TrajMath.hpp
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/****************************************************************************
*
* Copyright (c) 2019 PX4 Development Team. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
*
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
* 3. Neither the name PX4 nor the names of its contributors may be
* used to endorse or promote products derived from this software
* without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS
* OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED
* AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
* POSSIBILITY OF SUCH DAMAGE.
*
****************************************************************************/
/**
* @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));
// don't slow down more than the end speed, even if the conservative accel ramp time requests it
return max(max_speed, final_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;
}
/* Compute the braking distance given a maximum acceleration, maximum jerk and a maximum delay acceleration.
* We assume a constant acceleration profile with a delay of accel_delay_max/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 velocity initial velocity
* @param jerk maximum jerk
* @param accel maximum target acceleration during the braking maneuver
* @param accel_delay_max the acceleration defining the delay described above
*
* @return braking distance
*/
inline float computeBrakingDistanceFromVelocity(const float velocity, const float jerk, const float accel,
const float accel_delay_max)
{
return velocity * (velocity / (2.0f * accel) + accel_delay_max / jerk);
}
} /* namespace traj */
} /* namespace math */