Hybrid Event Shaping to Stabilize Periodic Hybrid Orbits
This work addresses stability challenges in legged robotics, offering a novel framework that generalizes existing control methods and enables optimization for improved performance.
The paper tackles the problem of stabilizing periodic hybrid orbits in legged robotic systems by introducing hybrid event shaping (HES), a generalized method that uses the saltation matrix and shape parameters to analyze and produce stable controllers, resulting in new optimally stable trajectories without continuous-domain feedback.
Many controllers for legged robotic systems leverage open- or closed-loop control at discrete hybrid events to enhance stability. These controllers appear in several well studied phenomena such as the Raibert stepping controller, paddle juggling and swing leg retraction. This work introduces hybrid event shaping (HES): a generalized method for analyzing and producing stable hybrid event controllers. HES utilizes the saltation matrix, which gives a closed-form equation for the effect that hybrid events have on stability. We also introduce shape parameters, which are higher order terms that can be tuned completely independently from the system dynamics to promote stability. Optimization methods are used to produce values of these parameters that optimize a stability measure. Hybrid event shaping captures previously developed control methods while also producing new optimally stable trajectories without the need for continuous-domain feedback.