update abstract_interpolation
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#ifndef INTERPOLATION_BASE_H
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#define INTERPOLATION_BASE_H
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#include "utils/math/geometry.h"
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#include <vector>
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#include <stdexcept>
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// 插值基类
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class AbstractInterpolation {
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protected:
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std::vector<double> x_points; // 已知点的x坐标
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std::vector<double> y_points; // 已知点的y坐标
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namespace cmvr::math {
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// 查找x所在的区间索引（二分查找）
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int findInterval(double x) const;
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/**
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* 插值基类，用于机械臂位姿插值
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* 支持三维位姿(Pose3d)和二维位姿(Pose2d)的插值
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*/
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class AbstractInterpolation {
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public:
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// 构造函数
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AbstractInterpolation(const std::vector<Pose3d>& waypoints);
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AbstractInterpolation(const std::vector<Pose2d>& waypoints);
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public:
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// 构造函数
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AbstractInterpolation(const std::vector<double>& x, const std::vector<double>& y);
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// 析构函数
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virtual ~AbstractInterpolation() = default;
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// 析构函数
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virtual ~AbstractInterpolation() = default;
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// 纯虚函数：单个点插值
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virtual double interpolate(double x) const = 0;
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/**
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* 插值计算接口
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* @param t 插值参数，范围[0, 1]，0表示起点，1表示终点
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* @return 插值得到的位姿
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*/
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virtual Pose3d interpolate_3d(double t) const = 0;
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virtual Pose2d interpolate_2d(double t) const = 0;
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// 批量插值（默认实现）
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virtual std::vector<double> interpolate(const std::vector<double>& x_values) const;
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};
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/**
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* 生成轨迹点序列
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* @param num_points 生成的轨迹点数量，包括起点和终点
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* @return 轨迹点序列
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*/
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std::vector<Pose3d> generate_trajectory_3d(size_t num_points) const;
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std::vector<Pose2d> generate_trajectory_2d(size_t num_points) const;
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protected:
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// 路径点存储
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std::vector<Pose3d> waypoints_3d_;
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std::vector<Pose2d> waypoints_2d_;
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/**
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* 辅助函数：线性插值单个数值
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* @param a 起始值
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* @param b 目标值
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* @param t 插值参数[0,1]
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* @return 插值结果
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*/
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static double linear_interpolate(double a, double b, double t);
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/**
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* 辅助函数：四元数球面线性插值(slerp)
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* @param q1 起始四元数
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* @param q2 目标四元数
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* @param t 插值参数[0,1]
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* @return 插值结果
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*/
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static Quat slerp(const Quat& q1, const Quat& q2, double t);
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/**
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* 检查t的范围并进行约束
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* @param t 原始参数
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* @return 约束在[0,1]范围内的参数
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*/
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static double clamp_t(double t);
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};
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} // namespace cmvr::math
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#endif // INTERPOLATION_BASE_H
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@ -1,73 +1,107 @@
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#include "utils/base/abstract_interpolation.h"
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#include <algorithm>
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#include <stdexcept>
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#include <cmath>
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namespace cmvr::math {
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// 构造函数实现
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AbstractInterpolation::AbstractInterpolation(const std::vector<double>& x, const std::vector<double>& y) {
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// 验证输入
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if (x.size() != y.size()) {
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throw std::invalid_argument("x和y的长度必须相同");
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}
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if (x.size() < 2) {
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throw std::invalid_argument("至少需要2个已知点才能进行插值");
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}
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// 复制并排序数据点
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std::vector<std::pair<double, double>> points;
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points.reserve(x.size());
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for (size_t i = 0; i < x.size(); ++i) {
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points.emplace_back(x[i], y[i]);
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}
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// 按x坐标排序
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std::sort(points.begin(), points.end());
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// 分离排序后的x和y
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x_points.reserve(points.size());
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y_points.reserve(points.size());
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for (const auto& p : points) {
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x_points.push_back(p.first);
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y_points.push_back(p.second);
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AbstractInterpolation::AbstractInterpolation(const std::vector<Pose3d>& waypoints)
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: waypoints_3d_(waypoints) {
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if (waypoints.size() < 2) {
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throw std::invalid_argument("至少需要2个路径点才能进行插值");
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}
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}
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// 查找区间索引实现
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int AbstractInterpolation::findInterval(double x) const {
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// 处理边界情况
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if (x <= x_points[0]) {
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return 0;
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AbstractInterpolation::AbstractInterpolation(const std::vector<Pose2d>& waypoints)
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: waypoints_2d_(waypoints) {
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if (waypoints.size() < 2) {
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throw std::invalid_argument("至少需要2个路径点才能进行插值");
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}
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if (x >= x_points.back()) {
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return static_cast<int>(x_points.size()) - 2;
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}
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// 二分查找
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int left = 0;
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int right = static_cast<int>(x_points.size()) - 1;
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while (right - left > 1) {
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int mid = (left + right) / 2;
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if (x < x_points[mid]) {
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right = mid;
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} else {
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left = mid;
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}
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}
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return left;
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}
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// 批量插值实现
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std::vector<double> AbstractInterpolation::interpolate(const std::vector<double>& x_values) const {
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std::vector<double> results;
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results.reserve(x_values.size());
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for (double x : x_values) {
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results.push_back(interpolate(x));
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// 生成3D轨迹
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std::vector<Pose3d> AbstractInterpolation::generate_trajectory_3d(size_t num_points) const {
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if (num_points < 2) {
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throw std::invalid_argument("轨迹点数量至少为2");
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}
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return results;
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std::vector<Pose3d> trajectory;
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trajectory.reserve(num_points);
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for (size_t i = 0; i < num_points; ++i) {
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double t = static_cast<double>(i) / (num_points - 1);
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trajectory.push_back(interpolate_3d(t));
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}
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return trajectory;
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}
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// 生成2D轨迹
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std::vector<Pose2d> AbstractInterpolation::generate_trajectory_2d(size_t num_points) const {
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if (num_points < 2) {
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throw std::invalid_argument("轨迹点数量至少为2");
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}
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std::vector<Pose2d> trajectory;
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trajectory.reserve(num_points);
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for (size_t i = 0; i < num_points; ++i) {
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double t = static_cast<double>(i) / (num_points - 1);
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trajectory.push_back(interpolate_2d(t));
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}
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return trajectory;
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}
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// 线性插值辅助函数
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double AbstractInterpolation::linear_interpolate(double a, double b, double t) {
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t = clamp_t(t);
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return a + t * (b - a);
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}
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// 四元数球面线性插值
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Quat AbstractInterpolation::slerp(const Quat& q1, const Quat& q2, double t) {
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t = clamp_t(t);
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Quat result;
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double dot = q1.w * q2.w + q1.x * q2.x + q1.y * q2.y + q1.z * q2.z;
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// 确保我们选择最短路径
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if (dot < 0.0) {
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Quat q2_neg = {-q2.w, -q2.x, -q2.y, -q2.z};
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return slerp(q1, q2_neg, t);
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}
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// 防止数值问题，接近时使用线性插值
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if (dot > 0.9995) {
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result.w = linear_interpolate(q1.w, q2.w, t);
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result.x = linear_interpolate(q1.x, q2.x, t);
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result.y = linear_interpolate(q1.y, q2.y, t);
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result.z = linear_interpolate(q1.z, q2.z, t);
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return result;
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}
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// 计算角度和插值系数
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double theta_0 = std::acos(dot);
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double theta = theta_0 * t;
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double sin_theta = std::sin(theta);
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double sin_theta_0 = std::sin(theta_0);
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double s1 = std::cos(theta) - dot * sin_theta / sin_theta_0;
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double s2 = sin_theta / sin_theta_0;
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result.w = s1 * q1.w + s2 * q2.w;
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result.x = s1 * q1.x + s2 * q2.x;
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result.y = s1 * q1.y + s2 * q2.y;
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result.z = s1 * q1.z + s2 * q2.z;
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return result;
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}
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// 参数范围约束
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double AbstractInterpolation::clamp_t(double t) {
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return std::max(0.0, std::min(1.0, t));
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}
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} // namespace cmvr::math
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