NMPC轨迹跟踪C代码

以下是一个简单的NMPC圆轨迹跟踪的C代码示例：

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

#define N 10 // 控制周期
#define T 0.1 // 控制周期时间间隔

int main() {
    // 初始化
    real_t r = 1; // 圆半径
    double x0[3] = {0, 0, 0}; // 初始状态
    double x[3] = {0, 0, 0}; // 记录状态历史
    double u[2][N] = {0}; // 记录控制历史

    // 设置系统模型
    DifferentialEquation f(0.0, T);
    DMatrix Q(3, 3), R(2, 2);
    Q.setIdentity();
    R.setIdentity();
    VariablesGrid states(3, N+1), controls(2, N);
    for (int i = 0; i <= N; i++) {
        states(0,i) = x0[0];
        states(1,i) = x0[1];
        states(2,i) = x0[2];
    }

    // 循环控制
    for (int i = 0; i < N; i++) {
        // 计算当前状态下期望的圆心位置
        double theta = x[2];
        double xc = r*cos(theta);
        double yc = r*sin(theta);

        // 计算当前状态下期望的圆心速度
        DMatrix J(2, 3);
        J(0,0) = -r*sin(theta);
        J(0,1) = cos(theta);
        J(1,0) = r*cos(theta);
        J(1,1) = sin(theta);
        DVector xc_dot = J*states.getVector(i);

        // 使用NMPC求解最优控制
        for (int j = 0; j < 2; j++) {
            controls(j,i) = 0.0;
        }
        OptimizationAlgorithm nmpc(N);
        nmpc.set( DISCRETIZATION_TYPE, SINGLE_SHOOTING );
        nmpc.set( HESSIAN_APPROXIMATION, EXACT_HESSIAN );
        nmpc.set( MAX_NUM_ITERATIONS, 1 );
        nmpc.set( PRINTLEVEL, LOW );
        nmpc.set( KKT_TOLERANCE, 1e-2 );
        nmpc.set( INTEGRATOR_TYPE, INT_RK45 );
        nmpc.set( QP_SOLVER, QP_QPOASES );
        nmpc.set( QP_SOLVER_ITERATIONS, 50 );
        Function h;
        h << states(0,i) - xc;
        h << states(1,i) - yc;
        h << states(2,i) - xc_dot(1)/xc - xc_dot(0)/yc;
        nmpc.set( CONSTRAINT, h );
        Function phi;
        phi << states(0,i+1) - (states(0,i) + T*f(states(0,i), states(1,i), states(2,i), controls(0,i), controls(1,i))(0));
        phi << states(1,i+1) - (states(1,i) + T*f(states(0,i), states(1,i), states(2,i), controls(0,i), controls(1,i))(1));
        phi << states(2,i+1) - (states(2,i) + T*f(states(0,i), states(1,i), states(2,i), controls(0,i), controls(1,i))(2));
        nmpc.set( OBJECTIVE, phi );
        nmpc.init( 0.0, states, controls );
        nmpc.solve();

        // 记录控制历史
        for (int j = 0; j < 2; j++) {
            u[j][i] = controls(j,i);
        }

        // 模拟下一步状态
        x[0] = states(0,i+1);
        x[1] = states(1,i+1);
        x[2] = states(2,i+1);
    }

    // 绘制轨迹
    FILE *fp = fopen("trajectory.dat", "w");
    for (int i = 0; i <= N; i++) {
        double theta = x0[2] + i*T*u[1][i];
        double xc = r*cos(theta);
        double yc = r*sin(theta);
        fprintf(fp, "%f %f\n", x[i][0], x[i][1]);
        fprintf(fp, "%f %f\n", xc, yc);
        fprintf(fp, "\n");
    }
    fclose(fp);

    return 0;
}

其中，`f`为系统模型，`Q`和`R`为控制代价函数的权重矩阵，`states`和`controls`为状态和控制量的变量网格，`h`为非线性约束函数，`phi`为控制代价函数。这些变量需要根据具体的系统模型和控制目标进行设置。