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allwpilib/wpimath/src/main/native/include/frc/trajectory/ExponentialProfile.inc
2023-10-19 17:26:32 -07:00

254 lines
8.4 KiB
C++

// Copyright (c) FIRST and other WPILib contributors.
// Open Source Software; you can modify and/or share it under the terms of
// the WPILib BSD license file in the root directory of this project.
#pragma once
#include <algorithm>
#include <fmt/core.h>
#include "frc/trajectory/ExponentialProfile.h"
#include "units/math.h"
namespace frc {
template <class Distance, class Input>
ExponentialProfile<Distance, Input>::ExponentialProfile(Constraints constraints)
: m_constraints(constraints) {}
template <class Distance, class Input>
typename ExponentialProfile<Distance, Input>::State
ExponentialProfile<Distance, Input>::Calculate(const units::second_t& t,
const State& current,
const State& goal) const {
auto direction = ShouldFlipInput(current, goal) ? -1 : 1;
auto u = direction * m_constraints.maxInput;
auto inflectionPoint = CalculateInflectionPoint(current, goal, u);
auto timing = CalculateProfileTiming(current, inflectionPoint, goal, u);
if (t < 0_s) {
return current;
} else if (t < timing.inflectionTime) {
return {ComputeDistanceFromTime(t, u, current),
ComputeVelocityFromTime(t, u, current)};
} else if (t < timing.totalTime) {
return {ComputeDistanceFromTime(t - timing.totalTime, -u, goal),
ComputeVelocityFromTime(t - timing.totalTime, -u, goal)};
} else {
return goal;
}
}
template <class Distance, class Input>
typename ExponentialProfile<Distance, Input>::State
ExponentialProfile<Distance, Input>::CalculateInflectionPoint(
const State& current, const State& goal) const {
auto direction = ShouldFlipInput(current, goal) ? -1 : 1;
auto u = direction * m_constraints.maxInput;
return CalculateInflectionPoint(current, goal, u);
}
template <class Distance, class Input>
typename ExponentialProfile<Distance, Input>::State
ExponentialProfile<Distance, Input>::CalculateInflectionPoint(
const State& current, const State& goal, const Input_t& input) const {
auto u = input;
if (current == goal) {
return current;
}
auto inflectionVelocity = SolveForInflectionVelocity(u, current, goal);
auto inflectionPosition =
ComputeDistanceFromVelocity(inflectionVelocity, -u, goal);
return {inflectionPosition, inflectionVelocity};
}
template <class Distance, class Input>
units::second_t ExponentialProfile<Distance, Input>::TimeLeftUntil(
const State& current, const State& goal) const {
auto timing = CalculateProfileTiming(current, goal);
return timing.totalTime;
}
template <class Distance, class Input>
typename ExponentialProfile<Distance, Input>::ProfileTiming
ExponentialProfile<Distance, Input>::CalculateProfileTiming(
const State& current, const State& goal) const {
auto direction = ShouldFlipInput(current, goal) ? -1 : 1;
auto u = direction * m_constraints.maxInput;
auto inflectionPoint = CalculateInflectionPoint(current, goal, u);
return CalculateProfileTiming(current, inflectionPoint, goal, u);
}
template <class Distance, class Input>
typename ExponentialProfile<Distance, Input>::ProfileTiming
ExponentialProfile<Distance, Input>::CalculateProfileTiming(
const State& current, const State& inflectionPoint, const State& goal,
const Input_t& input) const {
auto u = input;
auto u_dir = units::math::abs(u) / u;
units::second_t inflectionT_forward;
// We need to handle 5 cases here:
//
// - Approaching -maxVelocity from below
// - Approaching -maxVelocity from above
// - Approaching maxVelocity from below
// - Approaching maxVelocity from above
// - At +-maxVelocity
//
// For cases 1 and 3, we want to subtract epsilon from the inflection point
// velocity For cases 2 and 4, we want to add epsilon to the inflection point
// velocity. For case 5, we have reached inflection point velocity.
auto epsilon = Velocity_t(1e-9);
if (units::math::abs(u_dir * m_constraints.MaxVelocity() -
inflectionPoint.velocity) < epsilon) {
auto solvableV = inflectionPoint.velocity;
units::second_t t_to_solvable_v;
Distance_t x_at_solvable_v;
if (units::math::abs(current.velocity - inflectionPoint.velocity) <
epsilon) {
t_to_solvable_v = 0_s;
x_at_solvable_v = current.position;
} else {
if (units::math::abs(current.velocity) > m_constraints.MaxVelocity()) {
solvableV += u_dir * epsilon;
} else {
solvableV -= u_dir * epsilon;
}
t_to_solvable_v = ComputeTimeFromVelocity(solvableV, u, current.velocity);
x_at_solvable_v = ComputeDistanceFromVelocity(solvableV, u, current);
}
inflectionT_forward =
t_to_solvable_v + u_dir * (inflectionPoint.position - x_at_solvable_v) /
m_constraints.MaxVelocity();
} else {
inflectionT_forward =
ComputeTimeFromVelocity(inflectionPoint.velocity, u, current.velocity);
}
auto inflectionT_backward =
ComputeTimeFromVelocity(inflectionPoint.velocity, -u, goal.velocity);
return {inflectionT_forward, inflectionT_forward - inflectionT_backward};
}
template <class Distance, class Input>
typename ExponentialProfile<Distance, Input>::Distance_t
ExponentialProfile<Distance, Input>::ComputeDistanceFromTime(
const units::second_t& time, const Input_t& input,
const State& initial) const {
auto A = m_constraints.A;
auto B = m_constraints.B;
auto u = input;
return initial.position +
(-B * u * time +
(initial.velocity + B * u / A) * (units::math::exp(A * time) - 1)) /
A;
}
template <class Distance, class Input>
typename ExponentialProfile<Distance, Input>::Velocity_t
ExponentialProfile<Distance, Input>::ComputeVelocityFromTime(
const units::second_t& time, const Input_t& input,
const State& initial) const {
auto A = m_constraints.A;
auto B = m_constraints.B;
auto u = input;
return (initial.velocity + B * u / A) * units::math::exp(A * time) -
B * u / A;
}
template <class Distance, class Input>
units::second_t ExponentialProfile<Distance, Input>::ComputeTimeFromVelocity(
const Velocity_t& velocity, const Input_t& input,
const Velocity_t& initial) const {
auto A = m_constraints.A;
auto B = m_constraints.B;
auto u = input;
return units::math::log((A * velocity + B * u) / (A * initial + B * u)) / A;
}
template <class Distance, class Input>
typename ExponentialProfile<Distance, Input>::Distance_t
ExponentialProfile<Distance, Input>::ComputeDistanceFromVelocity(
const Velocity_t& velocity, const Input_t& input,
const State& initial) const {
auto A = m_constraints.A;
auto B = m_constraints.B;
auto u = input;
return initial.position + (velocity - initial.velocity) / A -
B * u / (A * A) *
units::math::log((A * velocity + B * u) /
(A * initial.velocity + B * u));
}
template <class Distance, class Input>
typename ExponentialProfile<Distance, Input>::Velocity_t
ExponentialProfile<Distance, Input>::SolveForInflectionVelocity(
const Input_t& input, const State& current, const State& goal) const {
auto A = m_constraints.A;
auto B = m_constraints.B;
auto u = input;
auto u_dir = u / units::math::abs(u);
auto position_delta = goal.position - current.position;
auto velocity_delta = goal.velocity - current.velocity;
auto scalar = (A * current.velocity + B * u) * (A * goal.velocity - B * u);
auto power = -A / B / u * (A * position_delta - velocity_delta);
auto a = -A * A;
auto c = B * B * u * u + scalar * units::math::exp(power);
if (-1e-9 < c.value() && c.value() < 0) {
// numeric instability - the heuristic gets it right but c is around -1e-13
return Velocity_t(0);
}
return u_dir * units::math::sqrt(-c / a);
}
template <class Distance, class Input>
bool ExponentialProfile<Distance, Input>::ShouldFlipInput(
const State& current, const State& goal) const {
auto u = m_constraints.maxInput;
auto v0 = current.velocity;
auto xf = goal.position;
auto vf = goal.velocity;
auto x_forward = ComputeDistanceFromVelocity(vf, u, current);
auto x_reverse = ComputeDistanceFromVelocity(vf, -u, current);
if (v0 >= m_constraints.MaxVelocity()) {
return xf < x_reverse;
}
if (v0 <= -m_constraints.MaxVelocity()) {
return xf < x_forward;
}
auto a = v0 >= Velocity_t(0);
auto b = vf >= Velocity_t(0);
auto c = xf >= x_forward;
auto d = xf >= x_reverse;
return (a && !d) || (b && !c) || (!c && !d);
}
} // namespace frc