LM : 摆杆重心到其转轴距离 + %T :驱动轮输出力矩 l : 机体重心到其转轴距离 + %Tp : 髋关节输出力矩 mw : 驱动轮转子质量 + %N :驱动轮对摆杆力的水平分量 mp : 摆杆质量 + %P :驱动轮对摆杆力的竖直分量 M : 机体质量 + %Nm :摆杆对机体力水平方向分量 Iw : 驱动轮转子转动惯量 + %Pm :摆杆对机体力竖直方向分量 Ip : 摆杆绕质心转动惯量 + %Nf : 地面对驱动轮摩擦力 Im : 机体绕质心转动惯量 + + syms x(t) T R Iw mw M L LM theta(t) l phi(t) mp g Tp Ip IM + syms f1 f2 f3 d_theta d_x d_phi theta0 x0 phi0 + + R1=0.072; %驱动轮半径 + L1=leg_length/2; %摆杆重心到驱动轮轴距离 + LM1=leg_length/2; %摆杆重心到其转轴距离 + l1=0.03; %机体质心距离转轴距离 + mw1=0.80; %驱动轮质量 + mp1=1.11; %杆质量 + M1=2.0; %机体质量 + Iw1=mw1*R1^2; %驱动轮转动惯量 + Ip1=mp1*((L1+LM1)^2+0.05^2)/12.0; %摆杆转动惯量 + IM1=M1*(0.3^2+0.12^2)/12.0; %机体绕质心转动惯量 + + + NM = M*diff(x + (L + LM )*sin(theta)-l*sin(phi),t,2); + N = NM + mp*diff(x + L*sin(theta),t,2); + PM = M*g + M*diff((L+LM)*cos(theta)+l*cos(phi),t,2); + P = PM +mp*g+mp*diff(L*cos(theta),t,2); + + eqn1 = diff(x,t,2) == (T -N*R)/(Iw/R + mw*R); + eqn2 = Ip*diff(theta,t,2) == (P*L + PM*LM)*sin(theta)-(N*L+NM*LM)*cos(theta)-T+Tp; + eqn3 = IM*diff(phi,t,2) == Tp +NM*l*cos(phi)+PM*l*sin(phi); + + eqn10 = subs(subs(subs(subs(subs(subs(subs(subs(subs(eqn1,diff(theta,t,2),f1),diff(x,t,2),f2),diff(phi,t,2),f3),diff(theta,t),d_theta),diff(x,t),d_x),diff(phi,t),d_phi),theta,theta0),x,x0),phi,phi0); + eqn20 = subs(subs(subs(subs(subs(subs(subs(subs(subs(eqn2,diff(theta,t,2),f1),diff(x,t,2),f2),diff(phi,t,2),f3),diff(theta,t),d_theta),diff(x,t),d_x),diff(phi,t),d_phi),theta,theta0),x,x0),phi,phi0); + eqn30 = subs(subs(subs(subs(subs(subs(subs(subs(subs(eqn3,diff(theta,t,2),f1),diff(x,t,2),f2),diff(phi,t,2),f3),diff(theta,t),d_theta),diff(x,t),d_x),diff(phi,t),d_phi),theta,theta0),x,x0),phi,phi0); + + [f1,f2,f3] = solve(eqn10,eqn20,eqn30,f1,f2,f3); + + A=subs(jacobian([d_theta,f1,d_x,f2,d_phi,f3],[theta0,d_theta,x0,d_x,phi0,d_phi]),[theta0,d_theta,d_x,phi0,d_phi,T,Tp],[0,0,0,0,0,0,0]); + A=subs(A,[R,L,LM,l,mw,mp,M,Iw,Ip,IM,g],[R1,L1,LM1,l1,mw1,mp1,M1,Iw1,Ip1,IM1,9.8]); + A=double(A); + B=subs(jacobian([d_theta,f1,d_x,f2,d_phi,f3],[T,Tp]),[theta0,d_theta,d_x,phi0,d_phi,T,Tp],[0,0,0,0,0,0,0]); + B=subs(B,[R,L,LM,l,mw,mp,M,Iw,Ip,IM,g],[R1,L1,LM1,l1,mw1,mp1,M1,Iw1,Ip1,IM1,9.8]); + B=double(B); + + Q=diag([100 1 500 100 5000 1]);%theta d_theta x d_x phi d_phi%700 1 600 200 1000 1 + R=[240 0;0 25]; %T Tp + + K=lqr(A,B,Q,R); + +end \ No newline at end of file diff --git a/utils/Simulation-master/balance/parallel_legs/physical_calc.mlx b/utils/Simulation-master/balance/parallel_legs/physical_calc.mlx new file mode 100644 index 0000000000000000000000000000000000000000..78bd3d3a082072ee86b1a69f5ccaeb9450444464 GIT binary patch literal 7539 zcmaKR1yCGYw>1nJU~mf(+}$U*yC=8@4-SL75AN;`!QEYggak=&Cs+t>A=n%K_v*j* z=6&yWSNEwtU3>L8Yp=b#YHw8qICxwb7#L*eMFF!oB2>-;3j zc*pPs;?(MvM)Wl$A9X9rnQX~RKNszc&4eOC;!H{e_j#&R4HV1LT`+_$Wg-*>$zs;ovm zTo8Hbq0|mkR47{x<5@p_@XQx+iYZ_{X1PtB$-|_wnPN5G zf>VL}=0U&p759Zax$46^rypL)k?WJ$ZmB^TS?d2lQya3Qfgl$cNC<8D#oERz!~gQw9d zOwdp^;*D$6ldpnf$k)Jj@sd;+>wq*^+V+vmNt0eH2HM{)I<(RPf**79zbeT}i zNec4k#+&VPSEW$cyTId;KxCm52QV{8DJwBx%kvsDf?r={;~QqEcAcnpEX?|zmY)^2 z^y-|XEH0*3#`^BwjwqKTNooK7RP<9T;!<4vO8Mrg^i+%(OB)S-Di8*#YT3p7bnI6+ zZ;hCM&aMrb+;1gn>R4nJI%FXdlJVK~juG3}@7<*1=+_igFFld*71}lCW!GZl(Ko0v zE6KR&Fs@Y;MgWhBNG_kX>%K}|qW_anOY5W3eyC*0U;MXh?M%S7ChyqH986v9pz3{= 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zI1xMEQ{rEeK7!B6T~bL;-aS^4_;R9h&Hi00@Ys;IaF4u&?-;wvHu~@KH$3M+aU8|} z6(~LXnL+5OJ~C3YDI{$Y&)@C;3+(ff4aeH7a`XPFj;1)W$ZtxJX9*LAcKjJ!F9l;a zz*%>^dOR-*HHpULubQ{-BgKATxBH`U3g!W=jmF#`Yq|#c|CQMj3MJ5^+?4ua7A#Uk pQHJN^|LDX0?+V>(hn`RCo;9$2(2y-gqLo5%b=m1${N2HXe*u(nS{48R literal 0 HcmV?d00001 diff --git a/utils/Simulation-master/balance/series_legs/doc/2连杆分析.md b/utils/Simulation-master/balance/series_legs/doc/2连杆分析.md new file mode 100644 index 0000000..a1667bd --- /dev/null +++ b/utils/Simulation-master/balance/series_legs/doc/2连杆分析.md @@ -0,0 +1,154 @@ +# 2连杆分析 + +参考:[五连杆运动学解算与VMC](https://zhuanlan.zhihu.com/p/613007726) + +![pic](./2_link.png) + +## 1 正运动学解算 + +$\phi_1$和$\phi_2$可由电机编码器测量得到。 + +$C$点坐标: + +$$ +\left \{ + \begin{array}{l} + x_C = l_1\cos\phi_1 + l_2\cos\phi_2\\ + y_C = l_1\sin\phi_1 + l_2\sin\phi_2 + \end{array} +\right . +$$ + +得: + +$$ +\left \{ + \begin{array}{l} + L0 = \sqrt{x_C^2 + y_C^2} \\ + \phi_0 = \arctan{\frac{y_C}{x_C}} + \end{array} +\right . +$$ + +## 2 逆运动学解算 + +由余弦定理易得: + +$$ +\phi_2+\phi_3 = \arccos\frac{l_1^2+l_2^2-L_0^2}{2l_1l_2} +$$ + +又: + +$$ +\phi_3 = \pi - \phi_1 +$$ + +得: + +$$ +\phi_2 = \arccos\frac{l_1^2+l_2^2-L_0^2}{2l_1l_2}+\phi_1-\pi +$$ + +## 3 雅可比矩阵 + + + +基于文中描述可得: + +$$ +\left \{ + \begin{array}{l} + \dot x_C = -l_1\dot\phi_1\sin\phi_1 - l_2\dot\phi_2\sin\phi_2\\ + \dot y_C = l_1\dot\phi_1\cos\phi_1 + l_2\dot\phi_2\cos\phi_2 + \end{array} +\right . +$$ + +即: + +$$ +\left [ + \begin{matrix} + \dot x_C \\ + \dot y_C + \end{matrix} +\right ] + + = +\left [ + \begin{matrix} + -l_1\sin\phi_1 & -l_2\sin\phi_2 \\ + l_1\cos\phi_1 & l_2\cos\phi_2 + \end{matrix} +\right ] + +\left [ + \begin{matrix} + \dot\phi_1 \\ + \dot\phi_2 + \end{matrix} +\right ] +$$ + +记作: + +$$ +\left [ + \begin{matrix} + \dot x_C \\ + \dot y_C + \end{matrix} +\right ] + + = +J_0 + +\left [ + \begin{matrix} + \dot\phi_1 \\ + \dot\phi_2 + \end{matrix} +\right ] +$$ + +下面操作与文中相同,可得: + +$$ +J^T = J_0^TRM = +\left[ + \begin{matrix} + l_1 \,\sin \left(\phi_0 -\phi_1 \right) & \frac{l_1 \,\cos \left(\phi_0 -\phi_1 \right)}{L_0 }\\ + l_2 \,\sin \left(\phi_0 -\phi_2 \right) & \frac{l_2 \,\cos \left(\phi_0 -\phi_2 \right)}{L_0 } + \end{matrix} +\right] +$$ + +即: + +$$ +J = +\left[ + \begin{matrix} + l_1 \,\sin \left(\phi_0 -\phi_1 \right) & l_2 \,\sin \left(\phi_0 -\phi_2 \right)\\ + \frac{l_1 \,\cos \left(\phi_0 -\phi_1 \right)}{L_0 } & \frac{l_2 \,\cos \left(\phi_0 -\phi_2 \right)}{L_0 } + \end{matrix} +\right] +$$ diff --git a/utils/Simulation-master/balance/series_legs/get_k.m b/utils/Simulation-master/balance/series_legs/get_k.m new file mode 100644 index 0000000..46e1806 --- /dev/null +++ b/utils/Simulation-master/balance/series_legs/get_k.m @@ -0,0 +1,82 @@ +%计算不同腿长下适合的K矩阵,再进行多项式拟合,得到2*6矩阵每个参数对应的多项式参数 +tic +j=1; +leg=0.1:0.01:0.4; +for i=leg + k=get_k_length(i); + k11(j) = k(1,1); + k12(j) = k(1,2); + k13(j) = k(1,3); + k14(j) = k(1,4); + k15(j) = k(1,5); + k16(j) = k(1,6); + + k21(j) = k(2,1); + k22(j) = k(2,2); + k23(j) = k(2,3); + k24(j) = k(2,4); + k25(j) = k(2,5); + k26(j) = k(2,6); + j=j+1; + + fprintf('leg_length=%d\n', i); +end +a11=polyfit(leg,k11,3); +a12=polyfit(leg,k12,3); +a13=polyfit(leg,k13,3); +a14=polyfit(leg,k14,3); +a15=polyfit(leg,k15,3); +a16=polyfit(leg,k16,3); + +a21=polyfit(leg,k21,3); +a22=polyfit(leg,k22,3); +a23=polyfit(leg,k23,3); +a24=polyfit(leg,k24,3); +a25=polyfit(leg,k25,3); +a26=polyfit(leg,k26,3); + +toc + +% x0=leg; %步长为0.1 +% y11=polyval(a11,x0); %返回值y0是对应于x0的函数值 +% y12=polyval(a12,x0); %返回值y0是对应于x0的函数值 +% y13=polyval(a13,x0); %返回值y0是对应于x0的函数值 +% y14=polyval(a14,x0); %返回值y0是对应于x0的函数值 +% y15=polyval(a15,x0); %返回值y0是对应于x0的函数值 +% y16=polyval(a16,x0); %返回值y0是对应于x0的函数值 +% +% y21=polyval(a21,x0); %返回值y0是对应于x0的函数值 +% y22=polyval(a22,x0); %返回值y0是对应于x0的函数值 +% y23=polyval(a23,x0); %返回值y0是对应于x0的函数值 +% y24=polyval(a24,x0); %返回值y0是对应于x0的函数值 +% y25=polyval(a25,x0); %返回值y0是对应于x0的函数值 +% y26=polyval(a26,x0); %返回值y0是对应于x0的函数值 +% subplot(3,4,1);plot(leg,k11,'o',x0,y11,'r');xlabel('x');ylabel('y');title('k11'); +% subplot(3,4,2);plot(leg,k12,'o',x0,y12,'r');xlabel('x');ylabel('y');title('k12'); +% subplot(3,4,5);plot(leg,k13,'o',x0,y13,'r');xlabel('x');ylabel('y');title('k13'); +% subplot(3,4,6);plot(leg,k14,'o',x0,y14,'r');xlabel('x');ylabel('y');title('k14'); +% subplot(3,4,9);plot(leg,k15,'o',x0,y15,'r');xlabel('x');ylabel('y');title('k15'); +% subplot(3,4,10);plot(leg,k16,'o',x0,y16,'r');xlabel('x');ylabel('y');title('k16'); +% +% subplot(3,4,3);plot(leg,k21,'o',x0,y21,'r');xlabel('x');ylabel('y');title('k21'); +% subplot(3,4,4);plot(leg,k22,'o',x0,y22,'r');xlabel('x');ylabel('y');title('k22'); +% subplot(3,4,7);plot(leg,k23,'o',x0,y23,'r');xlabel('x');ylabel('y');title('k23'); +% subplot(3,4,8);plot(leg,k24,'o',x0,y24,'r');xlabel('x');ylabel('y');title('k24'); +% subplot(3,4,11);plot(leg,k25,'o',x0,y25,'r');xlabel('x');ylabel('y');title('k25'); +% subplot(3,4,12);plot(leg,k26,'o',x0,y26,'r');xlabel('x');ylabel('y');title('k26'); +% grid on; %添加网格线 +% set(gca,'GridLineStyle',':','GridColor','k','GridAlpha',1); %将网格线变成虚线 +% fprintf('fp32 a11[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a11(1),a11(2),a11(3),a11(4)); +% fprintf('fp32 a12[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a12(1),a12(2),a12(3),a12(4)); +% fprintf('fp32 a13[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a13(1),a13(2),a13(3),a13(4)); +% fprintf('fp32 a14[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a14(1),a14(2),a14(3),a14(4)); +% fprintf('fp32 a15[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a15(1),a15(2),a15(3),a15(4)); +% fprintf('fp32 a16[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a16(1),a16(2),a16(3),a16(4)); +% +% fprintf('fp32 a21[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a21(1),a21(2),a21(3),a21(4)); +% fprintf('fp32 a22[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a22(1),a22(2),a22(3),a22(4)); +% fprintf('fp32 a23[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a23(1),a23(2),a23(3),a23(4)); +% fprintf('fp32 a24[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a24(1),a24(2),a24(3),a24(4)); +% fprintf('fp32 a25[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a25(1),a25(2),a25(3),a25(4)); +% fprintf('fp32 a26[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a26(1),a26(2),a26(3),a26(4)); +toc diff --git a/utils/Simulation-master/balance/series_legs/get_k_length.m b/utils/Simulation-master/balance/series_legs/get_k_length.m new file mode 100644 index 0000000..f5cc9e7 --- /dev/null +++ b/utils/Simulation-master/balance/series_legs/get_k_length.m @@ -0,0 +1,56 @@ +function K = get_k_length(leg_length) + + %theta : 摆杆与竖直方向夹角 R :驱动轮半径 + %x : 驱动轮位移 L : 摆杆重心到驱动轮轴距离 + %phi : 机体与水平夹角 LM : 摆杆重心到其转轴距离 + %T :驱动轮输出力矩 l : 机体重心到其转轴距离 + %Tp : 髋关节输出力矩 mw : 驱动轮转子质量 + %N :驱动轮对摆杆力的水平分量 mp : 摆杆质量 + %P :驱动轮对摆杆力的竖直分量 M : 机体质量 + %Nm :摆杆对机体力水平方向分量 Iw : 驱动轮转子转动惯量 + %Pm :摆杆对机体力竖直方向分量 Ip : 摆杆绕质心转动惯量 + %Nf : 地面对驱动轮摩擦力 Im : 机体绕质心转动惯量 + + syms x(t) T R Iw mw M L LM theta(t) l phi(t) mp g Tp Ip IM + syms f1 f2 f3 d_theta d_x d_phi theta0 x0 phi0 + + R1=0.072; %驱动轮半径 + L1=leg_length/2; %摆杆重心到驱动轮轴距离 + LM1=leg_length/2; %摆杆重心到其转轴距离 + l1=0.03; %机体质心距离转轴距离 + mw1=0.60; %驱动轮质量 + mp1=1.8; %杆质量 + M1=1.8; %机体质量 + Iw1=mw1*R1^2; %驱动轮转动惯量 + Ip1=mp1*((L1+LM1)^2+0.05^2)/12.0; %摆杆转动惯量 + IM1=M1*(0.3^2+0.12^2)/12.0; %机体绕质心转动惯量 + + + NM = M*diff(x + (L + LM )*sin(theta)-l*sin(phi),t,2); + N = NM + mp*diff(x + L*sin(theta),t,2); + PM = M*g + M*diff((L+LM)*cos(theta)+l*cos(phi),t,2); + P = PM +mp*g+mp*diff(L*cos(theta),t,2); + + eqn1 = diff(x,t,2) == (T -N*R)/(Iw/R + mw*R); + eqn2 = Ip*diff(theta,t,2) == (P*L + PM*LM)*sin(theta)-(N*L+NM*LM)*cos(theta)-T+Tp; + eqn3 = IM*diff(phi,t,2) == Tp +NM*l*cos(phi)+PM*l*sin(phi); + + eqn10 = subs(subs(subs(subs(subs(subs(subs(subs(subs(eqn1,diff(theta,t,2),f1),diff(x,t,2),f2),diff(phi,t,2),f3),diff(theta,t),d_theta),diff(x,t),d_x),diff(phi,t),d_phi),theta,theta0),x,x0),phi,phi0); + eqn20 = subs(subs(subs(subs(subs(subs(subs(subs(subs(eqn2,diff(theta,t,2),f1),diff(x,t,2),f2),diff(phi,t,2),f3),diff(theta,t),d_theta),diff(x,t),d_x),diff(phi,t),d_phi),theta,theta0),x,x0),phi,phi0); + eqn30 = subs(subs(subs(subs(subs(subs(subs(subs(subs(eqn3,diff(theta,t,2),f1),diff(x,t,2),f2),diff(phi,t,2),f3),diff(theta,t),d_theta),diff(x,t),d_x),diff(phi,t),d_phi),theta,theta0),x,x0),phi,phi0); + + [f1,f2,f3] = solve(eqn10,eqn20,eqn30,f1,f2,f3); + + A=subs(jacobian([d_theta,f1,d_x,f2,d_phi,f3],[theta0,d_theta,x0,d_x,phi0,d_phi]),[theta0,d_theta,d_x,phi0,d_phi,T,Tp],[0,0,0,0,0,0,0]); + A=subs(A,[R,L,LM,l,mw,mp,M,Iw,Ip,IM,g],[R1,L1,LM1,l1,mw1,mp1,M1,Iw1,Ip1,IM1,9.8]); + A=double(A); + B=subs(jacobian([d_theta,f1,d_x,f2,d_phi,f3],[T,Tp]),[theta0,d_theta,d_x,phi0,d_phi,T,Tp],[0,0,0,0,0,0,0]); + B=subs(B,[R,L,LM,l,mw,mp,M,Iw,Ip,IM,g],[R1,L1,LM1,l1,mw1,mp1,M1,Iw1,Ip1,IM1,9.8]); + B=double(B); + + Q=diag([100 1 500 100 5000 1]);%theta d_theta x d_x phi d_phi%700 1 600 200 1000 1 + R=[240 0;0 25]; %T Tp + + K=lqr(A,B,Q,R); + +end \ No newline at end of file diff --git a/utils/Simulation-master/balance/series_legs/leg_sim.slx b/utils/Simulation-master/balance/series_legs/leg_sim.slx new file mode 100644 index 0000000000000000000000000000000000000000..5afa5554d75df4f9f182d75da5c3652f9cfd9877 GIT binary patch literal 75122 zcma%h1CXUrvS!(~ZQHhOb=h`xxy!cg>auOywr#t%W@dL|=S9qWdn4|Dk2CX}{7&Yd zHx;CTL1+O003d$8gaFF?u7z_b002Di000C4C;(0tHZIl{wpR2`9!}0CHctQh_m`uc zoim-gjWr+u!q2>a|6J;7$E=Sy`aD+?7!PoWi7EY(aGg)#OvPPq2cEcq5i`18#R%?= z(_#*!RFYPDl6iW$ht8>R6wnee5V_jHM~o(Ov7>921C*)yHuV^C-SBe1=Q?JE|E7nr zs<$ASlkIza$#aP?eijOjzQ%tqOnwN3G>~>`IL1%NxM$Tr!lCVcWG5GZ2+j3A;|G#r zH~f(Ku1G~IA|RTDOb+p(FDM0#I&iGBM~5wb$W?9aHZ+*Z`dx_M+?H;vPlbg%gEfl~ zA>Gf=lPwk$2?KRD_$Tu2QrMTtKyN_IF<9BOLT$s#j$3aitYxZY#$Xe`XauvTjgW5u z^)J4TzGMqUwDf_zx+zPsH@?zL4%hij_#Gm%rF&7T6NWZ9>maJFf^nd0oOH-T01M3Y`W!3@ev6PNkcoAn#LO)Q@I&1wBmfvU9CL$(tvDDeFCu6 zLB}4Jo(p3-8OodVK+;z3fX1HcRkk|wv8vs{;)F+Ix_eOj2=%B(C9om$kwS|c5z4By 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zr9s^FBaCpA6~J>_26p~suLc(J-)VrS3h@n*a=sA^rmg&gb_@Ah8bnL3faYj+cpn6U zc89q#Hf+>?r?GIcL-a#lMKvrz;{zuIDd;OSJ>h?+u`;nhd~VjKg80n9OcQ_u2cZ3U z_62qJXN5KtNL|Rv(%#V0UR%N0+R#oD(h)(Xqi4qh_z7Y-5D4%AF92}$pg`KThURvR z4B$Vn+QMmP6gDp42Qh(^7P3n}IG}%F9_Iu-b1Qu_0~1|iTU`tAC?FD-oP==!R}6Fy zppsuA>KXonsBdLyWMV9DX#eLT4k9vsC~hhmzzt)7K-8Czc19PFf8T(g5BI`7I7IAj zm)aC8fNcRD8to;l{?m)t->0;5=Vzdu_cf?-0Rsn-G{z6-!Fk66k4Kf%AZ2t=^b$juVSU`vbt0{=O| zLIkH$>dpi94pa|&b;N#_{{{YY(1r-+VPL2LRteM#EZ&_zrK~Np^UAS zwV|!OiJ={&JxRuZ?+<!&9Ay5{1*N06d2UG+al6cub9myM+OHXe!Ou!XPf`V*TPG__6(SqR-o| zquqzNq^++ggGT_`dB4$%6V2|rj>ZmgNgKCoe84pHe=I^@?{&2EddjQjqIPEX5x8-{ zKWT^k*U}&^Db%gU%ixwJ|D;h2Uq|DFyb7ghWRRbm+}L$AE{LmextsjORdAcShW5L+ z{MF}nx!v?dTF%^cwDacES810!(q5zuE?!H6xC)nhR$iomR)ITvZJKd+;m_sh9TyWB(LA}#yqI@)4 z{UGSSKZmb=#{3rDze>BTn0=9^2zwpvTtE9N?XrOGMOqZ%b+mIi-K(_A`j;1J_fW2( zK@Q|!mdd*b6UMj>1~JZcSy1aD%>4E>uyc8>tJAzJyK@m1iGL03T!iN;?6Nw?MOZb_ zHL!E7j;pZCCG{6!viGimLH (L1 + L2) || r < abs(L1 - L2) - error('目标位置超出工作空间范围'); + % 检查三角形约束条件 + if BD_dist > (l2 + l3) || BD_dist < abs(l2 - l3) + warning('无法形成闭合五连杆机构!BD距离=%.3f, 需要满足: %.3f < BD < %.3f', ... + BD_dist, abs(l2-l3), l2+l3); + leg_length = NaN; + foot_pos = [NaN, NaN]; + return; end - % 使用余弦定理计算膝关节角度 - cos_q2 = (r^2 - L1^2 - L2^2) / (2*L1*L2); - q2 = acos(cos_q2); % 肘部向上的解 + % 使用余弦定理求解phi2 + cos_phi2_BD = (l2^2 + BD_dist^2 - l3^2) / (2 * l2 * BD_dist); - % 计算髋关节角度 - alpha = atan2(y, x); - beta = atan2(L2*sin(q2), L1 + L2*cos(q2)); - q1 = alpha - beta; -end - -function [angle_equiv, length_equiv] = serial_to_virtual_leg(L1, L2, q1, q2) -% 将串联腿转换为等效摆动杆表示 (对应C代码中的正运动学) -% -% 输入参数: -% L1: 大腿长度 (m) -% L2: 小腿长度 (m) -% q1: 髋关节角度 (rad) -% q2: 膝关节角度 (rad) -% -% 输出: -% angle_equiv: 等效摆动杆角度 (rad) -% length_equiv: 等效摆动杆长度 (m) - - % 对应C代码中的计算 - q4 = (pi - q1 - q2) / 2; - - % 使用余弦定理求解等效摆动杆长度 - a = 1.0; - b = -2.0 * L1 * cos(q4); - c = L1^2 - L2^2; - - discriminant = b^2 - 4*a*c; - - if discriminant < 0 - error('无实数解,配置不可达'); + % 检查余弦值是否在有效范围内 + if abs(cos_phi2_BD) > 1 + warning('余弦值超出范围: %.3f', cos_phi2_BD); + leg_length = NaN; + foot_pos = [NaN, NaN]; + return; end - sqrt_discriminant = sqrt(discriminant); - L3_1 = (-b + sqrt_discriminant) / (2*a); - L3_2 = (-b - sqrt_discriminant) / (2*a); + % 计算BD方向角 + alpha_BD = atan2(y_D - y_B, x_D - x_B); - % 选择正的解 - if L3_1 > 0 && L3_2 > 0 - L3 = min(L3_1, L3_2); % 选择较小的解 - elseif L3_1 > 0 - L3 = L3_1; - elseif L3_2 > 0 - L3 = L3_2; + % 计算phi2 (两个解,选择合理的一个) + angle_offset = acos(cos_phi2_BD); + phi2_solution1 = alpha_BD + angle_offset; + phi2_solution2 = alpha_BD - angle_offset; + + % 选择合理的解 (通常选择使机构在合理配置的解) + phi2 = phi2_solution1; % 可以根据实际需要调整选择逻辑 + + % 计算C点位置 (足端位置) + x_C = x_B + l2 * cos(phi2); + y_C = y_B + l2 * sin(phi2); + + % 验证C点到D点距离是否等于l3 + CD_dist = sqrt((x_D - x_C)^2 + (y_D - y_C)^2); + error_CD = abs(CD_dist - l3); + + if error_CD > 1e-6 + fprintf('警告: CD距离误差较大 (%.6f)\n', error_CD); + end + + % 计算腿长 (假设为原点到C点的距离) + leg_length = sqrt(x_C^2 + y_C^2); + foot_pos = [x_C, y_C]; + + % 输出结果 + fprintf('\n计算结果:\n'); + fprintf(' B点位置: (%.3f, %.3f)\n', x_B, y_B); + fprintf(' C点位置: (%.3f, %.3f)\n', x_C, y_C); + fprintf(' D点位置: (%.3f, %.3f)\n', x_D, y_D); + fprintf(' phi2角度: %.3f rad (%.1f°)\n', phi2, rad2deg(phi2)); + fprintf(' 腿长: %.3f m\n', leg_length); + fprintf(' BD距离: %.3f m\n', BD_dist); + fprintf(' CD验证: %.6f m (应该等于l3=%.3f)\n', CD_dist, l3); + + %% 可视化结果 + figure; + plot([0, x_B], [0, y_B], 'b-', 'LineWidth', 2); % 连杆1 + hold on; + plot([x_B, x_C], [y_B, y_C], 'r-', 'LineWidth', 2); % 连杆2 + plot([x_C, x_D], [y_C, y_D], 'g-', 'LineWidth', 2); % 连杆3 + plot([l5, x_D], [0, y_D], 'm-', 'LineWidth', 2); % 连杆4 + plot([0, l5], [0, 0], 'k-', 'LineWidth', 3); % 连杆5 (基座) + + % 标记关键点 + plot(0, 0, 'ko', 'MarkerSize', 8, 'MarkerFaceColor', 'k'); % A点 + plot(x_B, y_B, 'bo', 'MarkerSize', 8, 'MarkerFaceColor', 'b'); % B点 + plot(x_C, y_C, 'ro', 'MarkerSize', 8, 'MarkerFaceColor', 'r'); % C点 + plot(x_D, y_D, 'go', 'MarkerSize', 8, 'MarkerFaceColor', 'g'); % D点 + plot(l5, 0, 'ko', 'MarkerSize', 8, 'MarkerFaceColor', 'k'); % E点 + + % 标记腿长 + plot([0, x_C], [0, y_C], 'k--', 'LineWidth', 1); % 腿长线 + + % 图形设置 + grid on; + axis equal; + xlabel('X (m)'); + ylabel('Y (m)'); + title('五连杆机构示意图'); + legend('连杆1', '连杆2', '连杆3', '连杆4', '基座', 'Location', 'best'); + + % 添加文本标注 + text(0, 0-0.02, 'A', 'HorizontalAlignment', 'center'); + text(x_B, y_B+0.02, 'B', 'HorizontalAlignment', 'center'); + text(x_C, y_C+0.02, 'C(足端)', 'HorizontalAlignment', 'center'); + text(x_D, y_D+0.02, 'D', 'HorizontalAlignment', 'center'); + text(l5, 0-0.02, 'E', 'HorizontalAlignment', 'center'); + text(x_C/2, y_C/2, sprintf('腿长=%.3fm', leg_length), 'HorizontalAlignment', 'center'); + +catch ME + fprintf('计算过程中出现错误: %s\n', ME.message); + leg_length = NaN; + foot_pos = [NaN, NaN]; +end + +%% 多组参数测试 +fprintf('\n\n=== 多组参数测试 ===\n'); +test_cases = [ + pi/6, pi/4; % 30°, 45° + pi/4, pi/3; % 45°, 60° + -pi/6, pi/2; % -30°, 90° + 0, pi/6; % 0°, 30° +]; + +for i = 1:size(test_cases, 1) + phi1_test = test_cases(i, 1); + phi4_test = test_cases(i, 2); + + fprintf('\n测试 %d: phi1=%.1f°, phi4=%.1f°\n', i, rad2deg(phi1_test), rad2deg(phi4_test)); + + % 重复计算过程(简化版) + x_B_test = l1 * cos(phi1_test); + y_B_test = l1 * sin(phi1_test); + x_D_test = l5 + l4 * cos(phi4_test); + y_D_test = l4 * sin(phi4_test); + BD_dist_test = sqrt((x_D_test - x_B_test)^2 + (y_D_test - y_B_test)^2); + + if BD_dist_test <= (l2 + l3) && BD_dist_test >= abs(l2 - l3) + cos_phi2_BD_test = (l2^2 + BD_dist_test^2 - l3^2) / (2 * l2 * BD_dist_test); + if abs(cos_phi2_BD_test) <= 1 + alpha_BD_test = atan2(y_D_test - y_B_test, x_D_test - x_B_test); + angle_offset_test = acos(cos_phi2_BD_test); + phi2_test = alpha_BD_test + angle_offset_test; + x_C_test = x_B_test + l2 * cos(phi2_test); + y_C_test = y_B_test + l2 * sin(phi2_test); + leg_length_test = sqrt(x_C_test^2 + y_C_test^2); + fprintf(' 结果: 腿长=%.3f m, 足端位置=(%.3f, %.3f)\n', leg_length_test, x_C_test, y_C_test); + else + fprintf(' 结果: 余弦值超出范围\n'); + end else - error('无正解'); + fprintf(' 结果: 无法形成闭合机构\n'); end - - angle_equiv = q1 + q4; - length_equiv = L3; end -function [q1, q2] = virtual_to_serial_leg(L1, L2, angle_equiv, length_equiv) -% 将等效摆动杆转换为串联腿表示 (对应C代码中的逆运动学) -% -% 输入参数: -% L1: 大腿长度 (m) -% L2: 小腿长度 (m) -% angle_equiv: 等效摆动杆角度 (rad) -% length_equiv: 等效摆动杆长度 (m) -% -% 输出: -% q1: 髋关节角度 (rad) -% q2: 膝关节角度 (rad) - - h = length_equiv; - q = angle_equiv; - - % 计算cos(q4) - cos_q4 = (L1^2 + h^2 - L2^2) / (2.0 * L1 * h); - - % 检查范围 - if cos_q4 < -1.0 || cos_q4 > 1.0 - error('不可达配置'); - end - - q4 = acos(cos_q4); - - % 计算关节角度 - q1 = q - q4; - q2 = pi - 2.0 * q4 - q1; -end - -% 示例使用函数 -function demo_vmc_control() -% VMC控制示例 - - % 腿部参数 - L1 = 0.15; % 大腿长度 15cm - L2 = 0.15; % 小腿长度 15cm - - % 当前关节角度 - q1 = pi/6; % 30度 - q2 = pi/3; % 60度 - - % 期望的虚拟力 - F_virtual = 50; % 50N - theta_virtual = -pi/2; % 向下的力 - - % 计算所需关节力矩 - [tau_hip, tau_knee] = vmc_control(L1, L2, q1, q2, F_virtual, theta_virtual); - - fprintf('髋关节所需力矩: %.3f N*m\n', tau_hip); - fprintf('膝关节所需力矩: %.3f N*m\n', tau_knee); - - % 显示雅可比矩阵 - J = compute_jacobian(L1, L2, q1, q2); - fprintf('雅可比矩阵:\n'); - disp(J); - - % 测试等效摆动杆转换 - [angle_eq, length_eq] = serial_to_virtual_leg(L1, L2, q1, q2); - fprintf('等效摆动杆角度: %.3f rad (%.1f deg)\n', angle_eq, rad2deg(angle_eq)); - fprintf('等效摆动杆长度: %.3f m\n', length_eq); - - % 验证逆变换 - [q1_back, q2_back] = virtual_to_serial_leg(L1, L2, angle_eq, length_eq); - fprintf('验证 - 原始角度: q1=%.3f, q2=%.3f\n', q1, q2); - fprintf('验证 - 恢复角度: q1=%.3f, q2=%.3f\n', q1_back, q2_back); -end \ No newline at end of file +fprintf('\n计算完成!\n'); \ No newline at end of file

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z2JyH5OA9iss~sAR7vd=7 zXT#DALmbn+PG~efh@;RfR+I9t>*U3km-I7K8pKiXNyd))*YEZsO=bWJjhz+ZC}2^~ zQ+xrQ^zVt~G6IbT@j)-!c3*7Ti*cwhh!g9wvF}A%>ohdlxy|p@Z>P)FpBHJH^U!FJ zkEWO10WZ>smZ8!h4(Vn8t&23IAJAx!!wr{>W-ijKx1rI_ZD+3b+hrSxi?oS-XtZ-v ziL12BD(4qz5hu`SkdJ?tC5$i9PJo-P|NJ&(KNmE<+P2FAn-^&Xh|p*dhxD=%-$hs- zDiqkcF5lIbT^8)R2;0Yi0y~%Qx(d52>~j%Dgbf9DF7tC0c3J-8B1{Yq3hZ1A 1 && coefficients(i) > 0 + term = [' + ', term]; + end + equation = [equation, term]; + end + end + fprintf('%s;\n', equation); +end \ No newline at end of file diff --git a/utils/Simulation-master/balance/series_parallel_legs/get_k.m b/utils/Simulation-master/balance/series_parallel_legs/get_k.m new file mode 100644 index 0000000..46e1806 --- /dev/null +++ b/utils/Simulation-master/balance/series_parallel_legs/get_k.m @@ -0,0 +1,82 @@ +%计算不同腿长下适合的K矩阵,再进行多项式拟合,得到2*6矩阵每个参数对应的多项式参数 +tic +j=1; +leg=0.1:0.01:0.4; +for i=leg + k=get_k_length(i); + k11(j) = k(1,1); + k12(j) = k(1,2); + k13(j) = k(1,3); + k14(j) = k(1,4); + k15(j) = k(1,5); + k16(j) = k(1,6); + + k21(j) = k(2,1); + k22(j) = k(2,2); + k23(j) = k(2,3); + k24(j) = k(2,4); + k25(j) = k(2,5); + k26(j) = k(2,6); + j=j+1; + + fprintf('leg_length=%d\n', i); +end +a11=polyfit(leg,k11,3); +a12=polyfit(leg,k12,3); +a13=polyfit(leg,k13,3); +a14=polyfit(leg,k14,3); +a15=polyfit(leg,k15,3); +a16=polyfit(leg,k16,3); + +a21=polyfit(leg,k21,3); +a22=polyfit(leg,k22,3); +a23=polyfit(leg,k23,3); +a24=polyfit(leg,k24,3); +a25=polyfit(leg,k25,3); +a26=polyfit(leg,k26,3); + +toc + +% x0=leg; %步长为0.1 +% y11=polyval(a11,x0); %返回值y0是对应于x0的函数值 +% y12=polyval(a12,x0); %返回值y0是对应于x0的函数值 +% y13=polyval(a13,x0); %返回值y0是对应于x0的函数值 +% y14=polyval(a14,x0); %返回值y0是对应于x0的函数值 +% y15=polyval(a15,x0); %返回值y0是对应于x0的函数值 +% y16=polyval(a16,x0); %返回值y0是对应于x0的函数值 +% +% y21=polyval(a21,x0); %返回值y0是对应于x0的函数值 +% y22=polyval(a22,x0); %返回值y0是对应于x0的函数值 +% y23=polyval(a23,x0); %返回值y0是对应于x0的函数值 +% y24=polyval(a24,x0); %返回值y0是对应于x0的函数值 +% y25=polyval(a25,x0); %返回值y0是对应于x0的函数值 +% y26=polyval(a26,x0); %返回值y0是对应于x0的函数值 +% subplot(3,4,1);plot(leg,k11,'o',x0,y11,'r');xlabel('x');ylabel('y');title('k11'); +% subplot(3,4,2);plot(leg,k12,'o',x0,y12,'r');xlabel('x');ylabel('y');title('k12'); +% subplot(3,4,5);plot(leg,k13,'o',x0,y13,'r');xlabel('x');ylabel('y');title('k13'); +% subplot(3,4,6);plot(leg,k14,'o',x0,y14,'r');xlabel('x');ylabel('y');title('k14'); +% subplot(3,4,9);plot(leg,k15,'o',x0,y15,'r');xlabel('x');ylabel('y');title('k15'); +% subplot(3,4,10);plot(leg,k16,'o',x0,y16,'r');xlabel('x');ylabel('y');title('k16'); +% +% subplot(3,4,3);plot(leg,k21,'o',x0,y21,'r');xlabel('x');ylabel('y');title('k21'); +% subplot(3,4,4);plot(leg,k22,'o',x0,y22,'r');xlabel('x');ylabel('y');title('k22'); +% subplot(3,4,7);plot(leg,k23,'o',x0,y23,'r');xlabel('x');ylabel('y');title('k23'); +% subplot(3,4,8);plot(leg,k24,'o',x0,y24,'r');xlabel('x');ylabel('y');title('k24'); +% subplot(3,4,11);plot(leg,k25,'o',x0,y25,'r');xlabel('x');ylabel('y');title('k25'); +% subplot(3,4,12);plot(leg,k26,'o',x0,y26,'r');xlabel('x');ylabel('y');title('k26'); +% grid on; %添加网格线 +% set(gca,'GridLineStyle',':','GridColor','k','GridAlpha',1); %将网格线变成虚线 +% fprintf('fp32 a11[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a11(1),a11(2),a11(3),a11(4)); +% fprintf('fp32 a12[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a12(1),a12(2),a12(3),a12(4)); +% fprintf('fp32 a13[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a13(1),a13(2),a13(3),a13(4)); +% fprintf('fp32 a14[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a14(1),a14(2),a14(3),a14(4)); +% fprintf('fp32 a15[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a15(1),a15(2),a15(3),a15(4)); +% fprintf('fp32 a16[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a16(1),a16(2),a16(3),a16(4)); +% +% fprintf('fp32 a21[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a21(1),a21(2),a21(3),a21(4)); +% fprintf('fp32 a22[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a22(1),a22(2),a22(3),a22(4)); +% fprintf('fp32 a23[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a23(1),a23(2),a23(3),a23(4)); +% fprintf('fp32 a24[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a24(1),a24(2),a24(3),a24(4)); +% fprintf('fp32 a25[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a25(1),a25(2),a25(3),a25(4)); +% fprintf('fp32 a26[6] = {0,%.4f,%.4f,%.4f,%.4f};\n',a26(1),a26(2),a26(3),a26(4)); +toc diff --git a/utils/Simulation-master/balance/series_parallel_legs/get_k_length.m b/utils/Simulation-master/balance/series_parallel_legs/get_k_length.m new file mode 100644 index 0000000..9a1d58c --- /dev/null +++ b/utils/Simulation-master/balance/series_parallel_legs/get_k_length.m @@ -0,0 +1,56 @@ +function K = get_k_length(leg_length) + + %theta : 摆杆与竖直方向夹角 R :驱动轮半径 + %x : 驱动轮位移 L : 摆杆重心到驱动轮轴距离 + %phi : 机体与水平夹角 LM : 摆杆重心到其转轴距离 + %T :驱动轮输出力矩 l : 机体重心到其转轴距离 + %Tp : 髋关节输出力矩 mw : 驱动轮转子质量 + %N :驱动轮对摆杆力的水平分量 mp : 摆杆质量 + %P :驱动轮对摆杆力的竖直分量 M : 机体质量 + %Nm :摆杆对机体力水平方向分量 Iw : 驱动轮转子转动惯量 + %Pm :摆杆对机体力竖直方向分量 Ip : 摆杆绕质心转动惯量 + %Nf : 地面对驱动轮摩擦力 Im : 机体绕质心转动惯量 + + syms x(t) T R Iw mw M L LM theta(t) l phi(t) mp g Tp Ip IM + syms f1 f2 f3 d_theta d_x d_phi theta0 x0 phi0 + + R1=0.086; %驱动轮半径 + L1=leg_length/2; %摆杆重心到驱动轮轴距离 + LM1=leg_length/2; %摆杆重心到其转轴距离 + l1=0.03; %机体质心距离转轴距离 + mw1=1.18; %驱动轮质量 + mp1=1.11; %杆质量 + M1=10.3; %机体质量 + Iw1=mw1*R1^2; %驱动轮转动惯量 + Ip1=mp1*((L1+LM1)^2+0.05^2)/12.0; %摆杆转动惯量 + IM1=M1*(0.3^2+0.12^2)/12.0; %机体绕质心转动惯量 + + + NM = M*diff(x + (L + LM )*sin(theta)-l*sin(phi),t,2); + N = NM + mp*diff(x + L*sin(theta),t,2); + PM = M*g + M*diff((L+LM)*cos(theta)+l*cos(phi),t,2); + P = PM +mp*g+mp*diff(L*cos(theta),t,2); + + eqn1 = diff(x,t,2) == (T -N*R)/(Iw/R + mw*R); + eqn2 = Ip*diff(theta,t,2) == (P*L + PM*LM)*sin(theta)-(N*L+NM*LM)*cos(theta)-T+Tp; + eqn3 = IM*diff(phi,t,2) == Tp +NM*l*cos(phi)+PM*l*sin(phi); + + eqn10 = subs(subs(subs(subs(subs(subs(subs(subs(subs(eqn1,diff(theta,t,2),f1),diff(x,t,2),f2),diff(phi,t,2),f3),diff(theta,t),d_theta),diff(x,t),d_x),diff(phi,t),d_phi),theta,theta0),x,x0),phi,phi0); + eqn20 = subs(subs(subs(subs(subs(subs(subs(subs(subs(eqn2,diff(theta,t,2),f1),diff(x,t,2),f2),diff(phi,t,2),f3),diff(theta,t),d_theta),diff(x,t),d_x),diff(phi,t),d_phi),theta,theta0),x,x0),phi,phi0); + eqn30 = subs(subs(subs(subs(subs(subs(subs(subs(subs(eqn3,diff(theta,t,2),f1),diff(x,t,2),f2),diff(phi,t,2),f3),diff(theta,t),d_theta),diff(x,t),d_x),diff(phi,t),d_phi),theta,theta0),x,x0),phi,phi0); + + [f1,f2,f3] = solve(eqn10,eqn20,eqn30,f1,f2,f3); + + A=subs(jacobian([d_theta,f1,d_x,f2,d_phi,f3],[theta0,d_theta,x0,d_x,phi0,d_phi]),[theta0,d_theta,d_x,phi0,d_phi,T,Tp],[0,0,0,0,0,0,0]); + A=subs(A,[R,L,LM,l,mw,mp,M,Iw,Ip,IM,g],[R1,L1,LM1,l1,mw1,mp1,M1,Iw1,Ip1,IM1,9.8]); + A=double(A); + B=subs(jacobian([d_theta,f1,d_x,f2,d_phi,f3],[T,Tp]),[theta0,d_theta,d_x,phi0,d_phi,T,Tp],[0,0,0,0,0,0,0]); + B=subs(B,[R,L,LM,l,mw,mp,M,Iw,Ip,IM,g],[R1,L1,LM1,l1,mw1,mp1,M1,Iw1,Ip1,IM1,9.8]); + B=double(B); + + Q=diag([100 1 500 100 5000 1]);%theta d_theta x d_x phi d_phi%700 1 600 200 1000 1 + R=[240 0;0 25]; %T Tp + + K=lqr(A,B,Q,R); + +end \ No newline at end of file diff --git a/utils/Simulation-master/balance/series_parallel_legs/physical_calc.mlx b/utils/Simulation-master/balance/series_parallel_legs/physical_calc.mlx new file mode 100644 index 0000000000000000000000000000000000000000..78bd3d3a082072ee86b1a69f5ccaeb9450444464 GIT binary patch literal 7539 zcmaKR1yCGYw>1nJU~mf(+}$U*yC=8@4-SL75AN;`!QEYggak=&Cs+t>A=n%K_v*j* z=6&yWSNEwtU3>L8Yp=b#YHw8qICxwb7#L*eMFF!oB2>-;3j zc*pPs;?(MvM)Wl$A9X9rnQX~RKNszc&4eOC;!H{e_j#&R4HV1LT`+_$Wg-*>$zs;ovm zTo8Hbq0|mkR47{x<5@p_@XQx+iYZ_{X1PtB$-|_wnPN5G zf>VL}=0U&p759Zax$46^rypL)k?WJ$ZmB^TS?d2lQya3Qfgl$cNC<8D#oERz!~gQw9d zOwdp^;*D$6ldpnf$k)Jj@sd;+>wq*^+V+vmNt0eH2HM{)I<(RPf**79zbeT}i zNec4k#+&VPSEW$cyTId;KxCm52QV{8DJwBx%kvsDf?r={;~QqEcAcnpEX?|zmY)^2 z^y-|XEH0*3#`^BwjwqKTNooK7RP<9T;!<4vO8Mrg^i+%(OB)S-Di8*#YT3p7bnI6+ zZ;hCM&aMrb+;1gn>R4nJI%FXdlJVK~juG3}@7<*1=+_igFFld*71}lCW!GZl(Ko0v zE6KR&Fs@Y;MgWhBNG_kX>%K}|qW_anOY5W3eyC*0U;MXh?M%S7ChyqH986v9pz3{= 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