Superfast Configuration-Space Convex Set Computation on GPUs for Online Motion Planning

2025-04-15

AI Summary

To address the slow generation and low reliability of convex sets in configuration space for real-time robotic motion planning under dynamic environments, this paper proposes the first GPU-accelerated online probabilistic collision-free convex decomposition method—Safe Convex Sets (SCS). Our approach enables efficient iterative refinement of SCS sequences via parallelized configuration-space inflation, joint SCS optimization, trajectory-guided collision-feedback pruning, and Dynamic Random Map (DRM) search. Furthermore, we integrate piecewise-linear path inflation with nonlinear trajectory optimization subject to convex-set constraints to support perception-closed-loop online planning. Evaluated on standard simulation benchmarks, our method achieves a 17.1× speedup over CPU-based baselines and improves collision-free success rate by 27.9%. Real-world experiments on a KUKA iiwa 7 robot demonstrate millisecond-level response times and high robustness in dynamic settings.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

In this work, we leverage GPUs to construct probabilistically collision-free convex sets in robot configuration space on the fly. This extends the use of modern motion planning algorithms that leverage such representations to changing environments. These planners rapidly and reliably optimize high-quality trajectories, without the burden of challenging nonconvex collision-avoidance constraints. We present an algorithm that inflates collision-free piecewise linear paths into sequences of convex sets (SCS) that are probabilistically collision-free using massive parallelism. We then integrate this algorithm into a motion planning pipeline, which leverages dynamic roadmaps to rapidly find one or multiple collision-free paths, and inflates them. We then optimize the trajectory through the probabilistically collision-free sets, simultaneously using the candidate trajectory to detect and remove collisions from the sets. We demonstrate the efficacy of our approach on a simulation benchmark and a KUKA iiwa 7 robot manipulator with perception in the loop. On our benchmark, our approach runs 17.1 times faster and yields a 27.9% increase in reliability over the nonlinear trajectory optimization baseline, while still producing high-quality motion plans.

Problem

• Construct collision-free convex sets in robot configuration space using GPUs
• Enable real-time motion planning in dynamic environments with convex representations
• Optimize trajectories efficiently while probabilistically avoiding collision constraints

Innovation

• GPU-accelerated convex set computation
• Dynamic roadmap for rapid pathfinding
• Trajectory optimization within collision-free sets