Ship Path Planning and Tracking Based on Rapidly Exploring Random Tree and Convex Optimization

Abstract: ObjectivesTo address the challenges of path planning and tracking for underactuated ships in obstacle-infested waters, this paper proposes a ship path planning and tracking algorithm based on stochastic search trees and convex optimization. MethodsThe method utilizes the Rapidly Exploring Random Tree (RRT) algorithm to sample and plan feasible paths in a grid environment, resulting in a sequence of key points. For the key point sequence in the feasible path, optimization of the economic and safety aspects of the curve is achieved through Limited Memory BFGS (L-BFGS) convex optimization algorithm and Cubic spline curves, yielding smoother and safer ship paths parameterized by time. Finally, Model Predictive Control (MPC) algorithm is employed to plan ship control output sequences, guiding ships to navigate safely and economically around obstacles from the starting point to the destination. ResultsSimulation results demonstrate that with this algorithm, ships can achieve efficient path planning and trajectory tracking, with path search time less than 2e-5 seconds, path optimization time less than 0.5 seconds, and trajectory tracking absolute error less than 0.75 meters. ConclusionsThe simulation concludes that the proposed path planning and tracking algorithm ensures effective path search and optimization for ships, offering insights for further research and industrial applications of autonomous surface vehicles.