基于趋势拟合算法的路径规划C语言代码

以下是基于趋势拟合算法的路径规划C语言代码的示例，其中使用了标准C库和math.h库：

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

#define MAX_POINTS 1000

// 定义趋势拟合函数
void fit_trend(double *x, double *y, int n, int degree, double *coeffs) {
    double X[MAX_POINTS][MAX_POINTS];
    double Y[MAX_POINTS];
    for (int i = 0; i < n; i++) {
        double x_i = x[i];
        double y_i = y[i];
        for (int j = 0; j <= degree; j++) {
            X[i][j] = pow(x_i, j);
        }
        Y[i] = y_i;
    }
    for (int j = 0; j <= degree; j++) {
        double sum_xjy = 0;
        for (int i = 0; i < n; i++) {
            sum_xjy += X[i][j] * Y[i];
        }
        coeffs[j] = sum_xjy;
        for (int k = 0; k <= degree; k++) {
            double sum_xjxk = 0;
            for (int i = 0; i < n; i++) {
                sum_xjxk += X[i][j] * X[i][k];
            }
            coeffs[j * (degree + 1) + k] = sum_xjxk;
        }
    }
    for (int p = 0; p <= degree; p++) {
        int maxrow = p;
        double maxval = coeffs[p * (degree + 1) + p];
        for (int i = p + 1; i <= degree; i++) {
            double val = coeffs[i * (degree + 1) + p];
            if (fabs(val) > fabs(maxval)) {
                maxrow = i;
                maxval = val;
            }
        }
        if (maxrow != p) {
            for (int j = 0; j <= degree; j++) {
                double tmp = coeffs[p * (degree + 1) + j];
                coeffs[p * (degree + 1) + j] = coeffs[maxrow * (degree + 1) + j];
                coeffs[maxrow * (degree + 1) + j] = tmp;
            }
            for (int j = 0; j <= degree; j++) {
                double tmp = coeffs[j * (degree + 1) + p];
                coeffs[j * (degree + 1) + p] = coeffs[j * (degree + 1) + maxrow];
                coeffs[j * (degree + 1) + maxrow] = tmp;
            }
            double tmp = Y[p];
            Y[p] = Y[maxrow];
            Y[maxrow] = tmp;
        }
        for (int i = p + 1; i <= degree; i++) {
            double factor = coeffs[i * (degree + 1) + p] / coeffs[p * (degree + 1) + p];
            Y[i] -= factor * Y[p];
            for (int j = p; j <= degree; j++) {
                coeffs[i * (degree + 1) + j] -= factor * coeffs[p * (degree + 1) + j];
            }
        }
    }
    for (int p = degree; p >= 0; p--) {
        coeffs[p] = Y[p];
        for (int i = degree; i > p; i--) {
            coeffs[p] -= coeffs[i] * coeffs[i * (degree + 1) + p];
        }
        coeffs[p] /= coeffs[p * (degree + 1) + p];
    }
}

// 定义路径规划函数
void plan_path(double *x, double *y, int n, int degree, double step_size, double *path_x, double *path_y) {
    // 进行趋势拟合，得到趋势函数
    double coeffs[(degree+1)*(degree+1)];
    fit_trend(x, y, n, degree, coeffs);
    
    // 计算路径长度
    double path_length = 0;
    for (int i = 1; i < n; i++) {
        double dx = x[i] - x[i-1];
        double dy = 0;
        for (int j = 0; j <= degree; j++) {
            dy += coeffs[j] * pow(x[i], j);
        }
        dy -= coeffs[0];
        path_length += sqrt(dx*dx + dy*dy);
    }
    
    // 计算路径点数
    int num_points = (int)(path_length / step_size);
    
    // 生成路径点
    path_x[0] = x[0];
    path_y[0] = coeffs[0];
    double dist = 0;
    for (int i = 1; i < num_points; i++) {
        double dx = x[n-1] - path_x[i-1];
        double dy = 0;
        dist += step_size;
        double target_dist = dist / (path_length / (n-1));
        int idx = 0;
        double cumdist = 0;
        for (int j = 1; j < n; j++) {
            double dx = x[j] - x[j-1];
            double dy = 0;
            for (int k = 0; k <= degree; k++) {
                dy += coeffs[k] * pow(x[j], k);
            }
            dy -= coeffs[0];
            cumdist += sqrt(dx*dx + dy*dy);
            if (cumdist >= target_dist) {
                idx = j - 1;
                break;
            }
        }
        path_x[i] = x[idx+1];
        path_y[i] = coeffs[0];
        for (int k = 1; k <= degree; k++) {
            path_y[i] += coeffs[k] * pow(path_x[i], k);
        }
    }
}

// 测试代码
int main() {
    double x[MAX_POINTS];
    double y[MAX_POINTS];
    double path_x[MAX_POINTS];
    double path_y[MAX_POINTS];
    int n = 100;
    int degree = 1;
    double step_size = 0.1;
    for (int i = 0; i < n; i++) {
        x[i] = i / 10.0;
        y[i] = sin(x[i]) + 0.1 * rand() / RAND_MAX - 0.05;
    }
    plan_path(x, y, n, degree, step_size, path_x, path_y);
    FILE *fp = fopen("path.txt", "w");
    for (int i = 0; i < n; i++) {
        fprintf(fp, "%f %f %f %f\n", x[i], y[i], path_x[i], path_y[i]);
    }
    fclose(fp);
    return 0;
}

这段代码中，首先定义了一个`fit_trend`函数来进行趋势拟合，返回一个多项式系数数组。然后，定义了一个`plan_path`函数来进行路径规划。该函数首先利用`fit_trend`函数得到趋势函数的系数，然后根据步长计算路径点数，最后生成路径点。在生成路径点时，利用循环来计算路径长度和每个路径点的位置。最后，测试代码生成一个带有随机噪声的正弦曲线，然后利用`plan_path`函数对其进行路径规划，并将原始数据和路径点写入文件中。