266 lines
9.7 KiB
C
266 lines
9.7 KiB
C
/*
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* LQR控制器实现
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*/
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#include "lqr.h"
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#include <string.h>
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/* Private macros ----------------------------------------------------------- */
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#define LQR_LIMIT(x, min, max) ((x) < (min) ? (min) : ((x) > (max) ? (max) : (x)))
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/* Private variables -------------------------------------------------------- */
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/* 从MATLAB仿真get_k.m得到的默认增益矩阵多项式拟合系数 */
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/* 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 */
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static LQR_GainMatrix_t default_gain_matrix = {
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/* K矩阵第一行 - 轮毂力矩T的增益系数 */
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.k11_coeff = {0.0f, -2845.3f, 1899.4f, -123.8f}, /* theta */
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.k12_coeff = {0.0f, -89.7f, 61.2f, -4.8f}, /* d_theta */
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.k13_coeff = {0.0f, 5479.2f, -3298.6f, 489.8f}, /* x */
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.k14_coeff = {0.0f, 312.4f, -178.9f, 34.2f}, /* d_x */
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.k15_coeff = {0.0f, -31250.0f, 18750.0f, -3125.0f}, /* phi */
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.k16_coeff = {0.0f, -89.7f, 61.2f, -4.8f}, /* d_phi */
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/* K矩阵第二行 - 髋关节力矩Tp的增益系数 */
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.k21_coeff = {0.0f, 486.1f, -324.1f, 21.6f}, /* theta */
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.k22_coeff = {0.0f, 15.3f, -10.4f, 0.8f}, /* d_theta */
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.k23_coeff = {0.0f, -935.4f, 562.2f, -83.5f}, /* x */
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.k24_coeff = {0.0f, -53.3f, 30.5f, -5.8f}, /* d_x */
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.k25_coeff = {0.0f, 5333.3f, -3200.0f, 533.3f}, /* phi */
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.k26_coeff = {0.0f, 15.3f, -10.4f, 0.8f}, /* d_phi */
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};
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/* Private function prototypes ---------------------------------------------- */
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static int8_t LQR_CalculateErrorState(LQR_Controller_t *lqr);
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static int8_t LQR_ApplyControlLimits(LQR_Controller_t *lqr);
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/* Public functions --------------------------------------------------------- */
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int8_t LQR_Init(LQR_Controller_t *lqr, float max_wheel_torque, float max_joint_torque) {
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if (lqr == NULL) {
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return -1;
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}
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/* 清零结构体 */
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memset(lqr, 0, sizeof(LQR_Controller_t));
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/* 设置控制限制 */
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lqr->param.max_wheel_torque = max_wheel_torque;
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lqr->param.max_joint_torque = max_joint_torque;
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/* 设置默认系统物理参数（从MATLAB仿真get_k_length.m获取） */
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lqr->param.R = 0.072f; /* 驱动轮半径 */
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lqr->param.l = 0.03f; /* 机体重心到转轴距离 */
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lqr->param.mw = 0.60f; /* 驱动轮质量 */
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lqr->param.mp = 1.8f; /* 摆杆质量 */
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lqr->param.M = 1.8f; /* 机体质量 */
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lqr->param.g = 9.8f; /* 重力加速度 */
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/* 计算转动惯量 */
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lqr->param.Iw = lqr->param.mw * lqr->param.R * lqr->param.R;
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lqr->param.IM = lqr->param.M * (0.3f * 0.3f + 0.12f * 0.12f) / 12.0f;
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/* 设置默认增益矩阵 */
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lqr->gain_matrix = &default_gain_matrix;
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/* 设置默认目标状态（平衡状态） */
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memset(&lqr->param.target_state, 0, sizeof(LQR_State_t));
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/* 初始化当前腿长为中等值 */
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lqr->current_leg_length = 0.25f;
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/* 计算初始增益矩阵 */
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LQR_CalculateGainMatrix(lqr, lqr->current_leg_length);
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lqr->initialized = true;
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return 0;
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}
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int8_t LQR_SetGainMatrix(LQR_Controller_t *lqr, LQR_GainMatrix_t *gain_matrix) {
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if (lqr == NULL || gain_matrix == NULL) {
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return -1;
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}
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lqr->gain_matrix = gain_matrix;
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/* 重新计算增益矩阵 */
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return LQR_CalculateGainMatrix(lqr, lqr->current_leg_length);
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}
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int8_t LQR_UpdateState(LQR_Controller_t *lqr, const LQR_State_t *state) {
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if (lqr == NULL || state == NULL) {
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return -1;
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}
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/* 更新当前状态 */
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lqr->current_state = *state;
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/* 计算状态误差 */
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return LQR_CalculateErrorState(lqr);
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}
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int8_t LQR_SetTargetState(LQR_Controller_t *lqr, const LQR_State_t *target_state) {
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if (lqr == NULL || target_state == NULL) {
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return -1;
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}
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lqr->param.target_state = *target_state;
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/* 重新计算状态误差 */
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return LQR_CalculateErrorState(lqr);
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}
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int8_t LQR_CalculateGainMatrix(LQR_Controller_t *lqr, float leg_length) {
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if (lqr == NULL || lqr->gain_matrix == NULL) {
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return -1;
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}
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/* 限制腿长范围 */
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leg_length = LQR_LIMIT(leg_length, 0.1f, 0.4f);
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lqr->current_leg_length = leg_length;
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/* 更新与腿长相关的物理参数 */
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lqr->param.L = leg_length / 2.0f; /* 摆杆重心到驱动轮轴距离 */
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lqr->param.LM = leg_length / 2.0f; /* 摆杆重心到其转轴距离 */
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/* 计算摆杆转动惯量 */
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float leg_total_length = lqr->param.L + lqr->param.LM;
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lqr->param.Ip = lqr->param.mp * (leg_total_length * leg_total_length + 0.05f * 0.05f) / 12.0f;
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/* 使用多项式拟合计算当前增益矩阵 */
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lqr->K_matrix[0][0] = LQR_PolynomialCalc(lqr->gain_matrix->k11_coeff, leg_length); /* K11: theta */
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lqr->K_matrix[0][1] = LQR_PolynomialCalc(lqr->gain_matrix->k12_coeff, leg_length); /* K12: d_theta */
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lqr->K_matrix[0][2] = LQR_PolynomialCalc(lqr->gain_matrix->k13_coeff, leg_length); /* K13: x */
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lqr->K_matrix[0][3] = LQR_PolynomialCalc(lqr->gain_matrix->k14_coeff, leg_length); /* K14: d_x */
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lqr->K_matrix[0][4] = LQR_PolynomialCalc(lqr->gain_matrix->k15_coeff, leg_length); /* K15: phi */
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lqr->K_matrix[0][5] = LQR_PolynomialCalc(lqr->gain_matrix->k16_coeff, leg_length); /* K16: d_phi */
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lqr->K_matrix[1][0] = LQR_PolynomialCalc(lqr->gain_matrix->k21_coeff, leg_length); /* K21: theta */
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lqr->K_matrix[1][1] = LQR_PolynomialCalc(lqr->gain_matrix->k22_coeff, leg_length); /* K22: d_theta */
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lqr->K_matrix[1][2] = LQR_PolynomialCalc(lqr->gain_matrix->k23_coeff, leg_length); /* K23: x */
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lqr->K_matrix[1][3] = LQR_PolynomialCalc(lqr->gain_matrix->k24_coeff, leg_length); /* K24: d_x */
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lqr->K_matrix[1][4] = LQR_PolynomialCalc(lqr->gain_matrix->k25_coeff, leg_length); /* K25: phi */
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lqr->K_matrix[1][5] = LQR_PolynomialCalc(lqr->gain_matrix->k26_coeff, leg_length); /* K26: d_phi */
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return 0;
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}
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int8_t LQR_Control(LQR_Controller_t *lqr) {
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if (lqr == NULL || !lqr->initialized) {
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return -1;
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}
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/* LQR控制律: u = -K * x_error
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* 其中 u = [T; Tp], x_error = x_current - x_target
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*/
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/* 计算轮毂力矩T */
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lqr->control_output.T = -(
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lqr->K_matrix[0][0] * lqr->error_state.theta +
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lqr->K_matrix[0][1] * lqr->error_state.d_theta +
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lqr->K_matrix[0][2] * lqr->error_state.x +
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lqr->K_matrix[0][3] * lqr->error_state.d_x +
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lqr->K_matrix[0][4] * lqr->error_state.phi +
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lqr->K_matrix[0][5] * lqr->error_state.d_phi
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);
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/* 计算髋关节力矩Tp */
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lqr->control_output.Tp = -(
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lqr->K_matrix[1][0] * lqr->error_state.theta +
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lqr->K_matrix[1][1] * lqr->error_state.d_theta +
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lqr->K_matrix[1][2] * lqr->error_state.x +
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lqr->K_matrix[1][3] * lqr->error_state.d_x +
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lqr->K_matrix[1][4] * lqr->error_state.phi +
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lqr->K_matrix[1][5] * lqr->error_state.d_phi
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);
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/* 应用控制限制 */
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return LQR_ApplyControlLimits(lqr);
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}
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int8_t LQR_GetOutput(LQR_Controller_t *lqr, LQR_Input_t *output) {
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if (lqr == NULL || output == NULL) {
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return -1;
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}
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*output = lqr->control_output;
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return 0;
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}
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int8_t LQR_Reset(LQR_Controller_t *lqr) {
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if (lqr == NULL) {
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return -1;
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}
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/* 清零状态和输出 */
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memset(&lqr->current_state, 0, sizeof(LQR_State_t));
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memset(&lqr->error_state, 0, sizeof(LQR_State_t));
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memset(&lqr->control_output, 0, sizeof(LQR_Input_t));
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/* 重置限幅标志 */
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lqr->wheel_torque_limited = false;
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lqr->joint_torque_limited = false;
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return 0;
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}
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float LQR_PolynomialCalc(const float *coeff, float leg_length) {
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if (coeff == NULL) {
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return 0.0f;
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}
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/* 计算3阶多项式: coeff[0]*L^3 + coeff[1]*L^2 + coeff[2]*L + coeff[3] */
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float L = leg_length;
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float L2 = L * L;
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float L3 = L2 * L;
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return coeff[0] * L3 + coeff[1] * L2 + coeff[2] * L + coeff[3];
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}
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/* Private functions -------------------------------------------------------- */
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static int8_t LQR_CalculateErrorState(LQR_Controller_t *lqr) {
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if (lqr == NULL) {
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return -1;
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}
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/* 计算状态误差 */
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lqr->error_state.theta = lqr->current_state.theta - lqr->param.target_state.theta;
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lqr->error_state.d_theta = lqr->current_state.d_theta - lqr->param.target_state.d_theta;
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lqr->error_state.x = lqr->current_state.x - lqr->param.target_state.x;
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lqr->error_state.d_x = lqr->current_state.d_x - lqr->param.target_state.d_x;
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lqr->error_state.phi = lqr->current_state.phi - lqr->param.target_state.phi;
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lqr->error_state.d_phi = lqr->current_state.d_phi - lqr->param.target_state.d_phi;
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return 0;
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}
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static int8_t LQR_ApplyControlLimits(LQR_Controller_t *lqr) {
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if (lqr == NULL) {
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return -1;
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}
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/* 重置限幅标志 */
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lqr->wheel_torque_limited = false;
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lqr->joint_torque_limited = false;
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/* 限制轮毂力矩 */
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if (fabsf(lqr->control_output.T) > lqr->param.max_wheel_torque) {
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lqr->control_output.T = LQR_LIMIT(lqr->control_output.T,
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-lqr->param.max_wheel_torque,
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lqr->param.max_wheel_torque);
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lqr->wheel_torque_limited = true;
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}
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/* 限制髋关节力矩 */
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if (fabsf(lqr->control_output.Tp) > lqr->param.max_joint_torque) {
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lqr->control_output.Tp = LQR_LIMIT(lqr->control_output.Tp,
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-lqr->param.max_joint_torque,
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lqr->param.max_joint_torque);
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lqr->joint_torque_limited = true;
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}
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return 0;
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}
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