Nonlinear Extended State Observer for Hybrid Dynamical Systems

Abstract

This paper introduces a nonlinear disturbance observer for hybrid dynamical systems with continuous and discrete dynamics. The hybrid dynamical system considered in this work is a bipedal robot. The robot is modeled by a continuous mathematical model connected to a discrete reset functions. The continuous and discrete dynamics are exposed to model parameter uncertainties and external disturbances. The uncertainties and disturbances in the continuous dynamics are lumped into a total disturbance signal, which is estimated through a nonlinear extended state observer (NESO). The disturbance estimation is used to design an active disturbance rejection control (ADRC). To address the reset function uncertainties on the discrete dynamics, a reference trajectory generator is designed to achieve zero tracking error after each reset function using a smooth transition function from the system state to the nominal references. The control strategy proposed in this work is applied to the gait control of a planar, dynamic bipedal robot with point feet, five degrees of freedom, and one degree of underactuation. The gait stability is tested through a linearized Poincar\'e return map.