  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. Code and video of the experiments are available at
https://impact-invariant-control.github.io/.
