Robust Balancing Control of a Spring-legged Robot based on a High-order Sliding Mode Observer

Abstract

This paper presents a simulation study of the balancing problem for a monopod robot in which the lower body (the leg) has been modified to include a passively spring-loaded prismatic joint. Such a mechanism can move by hopping but can also stand and balance on a single point. We aim to investigate the extent to which a balance controller can deal with the large values and rapid changes in the spring-damper forces, while controlling the absolute positions and orientations of its parts and balancing on one leg. It can be shown that a good performance is achieved if the spring-loaded joint is instrumented and calibrated so that its position and velocity, as well as the stiffness and damping coefficients, are considered when calculating the controller state variables. We also demonstrate the effectiveness of the balance controller by adding a high-order sliding mode (HOSM) observer based on the finite-time algorithm for robust parameter estimation of the stiffness and damping coefficients. The stability analysis and convergence proofs are presented based on the Lyapunov stability theory. Numerical simulations are included to illustrate the performance and feasibility of the proposed methodology.