TrajMath.hpp

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/**
 * @file TrajMath.hpp
 *
 * collection of functions used for trajectory generation
 */

#pragma once

namespace math
{

namespace trajectory
{

/* Compute the maximum possible speed on the track given the desired speed,
 * remaining distance, the maximum acceleration and the maximum jerk.
 * We assume a constant acceleration profile with a delay of 2*accel/jerk
 * (time to reach the desired acceleration from opposite max acceleration)
 * Equation to solve: vel_final^2 = vel_initial^2 - 2*accel*(x - vel_initial*2*accel/jerk)
 *
 * @param jerk maximum jerk
 * @param accel maximum acceleration
 * @param braking_distance distance to the desired point
 * @param final_speed the still-remaining speed of the vehicle when it reaches the braking_distance
 *
 * @return maximum speed
 */
inline float computeMaxSpeedFromDistance(const float jerk, const float accel, const float braking_distance,
        const float final_speed)
{
    auto sqr = [](float f) {return f * f;};
    float b =  4.0f * sqr(accel) / jerk;
    float c = - 2.0f * accel * braking_distance - sqr(final_speed);
    float max_speed = 0.5f * (-b + sqrtf(sqr(b) - 4.0f * c));

    return max_speed;
}

/* Compute the maximum tangential speed in a circle defined by two line segments of length "d"
 * forming a V shape, opened by an angle "alpha". The circle is tangent to the end of the
 * two segments as shown below:
 *      \\
 *      | \ d
 *      /  \
 *  __='___a\
 *      d
 *  @param alpha angle between the two line segments
 *  @param accel maximum lateral acceleration
 *  @param d length of the two line segments
 *
 *  @return maximum tangential speed
 */
inline float computeMaxSpeedInWaypoint(const float alpha, const float accel, const float d)
{
    float tan_alpha = tanf(alpha / 2.0f);
    float max_speed_in_turn = sqrtf(accel * d * tan_alpha);

    return max_speed_in_turn;
}
} /* namespace traj */
} /* namespace math */