Impact-Invariant Control: Maximizing Control Authority During Impacts

1University of Pennsylvania,

Abstract

When legged robots impact their environment executing dynamic motions, they undergo large changes in their velocities in a short amount of time. Measuring and applying feedback to these velocities is challenging, further complicated by uncertainty in the impact model and impact timing. This work proposes a general framework for adapting feedback control during impact by projecting the control objectives to a subspace that is invariant to the impact event. The resultant controller is robust to uncertainties in the impact event while maintaining maximum control authority over the impact-invariant subspace. We demonstrate the improved performance of the projection over other commonly used heuristics on a walking controller for a planar five-link-biped. The projection is also applied to jumping, box jumping, and running controllers for the compliant 3D bipedal robot, Cassie. The modification is easily applied to these various controllers and is a critical component to deploying on the physical robot.

Impact-Invariance

Interpolate start reference image.

Generalized Velocities

Interpolate start reference image.

Impact-Invariant Velocities

Despite good tracking, the error for the generalized velocities spikes during the impact event due discontinuities from the impact event and inevitable mismatches in impact timing. Projecting those same velocities to the impact-invariant space eliminates the discontinuity from the impact event and thus provides robustness to uncertainty in the impact event.

Running Controller Highlights

BibTeX

@article{yang2023impact,
  title={Impact-invariant control: Maximizing control authority during impacts},
  author={Yang, William and Posa, Michael},
  journal={arXiv preprint arXiv:2303.00817},
  year={2023}
}