Efficient Collision Detection Oriented Motion Primitives for Path Planning (2312.01583v2)

Abstract: Mobile robots in dynamic environments require fast planning, especially when onboard computational resources are limited. While classic potential field based algorithms may suffice in simple scenarios, in most cases algorithms able to escape local minima are necessary. Configuration-space search algorithms have proven to provide a good trade-off between quality of the solutions and search time. Literature presents a wide variety of approaches that speed up this search by reducing the number of edges that need to be inspected. Much less attention was instead given to reducing the time necessary to evaluate the cost of a single edge. This paper addresses this point by associating edges to motion primitives that prioritize fast collision detection. We show how biarcs can be used as motion primitives that enable fast collision detection, while still providing smooth, tangent continuous paths. The proposed approach does not assume a disc shaped hitbox, making it appealing for all robots with very different width and length or for differential drive robots with active wheels located far from the robot's center.

• The paper introduces biarc motion primitives that enable low-cost collision detection through closed-form methods, significantly reducing planning times.
• It proposes an equal-chord biarc strategy to balance path length and curvature continuity for smooth, efficient trajectories.
• Experimental results demonstrate that the method achieves comparable path quality while outperforming traditional sampling techniques in computation speed.

Efficient Collision Detection Oriented Motion Primitives for Path Planning

Introduction

The paper addresses a critical challenge in mobile robotics, particularly in dynamic environments where fast and efficient path planning are paramount, especially given the constraints of limited onboard computational resources. Traditional potential field methods, while computationally efficient, often suffer from local minima entrapment, rendering them less suitable for complex, obstacle-rich environments. Local search techniques and discrete configuration space approaches, such as RRTs and PRMs, offer some advancements but prioritize node minimization over edge cost evaluation efficiency. This paper introduces a novel approach to path planning by focusing on motion primitives that enhance collision detection efficiency using biarcs.

Biarcs as Motion Primitives

Biarcs are introduced as a compelling motion primitive for efficient collision detection. Unlike splines or other curves, biarcs provide smooth, tangent-continuous paths with a low computational load for collision checking. They comprise two circular arcs joined at a point, ensuring $G_1$ continuity which suffices for holonomic and differential drive robots. The paper rigorously defines biarcs and develops a methodology to choose optimal joint points that balance path length and curvature discontinuity.

Path Planning and Replanning Strategies

The initial choice of joint location in biarcs is methodically analyzed, showing that an equal-chord biarc provides a practical compromise between path length and curvature continuity. For replanning scenarios, a heuristic is developed that tweaks the joint location to align with prior plans, thus avoiding drastic, jerky movements while maintaining computational simplicity.

Collision Detection

The standout contribution of the paper is its approach to collision detection, which eschews traditional sampling methods in favor of closed-form computations. For point obstacles, the paper delineates methods for both arc and straight-line movements. For line obstacles, it provides a profound analysis of intersection detection between the robot's edges and static environmental features.

Experimental Evaluation

The proposed biarc-based motion planner is integrated into a conformal lattice planner framework and benchmarked against MRPB, revealing computational efficiencies. The planner's ability to maintain comparable path lengths and travel times, while drastically reducing planning times, underscores the practical utility of biarcs.

Implications and Future Directions

This paper presents a robust methodology for enhancing robot path planning by combining theoretically sound biarc parameterizations with practical collision detection strategies. Future research should explore extending the method to handle dynamic obstacles and determining minimum obstacle distances for path optimization. Additionally, incorporating clothoid segments may improve continuity for high-speed platforms.

In summary, this paper makes significant contributions to motion planning by prioritizing collision detection efficiency through well-defined biarc motion primitives, offering practical and computational benefits for real-world robotics applications.