nmpc圆形轨迹跟踪C代码

以下是一个基于NMPC算法实现圆形轨迹跟踪的C代码示例：

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

#define PI 3.14159265358979323846

int main() {
    ACADOvariables acadoVariables;
    ACADOworkspace acadoWorkspace;
    ACADOsolver acadoSolver;
    ACADOproblem acadoProblem;

    double L = 1.0; // 车辆轴距
    double v = 5.0; // 目标速度
    double r = 10.0; // 圆形轨迹半径
    double dt = 0.1; // 时间间隔
    double T = 10.0; // 时间总长
    int N = (int)(T/dt); // 离散步数

    double x[N+1], y[N+1], theta[N+1], phi[N+1], delta[N]; // 状态变量和控制变量
    double x_ref[N+1], y_ref[N+1], theta_ref[N+1]; // 参考轨迹

    // 初始化状态变量和参考轨迹
    x[0] = 0.0;
    y[0] = 0.0;
    theta[0] = PI/2.0;
    phi[0] = 0.0;
    for (int i = 0; i < N+1; i++) {
        x_ref[i] = r*cos(2*PI*i/N);
        y_ref[i] = r*sin(2*PI*i/N);
        theta_ref[i] = atan2(y_ref[i+1]-y_ref[i], x_ref[i+1]-x_ref[i]);
    }

    // 初始化ACADO问题
    acadoVariables.x(1) << x[0];
    acadoVariables.x(2) << y[0];
    acadoVariables.x(3) << theta[0];
    acadoVariables.u(1) << phi[0];
    acadoProblem.setModel((acadoVariables.x == acadoVariables[0]) && (acadoVariables.u == acadoVariables[3]));
    acadoProblem.setTimeHorizon(dt);

    // 添加状态和控制变量的限制
    for (int i = 0; i < N; i++) {
        acadoProblem.subjectTo(acadoVariables.x(i+1) == acadoVariables.x(i) + v*cos(theta[i])*dt);
        acadoProblem.subjectTo(acadoVariables.y(i+1) == acadoVariables.y(i) + v*sin(theta[i])*dt);
        acadoProblem.subjectTo(acadoVariables.theta(i+1) == acadoVariables.theta(i) + v/L*tan(delta[i])*dt);
        acadoProblem.subjectTo(acadoVariables.phi(i) <= 0.5);
        acadoProblem.subjectTo(acadoVariables.phi(i) >= -0.5);
    }

    // 添加初始和终止状态的限制
    acadoProblem.subjectTo(acadoVariables.x(0) == x[0]);
    acadoProblem.subjectTo(acadoVariables.y(0) == y[0]);
    acadoProblem.subjectTo(acadoVariables.theta(0) == theta[0]);
    acadoProblem.subjectTo(acadoVariables.x(N) == x_ref[N]);
    acadoProblem.subjectTo(acadoVariables.y(N) == y_ref[N]);
    acadoProblem.subjectTo(acadoVariables.theta(N) == theta_ref[N]);

    // 添加目标函数
    acadoProblem.minimizeMayerTerm(acadoVariables.phi(N-1)*acadoVariables.phi(N-1));

    // 初始化ACADO求解器
    acadoWorkspace.init(N);
    acadoSolver.set(ACADO_NLP_SOLVER, ACADO_QPOASES);
    acadoSolver.set(ACADO_PRINTLEVEL, ACADO_SILENT);
    acadoSolver.init(acadoProblem, ACADO_INFINITY);

    // 求解非线性优化问题
    for (int i = 0; i < N; i++) {
        acadoVariables.x(0) = x[i];
        acadoVariables.y(0) = y[i];
        acadoVariables.theta(0) = theta[i];
        acadoSolver.solve(acadoVariables, acadoWorkspace);
        x[i+1] = acadoVariables.x(1);
        y[i+1] = acadoVariables.y(1);
        theta[i+1] = acadoVariables.theta(1);
        phi[i] = acadoVariables.phi(0);
        delta[i] = atan2(L*tan(phi[i]), 1.0);
    }

    // 绘制轨迹
    gnuplot_ctrl *plot = gnuplot_init();
    gnuplot_setstyle(plot, "lines");
    gnuplot_plot_xy(plot, x, y, N+1, "Trajectory");
    gnuplot_plot_xy(plot, x_ref, y_ref, N+1, "Reference");
    gnuplot_close(plot);

    return 0;
}

这个代码实现了一个简单的NMPC算法，使用车辆状态（位置、方向）和控制（方向盘转角）变量，通过优化控制输入使得车辆沿着圆形轨迹行驶。需要注意的是，这个代码并没有进行任何实际物理模型的建模，是一个非常简化的例子，仅用于演示NMPC算法的基本实现。如果要用于实际控制应用，需要根据实际物理模型进行更加精细的建模和实现。