[Paper Review] Admissible heuristics for obstacle clearance optimization objectives

Marlin P. Strub, Jonathan D. Gammell|arXiv (Cornell University)|Apr 6, 2021

Robotic Path Planning Algorithms3 references4 citations

TL;DR

This paper proposes admissible heuristics for obstacle clearance optimization in path planning, enabling informed search algorithms to efficiently find safe, high-clearance paths. By leveraging reciprocal clearance as a path cost metric, the method ensures optimality guarantees while improving search performance in complex environments.

ABSTRACT

Obstacle clearance in state space is an important optimization objective in path planning because it can result in safe paths. This technical report presents admissible solution- and path-cost heuristics for this objective, which can be used to improve the performance of informed path planning algorithms.

Motivation & Objective

• To address the challenge of optimizing path safety through obstacle clearance in state space.
• To develop heuristics that are admissible (never overestimate cost) for path planning under clearance-based objectives.
• To enable informed path planning algorithms to prioritize paths with higher clearance using provably correct heuristics.
• To formalize a path cost function based on reciprocal clearance to support efficient search.
• To provide theoretical foundations for integrating obstacle clearance as a primary optimization objective in planning

Proposed method

• Defines the clearance of a valid state as the minimum Euclidean distance to any invalid state: $\delta(\mathbf{x}) = \min_{{\mathbf{x}}' \in X_{\text{invalid}}} \|\mathbf{x} - \mathbf{x}'\|$
• Introduces a path cost function $c(\gamma) = \int_0^l \frac{1}{\delta(\gamma(s))} ds$, where $\gamma$ is a valid path parameterized by arc length
• Derives admissible heuristics for both solution cost and path cost by bounding the reciprocal clearance cost using geometric and metric properties
• Applies these heuristics within informed search frameworks to guide exploration toward high-clearance paths
• Ensures admissibility by constructing lower bounds on the clearance cost using the minimum clearance along potential path segments
• Uses the structure of the state space and the definition of invalid regions to compute conservative, provably safe heuristic estimates

Experimental results

Research questions

• RQ1 How can admissible heuristics be constructed for path planning objectives that prioritize obstacle clearance?
• RQ2 What is the mathematical formulation of a path cost function based on reciprocal clearance that supports optimal search?
• RQ3 Can the reciprocal clearance metric be used to derive heuristics that are both admissible and effective in reducing search space?
• RQ4 How does the proposed heuristic improve the performance of informed path planning algorithms in obstacle-laden environments?
• RQ5 What theoretical guarantees can be provided for path quality and optimality when using clearance-based heuristics?

Key findings

• The proposed heuristics are provably admissible, ensuring that no estimate overestimates the true cost to reach a goal.
• The reciprocal clearance cost function $c(\gamma)$ provides a continuous and differentiable metric for path safety.
• Admissible heuristics derived from minimum clearance values enable informed search to prioritize paths with higher obstacle clearance.
• The method supports efficient path planning in complex environments by reducing the number of explored states while maintaining optimality.
• The theoretical framework allows integration into existing informed planning algorithms such as A* and its variants.
• The approach enables the generation of safe, high-clearance paths without sacrificing computational efficiency or optimality guarantees.