AORRTC: Almost-Surely Asymptotically Optimal Planning with RRT-Connect

2025-05-15

AI Summary

To address the challenge of balancing real-time performance and asymptotic optimality in high-degree-of-freedom robot motion planning, this paper proposes AORRTC: the first connection-based sampling planner that integrates the Anytime Optimal (AO)-x-ary optimization framework into the RRT-Connect architecture. AORRTC achieves millisecond-scale initial solution generation while guaranteeing almost-sure asymptotic optimality (a.s.a.o.). We formally prove its probabilistic completeness and a.s.a.o. property. To accelerate convergence, we introduce SIMD-based parallelization and a heuristic fast-connect strategy. Experiments on the 7-DOF Panda and 8-DOF Fetch robots demonstrate that AORRTC matches RRT-Connect’s initial solution speed, yet converges to optimal solutions significantly faster than existing a.s.a.o. planners. Moreover, it achieves high success rates in complex environments with average computation times of only a few milliseconds.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Intelligent Robots: Motion and Path Planning

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Finding high-quality solutions quickly is an important objective in motion planning. This is especially true for high-degree-of-freedom robots. Satisficing planners have traditionally found feasible solutions quickly but provide no guarantees on their optimality, while almost-surely asymptotically optimal (a.s.a.o.) planners have probabilistic guarantees on their convergence towards an optimal solution but are more computationally expensive. This paper uses the AO-x meta-algorithm to extend the satisficing RRT-Connect planner to optimal planning. The resulting Asymptotically Optimal RRT-Connect (AORRTC) finds initial solutions in similar times as RRT-Connect and uses any additional planning time to converge towards the optimal solution in an anytime manner. It is proven to be probabilistically complete and a.s.a.o. AORRTC was tested with the Panda (7 DoF) and Fetch (8 DoF) robotic arms on the MotionBenchMaker dataset. These experiments show that AORRTC finds initial solutions as fast as RRT-Connect and faster than the tested state-of-the-art a.s.a.o. algorithms while converging to better solutions faster. AORRTC finds solutions to difficult high-DoF planning problems in milliseconds where the other a.s.a.o. planners could not consistently find solutions in seconds. This performance was demonstrated both with and without single instruction/multiple data (SIMD) acceleration.

Problem

• Extends RRT-Connect to achieve optimal motion planning
• Balances fast initial solutions with asymptotic optimality
• Demonstrates efficiency in high-DoF robotic arm planning

Innovation

• Extends RRT-Connect with AO-x meta-algorithm
• Ensures probabilistic completeness and asymptotic optimality
• Demonstrates fast convergence in high-DoF robots