Finding a needle in an exponential haystack: Discrete RRT for exploration of implicit roadmaps in multi-robot motion planning (1305.2889v3)

Abstract: We present a sampling-based framework for multi-robot motion planning which combines an implicit representation of a roadmap with a novel approach for pathfinding in geometrically embedded graphs tailored for our setting. Our pathfinding algorithm, discrete-RRT (dRRT), is an adaptation of the celebrated RRT algorithm for the discrete case of a graph, and it enables a rapid exploration of the high-dimensional configuration space by carefully walking through an implicit representation of a tensor product of roadmaps for the individual robots. We demonstrate our approach experimentally on scenarios of up to 60 degrees of freedom where our algorithm is faster by a factor of at least ten when compared to existing algorithms that we are aware of.

• The paper introduces the Discrete RRT (dRRT) algorithm and MRdRRT framework, which efficiently explores implicit composite roadmaps for multi-robot motion planning in high-dimensional spaces.
• dRRT adapts the RRT algorithm for discrete spaces and leverages implicit representations of composite roadmaps to avoid exponential complexity and accelerate search.
• Experiments show the MRdRRT framework improves pathfinding speed by at least a factor of ten compared to existing methods, demonstrating scalability for up to 60 degrees of freedom.

A Sampling-Based Approach to Multi-Robot Motion Planning: The Discrete RRT Algorithm

The paper "Finding a Needle in an Exponential Haystack: Discrete RRT for Exploration of Implicit Roadmaps in Multi-Robot Motion Planning" introduces a sophisticated technique for tackling the challenges of multi-robot motion planning. The authors propose a new framework utilizing a sampling-based algorithm, distinctively adapted from the well-established Rapidly-exploring Random Tree (RRT) for application in discrete settings, dubbed discrete-RRT (dRRT). This approach targets the efficient exploration of high-dimensional configuration spaces leveraging implicit representations of composite roadmaps derived from individual robot roadmaps.

Core Contributions

The primary contribution of this paper is the discrete-RRT (dRRT) algorithm, which modifies the traditional RRT framework for exploration of discrete graphs, specifically those embedded in Euclidean space. This adaptation is crucial for addressing the exponential growth of state spaces typical in multi-robot scenarios. The underlying methodology involves rapid exploration enabled by an implicit representation of a composite roadmap that comprises tensor products of individual robot roadmaps.

1. Implicit Composite Roadmap Representation: Unlike previous approaches that explicitly construct composite roadmaps, leading to exponential complexity, the authors propose maintaining an implicit representation. Such a structure inherently optimizes resource utilization by minimizing direct computation over explicit exponential graphs.
2. Pathfinding Using dRRT: By adapting RRT for pathfinding in discrete spaces, the paper introduces an algorithm capable of traversing implicitly represented, high-dimensional graphs effectively. This is particularly useful in scenarios involving greater degrees of robot coordination, where existing graph-based approaches suffer from inefficiencies due to the exponential nature of state space neighbors.
3. Experimental Validation: The authors demonstrate the efficacy of their method on scenarios encompassing up to 60 degrees of freedom, achieving performance improvements by at least a factor of ten compared to existing algorithms, highlighting its capabilities in high-dimensional, tightly coupled multi-robot environments.

Key Results and Implications

The synthesized framework, termed MRdRRT (Multi-Robot Discrete RRT), signifies considerable improvements in pathfinding speed while maintaining the probabilistic completeness typical of sampling-based methods. The improvement factor of at least ten over existing implementations, as claimed by the authors, signifies notable advancements in handling complex, high-dimensional motion planning problems.

The implications of this research are multifaceted:

• Increased Efficiency: By leveraging implicit composite roadmaps, MRdRRT reduces the computational overhead associated with explicit state space exploration in multi-robot settings.
• Scalability: The approach scales more effectively to scenarios with a large number of robots, attributed to its ability to rapidly reduce the search space explored.
• Minimalistic Graph Exploration: dRRT employs a minimalist search strategy, preferring exploratory expansion into unexplored regions, thus promoting rapid progress towards a solution.

Future Directions

The research paves the way for several advancements:

• Optimal Path Planning: Current work focuses on discovering feasible paths without optimality considerations. Future iterations might integrate techniques akin to RRT* to provide asymptotic optimality in the quality of discovered paths.
• Domain Extensions: While the application is predominantly focused on multi-robot planning, the discrete-RRT framework could be extended to other domains, such as multi-link robotic systems or large-scale robotic pathfinding, where implicit roadmap structures can yield significant computational benefits.
• Enhanced Local Connectors: Refining the local connectors used within dRRT could further improve efficiency, particularly in scenarios with necessarily tight operational coupling between robots.

This paper represents a significant step towards more efficient algorithms for multi-robot motion planning, providing both a refined theoretical basis and practical improvements over existing methodologies. By incorporating implicit roadmap strategies with discrete exploration techniques, the research sets a precedent for tackling similar exponential complexity challenges in robotics and beyond.