Sliding Mode Control of Underactuated Biped Robots

Abstract

This paper presents a robust tracking control algorithm for underactuated biped robots. The biped considered in this work is modeled as a five-link planar robot with four actuators located at hip and knee joints to control the joint angles. The control law is defined based on the sliding mode control approach. The objective of the controller is to generate stable walking based on predefined desired trajectories. The planning of the trajectory in swing phase is discussed while the double support phase is considered to be instantaneous and the impact of the swing leg with the ground is modeled as rigid body contact. In order to formulate the sliding control law, we define four first-order sliding surfaces, based on the number of actuators, as a linear combination of tracking joint positions and velocities. The control approach is shown to guarantee that all trajectories will reach and stay on these surfaces. The surface parameters are then selected to ensure the stability of the surfaces leading to an asymptotically stable control law. Numerical simulation is presented for tracking a multi-step walk of a biped robot.