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

Jatin Kumar Arora, Soutrik Bandyopadhyay, Sunil Sulania, Shubhendu Bhasin

Abstract

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.

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

Abstract

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.

Paper Structure

This paper contains 20 sections, 6 theorems, 62 equations, 5 figures, 5 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Unified Path Planner (UPP)
  4. Initial Parameter Selection
  5. Adaptation of Parameters
  6. Theoretical Properties
  7. Completeness of UPP
  8. Effect of adaptive $\beta$
  9. Effect of adaptive $\alpha$
  10. Algorithm
  11. OptiSafe Index
  12. Theoretical properties
  13. Algorithm
  14. Simulation results
  15. UPP ablation studies
  16. ...and 5 more sections

Key Result

Lemma 1

Provided the parametes $\alpha \in (0,1)$ and $\beta \in [\beta_{min}, \beta_{max}]$ are updated according to the update laws eq:alpha_update and eq:beta_update respectively, then the heuristic function $h(\cdot)$ is bounded by where $n$ denotes the dimension of the grid, $r$ denotes the distance at which the neighbors are considered, $\varepsilon \in \mathbb{R}$ is the parameter defined in eq:sa

Figures (5)

  • Figure 1: Level set visualization of the $\ell_1$ norm , the $\ell_\infty$ norm , and their convex combinations for multiple values of $\alpha$.
  • Figure 2: Safety Field on a grid, white area represents obstacles
  • Figure 3: Optisafe Index Surface
  • Figure 4: Planner comparison for random start and goal for Map 1
  • Figure 5: Planner comparison for random start and goal for Map 2

Theorems & Definitions (12)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Theorem 1
  • proof
  • Lemma 3
  • proof
  • Lemma 4
  • proof
  • ...and 2 more