AMRA*: Anytime Multi-Resolution Multi-Heuristic A* (2110.05328v2)

Abstract: Heuristic search-based motion planning algorithms typically discretise the search space in order to solve the shortest path problem. Their performance is closely related to this discretisation. A fine discretisation allows for better approximations of the continuous search space, but makes the search for a solution more computationally costly. A coarser resolution might allow the algorithms to find solutions quickly at the expense of quality. For large state spaces, it can be beneficial to search for solutions across multiple resolutions even though defining the discretisations is challenging. The recently proposed algorithm Multi-Resolution A* (MRA*) searches over multiple resolutions. It traverses large areas of obstacle-free space and escapes local minima at a coarse resolution. It can also navigate so-called narrow passageways at a finer resolution. In this work, we develop AMRA*, an anytime version of MRA*. AMRA* tries to find a solution quickly using the coarse resolution as much as possible. It then refines the solution by relying on the fine resolution to discover better paths that may not have been available at the coarse resolution. In addition to being anytime, AMRA* can also leverage information sharing between multiple heuristics. We prove that AMRA* is complete and optimal (in-the-limit of time) with respect to the finest resolution. We show its performance on 2D grid navigation and 4D kinodynamic planning problems.

• The paper introduces AMRA*, which combines anytime, multi-resolution, and multi-heuristic approaches to enhance motion planning speed and quality.
• The methodology employs concurrent heuristics and resolution-dependent graph expansion to reduce state expansions while ensuring completeness and optimality.
• Empirical evaluations in 2D grid and 4D UAV kinodynamic tasks confirm AMRA*'s ability to deliver rapid initial solutions and continuous refinement.

An Overview of AMRA*: Anytime Multi-Resolution Multi-Heuristic A* for Motion Planning

The paper presents AMRA*, an innovative search algorithm designed for heuristic-based motion planning. AMRA* is a generalization that integrates the principles of anytime algorithms, multi-resolution search, and multi-heuristic search within a unified framework. By addressing the challenges associated with the discretization of search spaces, AMRA* offers enhancements in terms of computational efficiency and solution quality for motion planning tasks.

Theoretical Foundations and Innovations of AMRA*

AMRA* extends upon the Multi-Resolution A* (MRA*) by introducing an anytime component that allows for the continuous refinement of solutions over time. This feature is critically important for large state spaces where an initial solution is required expediently, with subsequent improvements made as computational resources permit. The algorithm's design is influenced by its ability to operate across multiple resolutions, leveraging both fine and coarse discretizations when appropriate. This characteristic is particularly advantageous when navigating through narrow passageways, where fine resolution is necessary, or in large open spaces, where a coarse path can be computationally less demanding.

Furthermore, AMRA* incorporates multi-heuristic paradigms. By facilitating concurrent searches with multiple heuristics, it optimizes the balance of speed and solution quality. The capacity for information sharing between multiple heuristics within the search process drastically reduces the likelihood of local minima entrapment and provides robust exploration capabilities. As proven in the paper, AMRA* maintains theoretical completeness and optimality in the limit of time with respect to the finest resolution. This is achieved through structured priority queue management and a systematic resolution-dependent graph expansion strategy.

Empirical Evaluation

AMRA* was evaluated against established algorithms such as ARA*, MRA*, and RRT* across various tasks, including 2D grid navigation and 4D UAV kinodynamic planning. The results illustrate AMRA*'s competitiveness in terms of both computational efficiency and solution quality. The initial solution times and the quality of final solutions were favorably compared against traditional approaches, with significantly fewer state expansions recorded in AMRA* executions. Especially in kinodynamic scenarios, AMRA* demonstrated a consistent ability to find optimal or near-optimal paths faster than A-MHA* and certain variations of MRA*.

Practical Implications and Future Directions

AMRA* addresses significant limitations in traditional motion planning methodologies by allowing for adaptive resolution planning and heuristic versatility. This adaptability facilitates enhanced scalability across diverse robotic applications—ranging from intricate robotic manipulations requiring precise path planning to autonomous navigation in open terrains. For domains where real-time path updates and adaptability are critical, AMRA* stands as a promising algorithmic framework.

Looking forward, potential extensions of AMRA* could incorporate dynamically changing action spaces, where different sets of actions become viable in reaction to evolving state conditions. Such advancements may align well with complex robotic systems needing to perform under varying constraints and environments. Additionally, exploring the integration of learning-based strategies with AMRA* may further enhance its heuristic formulation, providing data-driven insights for even more efficient pathfinding in unfamiliar environments.

In summary, AMRA* presents a solid advancement within the heuristic search algorithms for motion planning, with its blend of efficiency and flexibility making it a valuable tool for complex robotic systems.