Unification of locomotion pattern generation and control Lyapunov function-based Quadratic Programs

Abstract

This paper presents a novel method of combining real-time walking pattern generation and constrained nonlinear control to achieve robotic walking under Zero-Moment Point (ZMP) and torque constraints. The proposed method leverages the fact that existing solutions to both walking pattern generation and constrained nonlinear control have been independently constructed as Quadratic Programs (QPs) and that these constructions can be related through an equality constraint on the instantaneous acceleration of the center of mass. Specifically, the proposed method solves a single Quadratic Program which incorporates elements from Model Predictive Control (MPC) based center of mass planning methods and from rapidly exponentially stabilizing control Lyapunov function (RES-CLF) methods. The resulting QP-based controller simultaneously solves for a COM trajectory that satisfies ZMP constraints over a future horizon while also producing joint torques consistent with instantaneous acceleration, torque, ZMP and RES-CLF constraints. The method is developed for simulation and experimental study on a seven-link, planar robot.

Modeling, Analysis, and Control of Mechanical Systems under Power Constraints

“…In other words, the existence of a CLF for tracking y (t) is equivalent to the existence of a stabilizing controller which satisfies the inequality (42). Such a controller and a CLF pair can be found by feedback linearization [46] systematically as follows : Considering ỹ(x, t) as the output function, input-output dynamics have a relative degree of two, hence taking the form . Position (top) and torque (bottom) trajectories of actuators whose settling times are marked with circles for optimal controllers C1 (solid-blue), C2 (dashed-red), and C3 (dotted-yellow).…”