nmpc圆形轨迹跟踪C代码

以下是一个基于NMPC算法的圆形轨迹跟踪C代码示例：

#include <stdio.h>
#include <math.h>

#define PI 3.1415926
#define N 10   // 控制时域
#define M 3    // 状态量
#define P 2    // 控制量

// 状态方程
void f(double x[M], double u[P], double dt, double y[M])
{
    y[0] = x[0] + dt * x[2] * cos(x[3]);
    y[1] = x[1] + dt * x[2] * sin(x[3]);
    y[2] = x[2] + dt * u[0];
    y[3] = x[3] + dt * u[1] / x[2];
}

// 预测误差函数
double h(double x[M], double u[P], double dt, double z[M])
{
    double y[M];
    f(x, u, dt, y);
    z[0] = x[0] - y[0];
    z[1] = x[1] - y[1];
    z[2] = x[2] - y[2];
    z[3] = x[3] - y[3];
    return sqrt(z[0]*z[0] + z[1]*z[1] + z[2]*z[2] + z[3]*z[3]);
}

// 优化目标函数
double obj(double u[P], double x0[M], double dt)
{
    double x1[M], x2[M], x3[M], x4[M], x5[M], x6[M], x7[M], x8[M], x9[M], x10[M];
    double z1[M], z2[M], z3[M], z4[M], z5[M], z6[M], z7[M], z8[M], z9[M], z10[M];
    f(x0, u, dt, x1);
    f(x1, u, dt, x2);
    f(x2, u, dt, x3);
    f(x3, u, dt, x4);
    f(x4, u, dt, x5);
    f(x5, u, dt, x6);
    f(x6, u, dt, x7);
    f(x7, u, dt, x8);
    f(x8, u, dt, x9);
    f(x9, u, dt, x10);
    double err = h(x1, u, dt, z1) + h(x2, u, dt, z2) + h(x3, u, dt, z3) + h(x4, u, dt, z4) + h(x5, u, dt, z5) + h(x6, u, dt, z6) + h(x7, u, dt, z7) + h(x8, u, dt, z8) + h(x9, u, dt, z9) + h(x10, u, dt, z10);
    return err;
}

// 优化算法
void nmpc(double x0[M], double u0[P], double dt, double u[P])
{
    double u1[P], u2[P], u3[P], u4[P], u5[P], u6[P], u7[P], u8[P], u9[P], u10[P];
    double obj0 = obj(u0, x0, dt);
    double obj1 = obj(u1, x0, dt);
    double obj2 = obj(u2, x0, dt);
    double obj3 = obj(u3, x0, dt);
    double obj4 = obj(u4, x0, dt);
    double obj5 = obj(u5, x0, dt);
    double obj6 = obj(u6, x0, dt);
    double obj7 = obj(u7, x0, dt);
    double obj8 = obj(u8, x0, dt);
    double obj9 = obj(u9, x0, dt);
    double obj10 = obj(u10, x0, dt);
    double obj_min = obj0;
    int idx_min = 0;
    if (obj1 < obj_min) { obj_min = obj1; idx_min = 1; }
    if (obj2 < obj_min) { obj_min = obj2; idx_min = 2; }
    if (obj3 < obj_min) { obj_min = obj3; idx_min = 3; }
    if (obj4 < obj_min) { obj_min = obj4; idx_min = 4; }
    if (obj5 < obj_min) { obj_min = obj5; idx_min = 5; }
    if (obj6 < obj_min) { obj_min = obj6; idx_min = 6; }
    if (obj7 < obj_min) { obj_min = obj7; idx_min = 7; }
    if (obj8 < obj_min) { obj_min = obj8; idx_min = 8; }
    if (obj9 < obj_min) { obj_min = obj9; idx_min = 9; }
    if (obj10 < obj_min) { obj_min = obj10; idx_min = 10; }
    switch (idx_min) {
        case 0: u[0] = u0[0]; u[1] = u0[1]; break;
        case 1: u[0] = u1[0]; u[1] = u1[1]; break;
        case 2: u[0] = u2[0]; u[1] = u2[1]; break;
        case 3: u[0] = u3[0]; u[1] = u3[1]; break;
        case 4: u[0] = u4[0]; u[1] = u4[1]; break;
        case 5: u[0] = u5[0]; u[1] = u5[1]; break;
        case 6: u[0] = u6[0]; u[1] = u6[1]; break;
        case 7: u[0] = u7[0]; u[1] = u7[1]; break;
        case 8: u[0] = u8[0]; u[1] = u8[1]; break;
        case 9: u[0] = u9[0]; u[1] = u9[1]; break;
        case 10: u[0] = u10[0]; u[1] = u10[1]; break;
    }
}

int main(void)
{
    double x[M] = {0, 0, 1, PI/2};   // 初始状态
    double u[P] = {0, 0};            // 初始控制量
    double dt = 0.1;                 // 时间间隔
    double r = 1;                    // 圆形半径
    double center_x = 0;             // 圆心横坐标
    double center_y = 0;             // 圆心纵坐标
    double theta = 0;                // 圆形轨迹的角度
    for (int i = 0; i < 100; i++) {
        // 计算圆心坐标
        center_x = x[0] + r * cos(theta);
        center_y = x[1] + r * sin(theta);
        // 计算控制量
        double u0[P] = {r * cos(theta+dt) - r * cos(theta), r * sin(theta+dt) - r * sin(theta)};
        nmpc(x, u, dt, u0);
        // 更新状态
        f(x, u, dt, x);
        // 更新角度
        theta = atan2(center_y - x[1], center_x - x[0]);
        printf("x=%.2f, y=%.2f, v=%.2f, theta=%.2f, u=[%.2f, %.2f]\n", x[0], x[1], x[2], x[3], u[0], u[1]);
    }
    return 0;
}

该代码实现了一个简单的NMPC算法，用于使一个小车沿着圆形轨迹移动。具体来说，每个时间步骤，代码会计算圆心坐标，然后用NMPC算法计算控制量，更新状态，最后更新角度。