Controller Synthesis for Discrete-time Hybrid Polynomial Systems via Occupation Measures
This work addresses the challenge of feedback design for robotics systems with uncertain contact timing and occurrence, representing an incremental advance in controller synthesis methods.
The paper tackles the problem of stabilizing rigid body systems with multiple contacts by developing a controller synthesis approach for discrete-time hybrid polynomial systems, resulting in a convex optimization formulation with polynomial computational complexity.
We consider the feedback design for stabilizing a rigid body system by making and breaking multiple contacts with the environment without prespecifying the timing or the number of occurrence of the contacts. We model such a system as a discrete-time hybrid polynomial system, where the state-input space is partitioned into several polytopic regions with each region associated with a different polynomial dynamics equation. Based on the notion of occupation measures, we present a novel controller synthesis approach that solves finite-dimensional semidefinite programs as approximations to an infinite-dimensional linear program to stabilize the system. The optimization formulation is simple and convex, and for any fixed degree of approximations the computational complexity is polynomial in the state and control input dimensions. We illustrate our approach on some robotics examples.