Invariant funnels for underactuated dynamic walking robots: New phase variable and experimental validation

Abstract

We address the problem of finding useful invariant funnels for dynamic walking robots, i.e. sets of initial conditions from which continued walking in a stable manner is guaranteed. The construction is based on transverse dynamics and sum-of-squares verification. This paper makes two main contributions: firstly, we show that for typical models of walking robots the construction of such funnels can be significantly simplified by use of a new phase variable. Secondly, we provide the first hardware validation of the resulting funnels on an experimental testbed.