Accelerating Mixed Discrete-Continuous Motion Planning via Neural Graphs of Convex Sets

2026-08-15

AI Summary

This study addresses the computational bottleneck of online replanning in Graphs of Convex Sets (GCS) for hybrid discrete-continuous motion planning by proposing a learning-based acceleration strategy. Specifically, we employ Graph Attention Networks to predict and rank candidate paths, replacing expensive convex relaxation steps with efficient neural network forward passes while incorporating an early-stopping mechanism. Evaluated across diverse robotic tasks, this approach achieves up to two orders of magnitude speedup compared to standard GCS solvers. Crucially, it maintains a 100% success rate with only negligible suboptimality, effectively resolving the challenge of meeting real-time requirements within the GCS framework for online planning applications.

Abstract

Motion planning problems such as collision-free navigation and contact-rich manipulation can be naturally formulated as optimization problems that couple discrete decisions with continuous trajectories. The Graphs of Convex Sets (GCS) framework offers a practical solution to these problems. It represents discrete decisions as nodes of a graph and encodes continuous trajectories in the edges connecting them. However, the resulting optimization subproblems can become computationally prohibitive for online replanning. In this work, we propose a learning-based strategy to mitigate this limitation. Specifically, we replace the costly convex relaxation step required by nominal GCS with a single forward pass through a Graph Attention Network that predicts a set of highly probable candidate paths through the graph. A lightweight ranking network then orders these candidates by their estimated trajectory cost. Evaluating them in this order, we terminate our search early while still recovering a near-optimal motion plan. We validate the resulting pipeline across diverse robotic tasks, including collision-free motion planning for a 3D quadrotor and a 7-DoF manipulator, and planning through contact for planar pushing. Across both convex and non-convex cost and constraint settings, our approach yields up to two orders of magnitude speedup over nominal GCS while maintaining a 100% success rate, at the cost of some suboptimality in the recovered solutions. Code implementations and video demonstrations can be found at https://neural-gcs.github.io/.

Problem

• Motion Planning
• Graphs of Convex Sets
• Computational Efficiency
• Online Replanning
• Mixed Discrete-Continuous Optimization

Innovation

• Graphs of Convex Sets
• Graph Attention Network
• Mixed Discrete-Continuous Motion Planning
• Learning-based Planning
• Convex Relaxation