Balancing Safety and Optimality in Robot Path Planning: Algorithm and Metric

Path planning for autonomous robots faces a fundamental trade-off between path length and obstacle clearance. While existing algorithms typically prioritize a single objective, we introduce the Unified Path Planner (UPP), a graph-search algorithm that dynamically balances safety and optimality via adaptive heuristic weighting. UPP employs a local inverse-distance safety field and auto-tunes its parameters based on real-time search progress, achieving provable suboptimality bounds while maintaining superior clearance. To enable rigorous evaluation, we introduce the OptiSafe index, a normalized metric that quantifies the trade-off between safety and optimality. Extensive evaluation across 10 environments shows that UPP achieves a 0.94 OptiSafe score in cluttered environments, compared with 0.22-0.85 for existing methods, with only 0.5-1% path-length overhead in simulation and a 100% success rate. Hardware validation on TurtleBot confirms practical advantages despite sim-to-real gaps.