Nearest-Neighbourless Asymptotically Optimal Motion Planning with Fully Connected Informed Trees (FCIT*)

2024-11-26

arXiv.org

AI Summary

High computational overhead from local validation and k-nearest neighbor (k-NN) queries severely hampers sampling-based motion planning for high-degree-of-freedom robots. Method: This paper introduces FCIT*, the first sampling-based planner that eliminates nearest-neighbor searches entirely while guaranteeing anytime convergence and almost-sure asymptotic optimality (ASAO). FCIT* constructs a fully connected graph by unifying informed sampling with random graph generation, thereby removing reliance on k-NN queries inherent in RRT*-type algorithms. It further incorporates SIMD-parallel edge validation, informed target-region pruning, and an anytime optimization framework. Results: Evaluated on the MotionBenchMaker benchmark, FCIT* achieves significantly faster initial solution times than state-of-the-art methods including VAMP and OMPL, while rigorously maintaining asymptotic optimality guarantees.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Replanning and Plan Repair

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Improving the performance of motion planning algorithms for high-degree-of-freedom robots usually requires reducing the cost or frequency of computationally expensive operations. Traditionally, and especially for asymptotically optimal sampling-based motion planners, the most expensive operations are local motion validation and querying the nearest neighbours of a configuration. Recent advances have significantly reduced the cost of motion validation by using single instruction/multiple data (SIMD) parallelism to improve solution times for satisficing motion planning problems. These advances have not yet been applied to asymptotically optimal motion planning. This paper presents Fully Connected Informed Trees (FCIT*), the first fully connected, informed, anytime almost-surely asymptotically optimal (ASAO) algorithm. FCIT* exploits the radically reduced cost of edge evaluation via SIMD parallelism to build and search fully connected graphs. This removes the need for nearest-neighbours structures, which are a dominant cost for many sampling-based motion planners, and allows it to find initial solutions faster than state-of-the-art ASAO (VAMP, OMPL) and satisficing (OMPL) algorithms on the MotionBenchMaker dataset while converging towards optimal plans in an anytime manner.

Problem

• Reduces computational cost in motion planning for robots.
• Eliminates need for nearest-neighbours structures using SIMD parallelism.
• Improves speed and optimality in high-degree-of-freedom robot planning.

Innovation

• FCIT* uses SIMD parallelism for edge evaluation.
• Eliminates nearest-neighbours structures in motion planning.
• Faster initial solutions than state-of-the-art ASAO algorithms.