Hybrid Event Shaping to Stabilize Periodic Hybrid Orbits

TL;DR

This paper introduces hybrid event shaping (HES), a method that uses the saltation matrix and shape parameters to analyze and optimize the stability of hybrid event controllers in legged robotics, enabling the creation of more stable trajectories without continuous feedback.

Contribution

The paper presents a generalized HES framework that unifies existing control methods and introduces new stability-optimized trajectories through independent shape parameter tuning.

Findings

HES effectively analyzes hybrid event stability using the saltation matrix.

Optimization of shape parameters enhances hybrid controller stability.

HES produces stable trajectories without continuous feedback.

Abstract

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.