Design an omnidirectional autonomous mobile robot based on non-linear optimal control to track a specified path

This paper explores two non-linear control techniques for designing an effective control system for an omnidirectional autonomous mobile robot with four Mecanum wheels. Due to the unique wheel structure and four separate wheels, the robot has non-linear dynamics, multiple inputs and outputs. The first technique uses the state-dependent Riccati equation (SDRE) to address optimal non-linear control while considering energy and time constraints. The second technique, using an intermediate variable $\theta$, has expanded the Hamilton-Jacobi-Belman equation in terms of the power series. Consequently, these equations are reduced to a set of recursive Lyapunov algebraic equations, leading to a closed-form solution for solving the non-linear optimal control problem. Finally, the maneuverability and path-tracking capability of the robot are examined by highlighting the non-linear term through numerical simulation.