Efficient optimal control problem solution for car-like mobile robots with the Picard-shooting method

This article investigates the optimal control problem of a Car-Like mobile robot, with our primary objective being the identification of the optimal control strategy that facilitates the transition from an initial point to an endpoint in the shortest possible time. To address this challenge, we employ Pontryagin?s Maximum Principle, coupling it with the shooting method to determine the initial condition of the adjoint state (p0), which is then integrated through the iterative Picard method. The validation of our approach is demonstrated through a numerical example utilizing real-world data, and we provide a comparative analysis of our results against those from previous studies for comprehensive assessment.