梯形速度规划算法原理及代码_梯形加减速算法 c语言

梯形速度规划的原理：梯形速度规划算法
对应的代码如下：

#pragma once
#include <cmath>
#include <iostream>
#include <vector>
struct SpeedPoint {
  SpeedPoint() {
    s = 0;
    speed = 0;
    t = 0;
  }
  double s;      // m
  double speed;  // m/s
  double t;      // s
};
inline std::tuple<double, double, double> trapezoidalSpeedPlanningGetS(
    const double& max_speed, const double& init_speed,
    const double& aim_distance, const double& aim_speed,
    const double& aim_acc) {
  // 分类讨论，初始车速&最高速度的大小
  double valid_aim_speed = aim_speed;
  if (aim_speed > max_speed) {
    valid_aim_speed = max_speed;
  }
  double s1 =
      (std::pow(max_speed, 2) - std::pow(init_speed, 2)) / (2 * aim_acc);
  double s3 =
      (std::pow(max_speed, 2) - std::pow(valid_aim_speed, 2)) / (2 * aim_acc);
  double s2 = aim_distance - fabs(s1) - s3;

  if (s2 < 0) {
    s2 = 0;
    s1 = (2 * aim_acc * aim_distance - std::pow(init_speed, 2) +
          std::pow(valid_aim_speed, 2)) /
         (4 * aim_acc);
    if (fabs(s1) > aim_distance) {
      s1 = std::copysign(aim_distance, s1);
      s2 = s3 = 0;
    } else
      s3 = aim_distance - fabs(s1);
  }
  return std::tuple<double, double, double>(s1, s2, s3);
}

inline SpeedPoint trapezoidalSpeedPlanningPointByS(
    const double& s1, const double& s2, const double& s3, const double& s,
    const double& init_speed, const double& aim_acc) {
  SpeedPoint speed_point;
  double speed_m = std::sqrt(2 * aim_acc * s1 + init_speed * init_speed);
  speed_point.s = s;
  double s1_sign = std::copysign(1, s1);
  if (s <= fabs(s1)) {
    double vt = sqrt(2 * aim_acc * s1_sign * s + init_speed * init_speed);
    speed_point.speed = vt;
    speed_point.t = (vt - init_speed) / (aim_acc * s1_sign);
  } else if (s < fabs(s1) + s2) {
    double v1_t = speed_m;
    speed_point.speed = v1_t;
    // s1_t + (s - fabs(s1)) / v1_t;
    speed_point.t =
        (v1_t - init_speed) / (aim_acc * s1_sign) + (s - fabs(s1)) / v1_t;
  } else {
    // 减速段
    double v1_t = speed_m;
    double t1 = fabs(speed_m - init_speed) / aim_acc;
    double t2 = s2 / v1_t;
    double end_speed_2 = v1_t * v1_t - 2 * aim_acc * (s - s2 - fabs(s1));
    if (end_speed_2 < 1e-2)
      speed_point.speed = 0;
    else
      speed_point.speed = sqrt(end_speed_2);
    speed_point.t = t1 + t2 + (v1_t - speed_point.speed) / aim_acc;
  }
  return speed_point;
}

/**
 * @brief trapezoidalSpeedPlanning: 梯形速度规划
 * @param max_speed
 * @param init_speed
 * @param aim_distance
 * @param aim_speed
 * @param aim_acc
 * s1: 加速段
 * s2: 匀速段
 * s3: 减速段
 * @return
 */
inline std::vector<SpeedPoint> trapezoidalSpeedPlanning(
    const double& max_speed, const double& init_speed,
    const double& aim_distance, const double& aim_speed,
    const double& aim_acc) {
  std::vector<SpeedPoint> results;
  if (max_speed <= 0) {
    // to zero.
    return results;
  }
  double s1, s2, sk, s3;
  std::tuple<double, double, double> result_ss = trapezoidalSpeedPlanningGetS(
      max_speed, init_speed, aim_distance, aim_speed, aim_acc);
  s1 = std::get<0>(result_ss);
  s2 = std::get<1>(result_ss);
  s3 = std::get<2>(result_ss);
  sk = fabs(s1) + s2;
  const double delta_t = 0.1;
  double acculate_s = 0;
  double acculate_v = init_speed;
  double acculate_t = 0;
  SpeedPoint speed_point;
  double s1_sign = std::copysign(1, s1);
  double speed_m = std::sqrt(2 * aim_acc * s1 + init_speed * init_speed);
  double speed_final =
      std::sqrt(std::max(speed_m * speed_m - 2 * aim_acc * s3, 0.0));
  double time_1 = fabs(speed_m - init_speed) / aim_acc, time_2 = s2 / speed_m,
         time_3 = (speed_m - speed_final) / aim_acc;
  for (; acculate_s < aim_distance;) {
    speed_point.s = acculate_s;
    speed_point.t = acculate_t;
    speed_point.speed = acculate_v;
    acculate_t += delta_t;
    results.push_back(speed_point);
    if (acculate_t < time_1) {
      acculate_s =
          init_speed * acculate_t + 0.5 * aim_acc * acculate_t * acculate_t;
      acculate_v = init_speed + aim_acc * acculate_t * s1_sign;
    } else if (acculate_t < time_1 + time_2) {
      double noacc_t = acculate_t - time_1;
      acculate_s = s1 + speed_m * noacc_t;
      acculate_v = speed_m;
    } else {
      // 减速段
      double deacc_t = acculate_t - time_1 - time_2;
      acculate_s =
          s1 + s2 + speed_m * deacc_t - 0.5 * aim_acc * deacc_t * deacc_t;
      acculate_v = speed_m - aim_acc * deacc_t;
      if (acculate_v <= 0 || deacc_t >= time_3) break;
    }
  }
  // 增加最后1个点
  {
    speed_point = trapezoidalSpeedPlanningPointByS(s1, s2, s3, aim_distance,
                                                   init_speed, aim_acc);
    results.push_back(speed_point);
  }

  return results;
}  // namespace planning

inline double trapezoidalSpeedPlanningTime(const double& max_speed,
                                           const double& init_speed,
                                           const double& aim_distance,
                                           const double& aim_speed,
                                           const double& aim_acc) {
  if (max_speed <= 0) {
    // to zero.
    return INFINITY;
  }
  double s1, s2, s3;
  std::tuple<double, double, double> result_ss = trapezoidalSpeedPlanningGetS(
      max_speed, init_speed, aim_distance, aim_speed, aim_acc);
  double valid_aim_speed = aim_speed;
  if (aim_speed > max_speed) {
    valid_aim_speed = max_speed;
  }
  s1 = std::get<0>(result_ss);
  s2 = std::get<1>(result_ss);
  s3 = std::get<2>(result_ss);

  //  std::cout << "s1: " << s1 << ", s2: " << s2 << ", s3: " << s3 <<
  //  std::endl;
  double speed_m = std::sqrt(2 * aim_acc * s1 + init_speed * init_speed);
  double speed_final =
      std::sqrt(std::max(speed_m * speed_m - 2 * aim_acc * s3, 0.0));
  if (fabs(speed_final - valid_aim_speed) > 1) return INFINITY;
  double time_1 = fabs(speed_m - init_speed) / aim_acc, time_2 = s2 / speed_m,
         time_3 = (speed_m - speed_final) / aim_acc;
  return time_1 + time_2 + time_3;
}

inline double GetSpeedPlanningTimeByReultS(
    const std::tuple<double, double, double>& result_ss,
    const double& max_speed, const double& init_speed,
    const double& aim_distance, const double& aim_speed,
    const double& aim_acc) {
  if (max_speed <= 0) {
    // to zero.
    return INFINITY;
  }
  double s1, s2, s3;
  double valid_aim_speed = aim_speed;
  if (aim_speed > max_speed) {
    valid_aim_speed = max_speed;
  }
  s1 = std::get<0>(result_ss);
  s2 = std::get<1>(result_ss);
  s3 = std::get<2>(result_ss);

  //  std::cout << "s1: " << s1 << ", s2: " << s2 << ", s3: " << s3 <<
  //  std::endl;
  double speed_m = std::sqrt(2 * aim_acc * s1 + init_speed * init_speed);
  double speed_final =
      std::sqrt(std::max(speed_m * speed_m - 2 * aim_acc * s3, 0.0));
  if (fabs(speed_final - valid_aim_speed) > 1) return INFINITY;
  double time_1 = fabs(speed_m - init_speed) / aim_acc, time_2 = s2 / speed_m,
         time_3 = (speed_m - speed_final) / aim_acc;
  return time_1 + time_2 + time_3;
}
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