Connectivity-Aware Representations for Constrained Motion Planning via Multi-Scale Contrastive Learning

The objective of constrained motion planning is to connect start and goal configurations while satisfying task-specific constraints. Motion planning becomes inefficient or infeasible when the configurations lie in disconnected regions, known as essentially mutually disconnected (EMD) components. Constraints further restrict feasible space to a lower-dimensional submanifold, while redundancy introduces additional complexity because a single end-effector pose admits infinitely many inverse kinematic solutions that may form discrete self-motion manifolds. This paper addresses these challenges by learning a connectivity-aware representation for selecting start and goal configurations prior to planning. Joint configurations are embedded into a latent space through multi-scale manifold learning across neighborhood ranges from local to global, and clustering generates pseudo-labels that supervise a contrastive learning framework. The proposed framework provides a connectivity-aware measure that biases the selection of start and goal configurations in connected regions, avoiding EMDs and yielding higher success rates with reduced planning time. Experiments on various manipulation tasks showed that our method achieves 1.9 times higher success rates and reduces the planning time by a factor of 0.43 compared to baselines.