Linear quadratic regulator control of an under actuated five-degree-of-freedom planar biped walking robot

Abstract

Modern robotic systems are fully actuated with full information of themselves and their immediate surroundings. If faced with a failure or damage, robotic systems cannot function properly and can quickly damage themselves. A Linear Quadratic Regulator (LQR) control system is proposed to allow an under actuated (damaged) robotic system (five-degrees-of-freedom, planar, biped, walking robot) to continue to follow a human-like walking gait in a series of Matlab and Simulink simulations. The proposed LQR controller keeps joint position errors to below 4 degrees for the fully actuated system, performing the entire gait within the given step time and length. The under actuated control system can match the fully actuated system using a separate LQR controller. Use of time-varying control and Markovian jump methods can compile both controllers into a dynamically adaptive whole, capable of full to partial gait during both locked joint and free joint failures with brakes applied as needed.