A Model-Free Solution for Stable Balancing and Locomotion of Floating-base Legged Systems

Abstract

This paper presents novel control techniques for passivation and stabilisation of floating-base systems with contacts, whose dynamical models comprise both joint-space, and Cartesian floating-base coordinates. The aforementioned results are achieved using both minimally model-based, and completely model-free controllers that employ power-shaping signals. Model-free control is permitted through usage of a decoupled dynamical model, procured via coordinate transformation operations. It is demonstrated that even though passive closed-loop systems are attainable without utilisation of exteroceptive feedback, global stabilisation of a floating-base robot necessitates direct usage of either measured or estimated external forces. The presented asymptotical stabilisation results pertain to both the set-point regulation, and trajectory-tracking cases, thereby ensuring suitability for static balancing, and dynamical locomotion tasks. To ensure practicability and production of feasible input signals, a variable impedance control, power-shaping term is appended to the original design, wherein it circumstantially serves as either a power-dissipating, or power-injecting element. This enhancement provably preserves closed-loop stability, by appositely shaping the system's power. Experiments involving a metamorphic, quadrupedal walking robot, corroborate the theoretical analysis, as they attest to the system's ability to stably execute locomotory tasks using a single, unified, model-free control scheme.