A Spectral-Linear Trajectory Representation for Guided Diffusion-Based Manipulator Motion Planning in Constrained Environments
TL;DR
Spectral-linear representation is introduced as a compact joint-space representation that combines an endpoint-conditioned linear reference path with a small set of globally supported eigenmodes derived from a conditioned temporal kernel that is more predictive of bottleneck success than latent width alone.
Abstract
Guided diffusion planners for robot manipulators often fail in bottleneck scenes. The reason is that local collision corrections must be coordinated through a limited latent parameterization. This study examines the issue at the level of trajectory representation. Spectral-linear representation is introduced as a compact joint-space representation that combines an endpoint-conditioned linear reference path with a small set of globally supported eigenmodes derived from a conditioned temporal kernel. Using a shared training corpus, conditioning scheme, guidance rule, and dense-evaluation protocol, spectral-linear representation is compared with five representative alternatives across six representation families and dimensionality sweeps from 14 to 448 dimensions. With 14 latent dimensions, spectral-linear representation attains the highest structured-scene success rates among the tested families, reaching 74.2% on narrow-passage scenes and 84.5% on rack-like scenes. Expert-only controls, per-family guidance tuning, and a Transformer-backbone rerun are consistent with the same broad ranking pattern. These results indicate that, under limited guidance budgets and within the tested protocol, the representation structure is more predictive of bottleneck success than latent width alone.