NMPC圆形轨迹跟踪C代码

以下是一个简单的NMPC控制器，用于将小车跟踪一个圆形轨迹。其中，小车的状态变量为x和y，控制变量为v和theta（车速和车头方向角度），轨迹参数为圆心坐标xc和yc，及半径r。该控制器使用了CasADi库来进行数学建模和求解。

#include <casadi/casadi.hpp>
#include <iostream>

using namespace casadi;

int main()
{
    // Define symbolic variables
    SX x = SX::sym("x");
    SX y = SX::sym("y");
    SX v = SX::sym("v");
    SX theta = SX::sym("theta");

    // Define model and constraints
    Function f = Function("f", {x, y, v, theta}, {v*cos(theta), v*sin(theta), 0, 0});
    Function h = Function("h", {x, y}, {pow(x - xc, 2) + pow(y - yc, 2) - pow(r, 2)});

    // Define optimization variables
    SX xc = SX::sym("xc");
    SX yc = SX::sym("yc");
    SX r = SX::sym("r");
    SX dt = SX::sym("dt");
    SX p = SX::vertcat({xc, yc, r, dt});
    SX u = SX::vertcat({v, theta});
    SX n_states = 4;
    SX n_controls = 2;
    SX n_params = 4;

    // Define cost function
    SX L = pow(v, 2) + pow(theta, 2);
    Function lag = Function("lag", {x, y, v, theta, xc, yc, r}, {L});

    // Define NMPC problem
    SXDict nlp = {{"x", SX::vertcat({x, y, v, theta})},
                 {"p", p},
                 {"f", f(x, y, v, theta)},
                 {"g", h(x, y)},
                 {"u", u},
                 {"lbg", 0},
                 {"ubg", 0},
                 {"lbx", SX::vertcat({-Inf, -Inf, 0, -Inf})},
                 {"ubx", SX::vertcat({Inf, Inf, Inf, Inf})},
                 {"p_min", SX::vertcat({-Inf, -Inf, 0, 0.1})},
                 {"p_max", SX::vertcat({Inf, Inf, Inf, 0.5})}
                 };

    // Define solver and options
    std::map<std::string, std::string> options;
    options["ipopt.print_level"] = "0";
    options["ipopt.max_iter"] = "100";
    options["ipopt.tol"] = "1e-6";
    options["ipopt.warm_start_init_point"] = "yes";
    options["ipopt.warm_start_bound_push"] = "1e-8";
    options["ipopt.warm_start_bound_frac"] = "1e-8";
    options["ipopt.warm_start_slack_bound_frac"] = "1e-8";
    options["ipopt.warm_start_slack_bound_push"] = "1e-8";
    options["ipopt.mu_init"] = "1e-6";
    options["ipopt.mu_strategy"] = "adaptive";
    options["ipopt.hessian_approximation"] = "limited-memory";
    options["ipopt.linear_solver"] = "ma57";
    options["print_time"] = "0";

    std::vector<SX> w0, lbw, ubw, lbg, ubg, p_min, p_max;
    lbw = {0, 0, 0, -pi};
    ubw = {0, 0, 1, pi};
    w0 = {0, 0, 0.2, 0};
    lbg = {0};
    ubg = {0};
    p_min = {-1, -1, 0, 0.1};
    p_max = {1, 1, 1, 0.5};

    // Create solver instance
    Function nlp_fcn = Function("nlp_fcn", nlp);
    nlpsol_solver nlpsol("nlpsol", "ipopt", nlp_fcn, options);
    nlpsol.setInput("x0", w0);
    nlpsol.setInput("lbx", lbw);
    nlpsol.setInput("ubx", ubw);
    nlpsol.setInput("lbg", lbg);
    nlpsol.setInput("ubg", ubg);
    nlpsol.setInput("p_min", p_min);
    nlpsol.setInput("p_max", p_max);

    // Loop over time steps
    double t = 0;
    double T = 10;
    double dt_val = 0.1;
    while (t < T) {
        // Solve NMPC
        nlpsol.setInput("x0", w0);
        nlpsol.setInput("p", {xc_val, yc_val, r_val, dt_val});
        nlpsol.evaluate();
        std::vector<double> w_opt = nlpsol.getOutput("x").asVector();
        std::vector<double> u_opt = {w_opt[2], w_opt[3]};

        // Simulate system
        std::vector<double> x_val = {w0[0], w0[1], w_opt[0], w_opt[1]};
        std::vector<double> xdot_val = f(x_val, u_opt).asVector();
        std::vector<double> x_next = {x_val[0] + xdot_val[0]*dt_val,
                                      x_val[1] + xdot_val[1]*dt_val,
                                      xdot_val[2],
                                      xdot_val[3]};

        // Update variables and time
        w0 = {x_next[0], x_next[1], u_opt[0], u_opt[1]};
        t += dt_val;
    }

    return 0;
}

此代码实现的是一个基于NMPC的控制器，用于将小车跟踪圆形轨迹。其中，控制器将小车当前状态和轨迹参数作为输入，然后基于数学模型求解控制变量，即车速和车头方向角度。该控制器的优化问题由一个非线性规划（NLP）问题描述，可以使用IPOPT求解器求解。通过在时间上循环执行此代码，可以实现小车沿圆形轨迹运动的目的。