[wpimath] ExponentialProfile doesn't enter the correct limit cycle for nonzero velocity goals

[jwbonner]

Under certain conditions, an exponential profile with a constant goal can produce oscillations that prevent it from finishing the profile. The graph below shows the position setpoint for one such profile.

This behavior appears to be extremely sensitive to the initial inputs. The example below produces the issue consistently, but changing the goal velocity to 2.99999 or 3.00001 fixes the issue. It's not clear whether this might be related to using a nonzero goal velocity given how sensitive it is to the exact values.

ExponentialProfile profile = new ExponentialProfile(
    ExponentialProfile.Constraints.fromStateSpace(206.18996798292426, -4.0508214770151705, 0.07795421563066239));
ExponentialProfile.State state = new ExponentialProfile.State(0.1, 0.0);
ExponentialProfile.State goal = new ExponentialProfile.State(1.75, 3);

@Override
public void robotPeriodic() {
  SmartDashboard.putNumber("Position", state.position);
  SmartDashboard.putNumber("Velocity", state.velocity);
}

@Override
public void teleopPeriodic() {
  state = profile.calculate(0.02, state, goal);
}

This log includes the positions and velocities of the setpoints for the example above: exponentialprofilebug.wpilog.zip

Desktop (please complete the following information):

• OS: macOS 15.2
• Project Information:

WPILib Information:
Project Version: 2025.2.1
VS Code Version: 1.96.4
WPILib Extension Version: 2025.2.1
C++ Extension Version: 1.23.2
Java Extension Version: 1.38.0
Java Debug Extension Version: 0.58.1
Java Dependencies Extension Version 0.24.1
Java Version: 17
Java Location: /Users/jonah/wpilib/2025/jdk
Vendor Libraries:

[calcmogul]

This is intended behavior. If you provide a constant goal with a nonzero velocity, the system will enter a limit cycle in phase space to hit the goal repeatedly. If you want the profile to reach steady-state, you should pass a zero velocity.

[jwbonner]

Why is the behavior entirely different with a velocity of 2.99999 and 3.00000 in that case? It seems like the resulting profile should be nearly identical in those cases.

[jwbonner]

After the initial movement, the profile also fails to reach the goal again afterwards (and doesn’t follow a normal cycle). If it cycles to hit the goal repeatedly, I would have expected both of those to be true.

[calcmogul]

Could you be more specific about the behavior you saw instead of a limit cycle?

[calcmogul]

A position vs velocity plot would be much more informative than a time domain plot.

[jwbonner]

This is with a setpoint of 2.99999:

And with a setpoint of 3.00000:

I marked the goal with a red X on both plots.

[jwbonner]

(The first example is stable after it reaches the goal)

[calcmogul]

It shouldn't be stable tho, because it's not physically possible to stay at a given position-velocity pair in steady-state when that velocity is nonzero; the nonzero velocity necessarily makes the position diverge.