Decentralized LQR Joint Servo Design for a Compliant Humanoid Robot via LMI Optimisation

Enhancing bipedal walking safety, robustness and efficiency has led to design of compliant humanoid robots. However, the links' interactions and coupling effects are often neglected in the design of their trajectory tracking controller. Moreover, there is not a direct decentralized approach for designing the PD-PID gains given a multivariable model of the compliant humanoid robot. This paper proposes an LMI formulation for designing decentralized PID gains in discrete time. It is shown that this method can be used to design a full state feedback for trajectory tracking which includes the compliance and links' interactions in the feedback design. Numerical simulations for a compliant compass gait and a 10 DoF humanoid models are provided to illustrate the use of this method.