Improving Path Accuracy for Autonomous Parking Systems: An Optimal Control Approach

Kinodynamic planning explores the collision-free configuration space by constructing a tree on-the-fly. The process terminates when the tree expands into a specified neighborhood of the goal configuration. Often, the resultant path does not reach the goal accurately enough, which raises the question: how does one make an accurate, kinematically feasible connection between the tree and the goal. This is the non-trivial steering problem. Aiming to balance computational efficiency and position accuracy, this work solves an approximate steering problem through applying Pontryagin's Maximum Principle (PMP). The main contributions of this work are: establishment of an exhaustive set of possible structures of optimal control solutions; and development of a custom solver based on the these structures. Simulations demonstrate the PMP-based custom solver achieves better accuracy than a PID feedback control-based approach, and is more computationally efficient than a gradient descent-based numerical optimization approach.