mirror of
https://github.com/wpilibsuite/allwpilib
synced 2026-06-21 01:01:43 +00:00
[wpimath] Add Exponential motion profile (#5720)
This commit is contained in:
Jordan McMichael
@@ -0,0 +1,449 @@
|
||||
// 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.
|
||||
|
||||
package edu.wpi.first.math.trajectory;
|
||||
|
||||
import java.util.Objects;
|
||||
|
||||
/**
|
||||
* A exponential curve-shaped velocity profile.
|
||||
*
|
||||
* <p>While this class can be used for a profiled movement from start to finish, the intended usage
|
||||
* is to filter a reference's dynamics based on state-space model dynamics. To compute the reference
|
||||
* obeying this constraint, do the following.
|
||||
*
|
||||
* <p>Initialization:
|
||||
*
|
||||
* <pre><code>
|
||||
* ExponentialProfile.Constraints constraints =
|
||||
* ExponentialProfile.Constraints.fromCharacteristics(kMaxV, kV, kA);
|
||||
* ExponentialProfile.State previousProfiledReference =
|
||||
* new ExponentialProfile.State(initialReference, 0.0);
|
||||
* ExponentialProfile profile = new ExponentialProfile(constraints);
|
||||
* </code></pre>
|
||||
*
|
||||
* <p>Run on update:
|
||||
*
|
||||
* <pre><code>
|
||||
* previousProfiledReference =
|
||||
* profile.calculate(timeSincePreviousUpdate, previousProfiledReference, unprofiledReference);
|
||||
* </code></pre>
|
||||
*
|
||||
* <p>where `unprofiledReference` is free to change between calls. Note that when the unprofiled
|
||||
* reference is within the constraints, `calculate()` returns the unprofiled reference unchanged.
|
||||
*
|
||||
* <p>Otherwise, a timer can be started to provide monotonic values for `calculate()` and to
|
||||
* determine when the profile has completed via `isFinished()`.
|
||||
*/
|
||||
public class ExponentialProfile {
|
||||
private final Constraints m_constraints;
|
||||
|
||||
public static class ProfileTiming {
|
||||
public final double inflectionTime;
|
||||
public final double totalTime;
|
||||
|
||||
protected ProfileTiming(double inflectionTime, double totalTime) {
|
||||
this.inflectionTime = inflectionTime;
|
||||
this.totalTime = totalTime;
|
||||
}
|
||||
|
||||
/**
|
||||
* Decides if the profile is finished by time t.
|
||||
*
|
||||
* @param t The time since the beginning of the profile.
|
||||
* @return if the profile is finished at time t.
|
||||
*/
|
||||
public boolean isFinished(double t) {
|
||||
return t > inflectionTime;
|
||||
}
|
||||
}
|
||||
|
||||
public static class Constraints {
|
||||
public final double maxInput;
|
||||
|
||||
public final double A;
|
||||
public final double B;
|
||||
|
||||
/**
|
||||
* Construct constraints for an ExponentialProfile.
|
||||
*
|
||||
* @param maxInput maximum unsigned input voltage
|
||||
* @param A The State-Space 1x1 system matrix.
|
||||
* @param B The State-Space 1x1 input matrix.
|
||||
*/
|
||||
private Constraints(double maxInput, double A, double B) {
|
||||
this.maxInput = maxInput;
|
||||
this.A = A;
|
||||
this.B = B;
|
||||
}
|
||||
|
||||
/**
|
||||
* Computes the max achievable velocity for an Exponential Profile.
|
||||
*
|
||||
* @return The seady-state velocity achieved by this profile.
|
||||
*/
|
||||
public double maxVelocity() {
|
||||
return -maxInput * B / A;
|
||||
}
|
||||
|
||||
/**
|
||||
* Construct constraints for an ExponentialProfile from characteristics.
|
||||
*
|
||||
* @param maxInput maximum unsigned input voltage
|
||||
* @param kV The velocity gain.
|
||||
* @param kA The acceleration gain.
|
||||
* @return The Constraints object.
|
||||
*/
|
||||
public static Constraints fromCharacteristics(double maxInput, double kV, double kA) {
|
||||
return new Constraints(maxInput, -kV / kA, 1.0 / kA);
|
||||
}
|
||||
|
||||
/**
|
||||
* Construct constraints for an ExponentialProfile from State-Space parameters.
|
||||
*
|
||||
* @param maxInput maximum unsigned input voltage
|
||||
* @param A The State-Space 1x1 system matrix.
|
||||
* @param B The State-Space 1x1 input matrix.
|
||||
* @return The Constraints object.
|
||||
*/
|
||||
public static Constraints fromStateSpace(double maxInput, double A, double B) {
|
||||
return new Constraints(maxInput, A, B);
|
||||
}
|
||||
}
|
||||
|
||||
public static class State {
|
||||
public final double position;
|
||||
|
||||
public final double velocity;
|
||||
|
||||
/**
|
||||
* Construct a state within an exponential profile.
|
||||
*
|
||||
* @param position The position at this state.
|
||||
* @param velocity The velocity at this state.
|
||||
*/
|
||||
public State(double position, double velocity) {
|
||||
this.position = position;
|
||||
this.velocity = velocity;
|
||||
}
|
||||
|
||||
@Override
|
||||
public boolean equals(Object other) {
|
||||
if (other instanceof State) {
|
||||
State rhs = (State) other;
|
||||
return this.position == rhs.position && this.velocity == rhs.velocity;
|
||||
} else {
|
||||
return false;
|
||||
}
|
||||
}
|
||||
|
||||
@Override
|
||||
public int hashCode() {
|
||||
return Objects.hash(position, velocity);
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* Construct an ExponentialProfile.
|
||||
*
|
||||
* @param constraints The constraints on the profile, like maximum input.
|
||||
*/
|
||||
public ExponentialProfile(Constraints constraints) {
|
||||
m_constraints = constraints;
|
||||
}
|
||||
|
||||
/**
|
||||
* Calculate the correct position and velocity for the profile at a time t where the current state
|
||||
* is at time t = 0.
|
||||
*
|
||||
* @param t The time since the beginning of the profile.
|
||||
* @param current The current state.
|
||||
* @param goal The desired state when the profile is complete.
|
||||
* @return The position and velocity of the profile at time t.
|
||||
*/
|
||||
public State calculate(double t, State current, State goal) {
|
||||
var direction = shouldFlipInput(current, goal) ? -1 : 1;
|
||||
var u = direction * m_constraints.maxInput;
|
||||
|
||||
var inflectionPoint = calculateInflectionPoint(current, goal, u);
|
||||
var timing = calculateProfileTiming(current, inflectionPoint, goal, u);
|
||||
|
||||
if (t < 0) {
|
||||
return current;
|
||||
} else if (t < timing.inflectionTime) {
|
||||
return new State(
|
||||
computeDistanceFromTime(t, u, current), computeVelocityFromTime(t, u, current));
|
||||
} else if (t < timing.totalTime) {
|
||||
return new State(
|
||||
computeDistanceFromTime(t - timing.totalTime, -u, goal),
|
||||
computeVelocityFromTime(t - timing.totalTime, -u, goal));
|
||||
} else {
|
||||
return goal;
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* Calculate the point after which the fastest way to reach the goal state is to apply input in
|
||||
* the opposite direction.
|
||||
*
|
||||
* @param current The current state.
|
||||
* @param goal The desired state when the profile is complete.
|
||||
* @return The position and velocity of the profile at the inflection point.
|
||||
*/
|
||||
public State calculateInflectionPoint(State current, State goal) {
|
||||
var direction = shouldFlipInput(current, goal) ? -1 : 1;
|
||||
var u = direction * m_constraints.maxInput;
|
||||
|
||||
return calculateInflectionPoint(current, goal, u);
|
||||
}
|
||||
|
||||
/**
|
||||
* Calculate the point after which the fastest way to reach the goal state is to apply input in
|
||||
* the opposite direction.
|
||||
*
|
||||
* @param current The current state.
|
||||
* @param goal The desired state when the profile is complete.
|
||||
* @param input The signed input applied to this profile from the current state.
|
||||
* @return The position and velocity of the profile at the inflection point.
|
||||
*/
|
||||
private State calculateInflectionPoint(State current, State goal, double input) {
|
||||
var u = input;
|
||||
|
||||
if (current.equals(goal)) {
|
||||
return current;
|
||||
}
|
||||
|
||||
var inflectionVelocity = solveForInflectionVelocity(u, current, goal);
|
||||
var inflectionPosition = computeDistanceFromVelocity(inflectionVelocity, -u, goal);
|
||||
|
||||
return new State(inflectionPosition, inflectionVelocity);
|
||||
}
|
||||
|
||||
/**
|
||||
* Calculate the time it will take for this profile to reach the goal state.
|
||||
*
|
||||
* @param current The current state.
|
||||
* @param goal The desired state when the profile is complete.
|
||||
* @return The total duration of this profile.
|
||||
*/
|
||||
public double timeLeftUntil(State current, State goal) {
|
||||
var timing = calculateProfileTiming(current, goal);
|
||||
|
||||
return timing.totalTime;
|
||||
}
|
||||
|
||||
/**
|
||||
* Calculate the time it will take for this profile to reach the inflection point, and the time it
|
||||
* will take for this profile to reach the goal state.
|
||||
*
|
||||
* @param current The current state.
|
||||
* @param goal The desired state when the profile is complete.
|
||||
* @return The timing information for this profile.
|
||||
*/
|
||||
public ProfileTiming calculateProfileTiming(State current, State goal) {
|
||||
var direction = shouldFlipInput(current, goal) ? -1 : 1;
|
||||
var u = direction * m_constraints.maxInput;
|
||||
|
||||
var inflectionPoint = calculateInflectionPoint(current, goal, u);
|
||||
return calculateProfileTiming(current, inflectionPoint, goal, u);
|
||||
}
|
||||
|
||||
/**
|
||||
* Calculate the time it will take for this profile to reach the inflection point, and the time it
|
||||
* will take for this profile to reach the goal state.
|
||||
*
|
||||
* @param current The current state.
|
||||
* @param inflectionPoint The inflection point of this profile.
|
||||
* @param goal The desired state when the profile is complete.
|
||||
* @param input The signed input applied to this profile from the current state.
|
||||
* @return The timing information for this profile.
|
||||
*/
|
||||
private ProfileTiming calculateProfileTiming(
|
||||
State current, State inflectionPoint, State goal, double input) {
|
||||
var u = input;
|
||||
|
||||
double 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.
|
||||
double epsilon = 1e-9;
|
||||
if (Math.abs(Math.signum(input) * m_constraints.maxVelocity() - inflectionPoint.velocity)
|
||||
< epsilon) {
|
||||
double solvableV = inflectionPoint.velocity;
|
||||
double t_to_solvable_v;
|
||||
double x_at_solvable_v;
|
||||
if (Math.abs(current.velocity - inflectionPoint.velocity) < epsilon) {
|
||||
t_to_solvable_v = 0;
|
||||
x_at_solvable_v = current.position;
|
||||
} else {
|
||||
if (Math.abs(current.velocity) > m_constraints.maxVelocity()) {
|
||||
solvableV += Math.signum(u) * epsilon;
|
||||
} else {
|
||||
solvableV -= Math.signum(u) * epsilon;
|
||||
}
|
||||
|
||||
t_to_solvable_v = computeTimeFromVelocity(solvableV, u, current.velocity);
|
||||
x_at_solvable_v = computeDistanceFromVelocity(solvableV, u, current);
|
||||
}
|
||||
|
||||
inflectionT_forward =
|
||||
t_to_solvable_v
|
||||
+ Math.signum(input)
|
||||
* (inflectionPoint.position - x_at_solvable_v)
|
||||
/ m_constraints.maxVelocity();
|
||||
} else {
|
||||
inflectionT_forward = computeTimeFromVelocity(inflectionPoint.velocity, u, current.velocity);
|
||||
}
|
||||
|
||||
var inflectionT_backward = computeTimeFromVelocity(inflectionPoint.velocity, -u, goal.velocity);
|
||||
|
||||
return new ProfileTiming(inflectionT_forward, inflectionT_forward - inflectionT_backward);
|
||||
}
|
||||
|
||||
/**
|
||||
* Calculate the position reached after t seconds when applying an input from the initial state.
|
||||
*
|
||||
* @param t The time since the initial state.
|
||||
* @param input The signed input applied to this profile from the initial state.
|
||||
* @param initial The initial state.
|
||||
* @return The distance travelled by this profile.
|
||||
*/
|
||||
private double computeDistanceFromTime(double t, double input, State initial) {
|
||||
var A = m_constraints.A;
|
||||
var B = m_constraints.B;
|
||||
var u = input;
|
||||
|
||||
return initial.position
|
||||
+ (-B * u * t + (initial.velocity + B * u / A) * (Math.exp(A * t) - 1)) / A;
|
||||
}
|
||||
|
||||
/**
|
||||
* Calculate the velocity reached after t seconds when applying an input from the initial state.
|
||||
*
|
||||
* @param t The time since the initial state.
|
||||
* @param input The signed input applied to this profile from the initial state.
|
||||
* @param initial The initial state.
|
||||
* @return The distance travelled by this profile.
|
||||
*/
|
||||
private double computeVelocityFromTime(double t, double input, State initial) {
|
||||
var A = m_constraints.A;
|
||||
var B = m_constraints.B;
|
||||
var u = input;
|
||||
|
||||
return (initial.velocity + B * u / A) * Math.exp(A * t) - B * u / A;
|
||||
}
|
||||
|
||||
/**
|
||||
* Calculate the time required to reach a specified velocity given the initial velocity.
|
||||
*
|
||||
* @param velocity The goal velocity.
|
||||
* @param input The signed input applied to this profile from the initial state.
|
||||
* @param initial The initial velocity.
|
||||
* @return The time required to reach the goal velocity.
|
||||
*/
|
||||
private double computeTimeFromVelocity(double velocity, double input, double initial) {
|
||||
var A = m_constraints.A;
|
||||
var B = m_constraints.B;
|
||||
var u = input;
|
||||
|
||||
return Math.log((A * velocity + B * u) / (A * initial + B * u)) / A;
|
||||
}
|
||||
|
||||
/**
|
||||
* Calculate the distance reached at the same time as the given velocity when applying the given
|
||||
* input from the initial state.
|
||||
*
|
||||
* @param velocity The velocity reached by this profile
|
||||
* @param input The signed input applied to this profile from the initial state.
|
||||
* @param initial The initial state.
|
||||
* @return The distance reached when the given velocity is reached.
|
||||
*/
|
||||
private double computeDistanceFromVelocity(double velocity, double input, State initial) {
|
||||
var A = m_constraints.A;
|
||||
var B = m_constraints.B;
|
||||
var u = input;
|
||||
|
||||
return initial.position
|
||||
+ (velocity - initial.velocity) / A
|
||||
- B * u / (A * A) * Math.log((A * velocity + B * u) / (A * initial.velocity + B * u));
|
||||
}
|
||||
|
||||
/**
|
||||
* Calculate the velocity at which input should be reversed in order to reach the goal state from
|
||||
* the current state.
|
||||
*
|
||||
* @param input The signed input applied to this profile from the current state.
|
||||
* @param current The current state.
|
||||
* @param goal The goal state.
|
||||
* @return The inflection velocity.
|
||||
*/
|
||||
private double solveForInflectionVelocity(double input, State current, State goal) {
|
||||
var A = m_constraints.A;
|
||||
var B = m_constraints.B;
|
||||
var u = input;
|
||||
|
||||
var U_dir = Math.signum(u);
|
||||
|
||||
var position_delta = goal.position - current.position;
|
||||
var velocity_delta = goal.velocity - current.velocity;
|
||||
|
||||
var scalar = (A * current.velocity + B * u) * (A * goal.velocity - B * u);
|
||||
var power = -A / B / u * (A * position_delta - velocity_delta);
|
||||
|
||||
var a = -A * A;
|
||||
var c = (B * B) * (u * u) + scalar * Math.exp(power);
|
||||
|
||||
if (-1e-9 < c && c < 0) {
|
||||
// Numerical stability issue - the heuristic gets it right but c is around -1e-13
|
||||
return 0;
|
||||
}
|
||||
|
||||
return U_dir * Math.sqrt(-c / a);
|
||||
}
|
||||
|
||||
/**
|
||||
* Returns true if the profile should be inverted.
|
||||
*
|
||||
* <p>The profile is inverted if we should first apply negative input in order to reach the goal
|
||||
* state.
|
||||
*
|
||||
* @param current The initial state (usually the current state).
|
||||
* @param goal The desired state when the profile is complete.
|
||||
*/
|
||||
@SuppressWarnings("UnnecessaryParentheses")
|
||||
private boolean shouldFlipInput(State current, State goal) {
|
||||
var u = m_constraints.maxInput;
|
||||
|
||||
var xf = goal.position;
|
||||
var v0 = current.velocity;
|
||||
var vf = goal.velocity;
|
||||
|
||||
var x_forward = computeDistanceFromVelocity(vf, u, current);
|
||||
var x_reverse = computeDistanceFromVelocity(vf, -u, current);
|
||||
|
||||
if (v0 >= m_constraints.maxVelocity()) {
|
||||
return xf < x_reverse;
|
||||
}
|
||||
|
||||
if (v0 <= -m_constraints.maxVelocity()) {
|
||||
return xf < x_forward;
|
||||
}
|
||||
|
||||
var a = v0 >= 0;
|
||||
var b = vf >= 0;
|
||||
var c = xf >= x_forward;
|
||||
var d = xf >= x_reverse;
|
||||
|
||||
return (a && !d) || (b && !c) || (!c && !d);
|
||||
}
|
||||
}
|
||||
Reference in New Issue
Block a user