Unified Path Planner with Adaptive Safety and Optimality

Path planning for autonomous robots presents a fundamental trade-off between optimality and safety. While conventional algorithms typically prioritize one of these objectives, we introduce the Unified Path Planner (UPP), a unified framework that simultaneously addresses both. UPP is a graph-search-based algorithm that employs a modified heuristic function incorporating a dynamic safety cost, enabling an adaptive balance between path length and obstacle clearance. We establish theoretical sub-optimality bounds for the planner and demonstrate that its safety-to-optimality ratio can be tuned via adjustable parameters, with a trade-off in computational complexity. Extensive simulations show that UPP achieves a high success rate, generating near-optimal paths with only a negligible increase in cost over traditional A*, while ensuring safety margins that closely approach those of the classical Voronoi planner. Finally, the practical efficacy of UPP is validated through a hardware implementation on a TurtleBot, confirming its ability to navigate cluttered environments by generating safe, sub-optimal paths.