LQR control of an under actuated planar biped robot

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. In this paper, we study the motion control of an under actuated five-degree-of-freedom planar biped. Once the fully actuated system is established, it is made under actuated by removing control over a specific joint actuator. This is done to represent damage to the robotic system in the form of a failed or unresponsive actuator motor. A Linear Quadratic Regulator (LQR) controller is then designed to allow the under actuated (damaged) robotic system to continue to follow a human-like walking gait. Using the under actuated control, the walking gait is preformed without the use of the uncontrolled joint and overall effectiveness is compared with the fully actuated system performance. Simulation results indicates that one single LQR controller, designed based on the linearized model at the beginning of the single support phase, is sufficient to perform the desired walking gait even though the biped model is highly nonlinear. This study demonstrates the effectiveness of the LQR control to the under actuated biped robot.