Grey Wolf Optimizer Based Tuning of a Hybrid LQR-PID Controller for Foot Trajectory Control of a Quadruped Robot

Quadruped robots have generally complex construction, so designing a stable controller for them is a major struggle task. This paper presents designing and optimization of an effective hybrid control by combining LQR and PID controllers. In this study, the tuning of a hybrid LQR-PID controller for foot trajectory control of a quadruped robot during step motion using Grey Wolf Optimizer (GWO) algorithm which is an alternative method are comparatively investigated with two traditional benchmarking algorithms (PSO and GA). The principal goal of this work is the tuning of the LQR controller parameters (Q and R weight matrices) and the PID controllers gains (kp, ki and kd) using the proposed algorithms. Initially, the designed solid model of the quadruped robot is imported into Simulink/SimMechanics which are simulation tools of MATLAB and then obtained the mathematical model of system which is at State-Space form with Linear Analysis Tools considering the step motion of robot leg in sagittal plane. Later, the hybrid LQR-PID control system is designed and its parameters are tuned to get optimal values which guarantee best trajectory tracing in Simulink with the three proposed algorithms. Subsequently, the system is simulated separately with optimal control parameters which provide from the algorithms. The simulation outcomes are indicating that GWO algorithm is more efficiently and quickly within similar torques to tuning the hybrid controller based on LQR&PID than the other conventional algorithms.