<p>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 <a href="https://impact-invariant-control.github.io/">https://impact-invariant-control.github.io/</a>.</p>