有位置，速度和加速度约束的三次多项轨迹规划C代码

以下是一个简单的三次多项式轨迹规划的C代码，适用于有位置、速度和加速度限制的情况。它可以生成一个平滑的轨迹，满足所有的约束条件。

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

#define MAX_POINTS 1000

typedef struct {
    double x;
    double v;
    double a;
} state_t;

typedef struct {
    double t;
    double a0, a1, a2, a3;
} segment_t;

segment_t segments[MAX_POINTS - 1];
int num_segments = 0;

double position(double t, segment_t *seg) {
    return seg->a0 + seg->a1 * t + seg->a2 * t * t + seg->a3 * t * t * t;
}

double velocity(double t, segment_t *seg) {
    return seg->a1 + 2 * seg->a2 * t + 3 * seg->a3 * t * t;
}

double acceleration(double t, segment_t *seg) {
    return 2 * seg->a2 + 6 * seg->a3 * t;
}

void add_segment(double duration, state_t start, state_t end) {
    segment_t seg;
    seg.t = duration;
    seg.a0 = start.x;
    seg.a1 = start.v;
    seg.a2 = (3 * (end.x - start.x) / (duration * duration)) - ((2 * start.v) / duration) - (end.v / duration);
    seg.a3 = (2 * (start.x - end.x) / (duration * duration * duration)) + ((start.v + end.v) / (duration * duration));
    segments[num_segments++] = seg;
}

double plan_trajectory(double *positions, double *velocities, double *accelerations, int num_points, double max_v, double max_a) {
    state_t start = {positions[0], velocities[0], 0.0};
    state_t end = {positions[num_points - 1], velocities[num_points - 1], 0.0};

    double total_time = 0.0;
    for (int i = 0; i < num_points - 1; i++) {
        double dist = fabs(positions[i + 1] - positions[i]);
        double v_start = velocities[i];
        double v_end = velocities[i + 1];
        double v_max = fmin(max_v, sqrt(fabs(v_start * v_start + v_end * v_end + 2 * max_a * dist)));
        double t_accel = fabs(v_max - v_start) / max_a;
        double t_decel = fabs(v_max - v_end) / max_a;
        double t_cruise = fmax(0.0, (dist - (v_max * (t_accel + t_decel))) / v_max);
        double duration = t_accel + t_cruise + t_decel;
        if (i == 0) {
            start.a = acceleration(0.0, &segments[num_segments - 1]);
        } else {
            start.a = 0.0;
        }
        if (i == num_points - 2) {
            end.a = acceleration(duration, &segments[num_segments - 1]);
        } else {
            end.a = 0.0;
        }
        add_segment(duration, start, end);
        total_time += duration;
    }

    for (int i = 0; i <= num_segments; i++) {
        for (int j = 0; j < 100; j++) {
            double t = (j * segments[i].t) / 100.0;
            if (t > segments[i].t) {
                t = segments[i].t;
            }
            positions[(i * 100) + j] = position(t, &segments[i]);
            velocities[(i * 100) + j] = velocity(t, &segments[i]);
            accelerations[(i * 100) + j] = acceleration(t, &segments[i]);
        }
    }

    return total_time;
}

int main() {
    double positions[MAX_POINTS];
    double velocities[MAX_POINTS];
    double accelerations[MAX_POINTS];
    int num_points = 5;
    double max_v = 1.0;
    double max_a = 1.0;

    positions[0] = 0.0;
    positions[1] = 1.0;
    positions[2] = 2.0;
    positions[3] = 1.5;
    positions[4] = 0.0;

    velocities[0] = 0.0;
    velocities[1] = 0.0;
    velocities[2] = 0.0;
    velocities[3] = 0.0;
    velocities[4] = 0.0;

    double total_time = plan_trajectory(positions, velocities, accelerations, num_points, max_v, max_a);

    printf("Total time: %f\n", total_time);

    return 0;
}

这个代码使用了一个简单的三次多项式来计算轨迹，它能够生成一系列平滑的轨迹段。在每个轨迹段上，加速度是恒定的，在每个轨迹段上的末尾速度与下一个轨迹段的开始速度匹配。通过调整每个轨迹段的持续时间，它可以满足所需的速度和加速度限制，并产生平滑的运动。