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This paper presents an enhanced direct-method-based approach for thereal-time solution of optimal control problems to handle path constraints, suchas obstacles. The principal contributions of this work are twofold: first, theexisting methods for constructing reachability sets in the literature areextended to derive the envelope of these sets, which determines the regionswept by all feasible trajectories between adjacent sample points. Second, wepropose a novel method to guarantee constraint violation-free between discretestates in two dimensions through mesh refinement approach. To illustrate theeffectiveness of the proposed methodology, numerical simulations are conductedon real-time path planning for fixed-wing unmanned aerial vehicles.

Constraint-Aware Mesh Refinement Method by Reachability Set Envelope of Curvature Bounded Paths