Model Predictive Control of Underactuated Bipedal Robotic Walking

This paper addresses the problem of controlling underactuated bipedal walking robots in the presence of actuator torque saturation. The proposed method synthesizes elements of the Human-Inspired Control (HIC) approach for generating provably-stable walking controllers, rapidly exponentially stabilizing control Lyapunov functions (RES-CLFs) and standard model predictive control (MPC). Specifically, the proposed controller uses feedback linearization to construct a linear control system describing the dynamics of the walking outputs. The input to this linear system is designed to be the solution of a MPC-based Quadratic Program which minimizes the sum of the values of a RES-CLF-describing the walking control objectives-over a finite-time horizon. Future values of the torque constraints are mapped into the linear control system using the Hybrid Zero Dynamics property of HIC and subsequently incorporated in the Quadratic Program. The proposed method is implemented in a rigid-body dynamics simulation and initial experiments with the Durus robot.