Coupling Tensor Trains with Graph of Convex Sets: Effective Compression, Exploration, and Planning in the C-Space
Gerhard Reinerth, Riddhiman Laha, Marcello Romano
AI summary
Problem
Optimization-based planners require predefined convex characterizations of high-dimensional configuration spaces, which are often intractable, while sampling-based planners struggle with constrained manifolds where random sampling fails to satisfy task constraints.
Approach
The framework uses tensor train decomposition to approximate task-specific probability density functions for targeted sampling of feasible and infeasible regions, then discovers safe convex sets via IRIS to construct a Graph of Convex Sets for shortest-path planning.
Key results
- Principled configuration space exploration using tensor train decomposition
- Enhanced shortest-path planning within convex relaxation frameworks
- Experimentally verified paths with higher manipulability than sampling-based planners
- Demonstrated effective compression and scalability on planar and real robots
Why it matters
Provides a scalable, geometry-aware planning framework that overcomes the curse of dimensionality in robotic configuration spaces, benefiting autonomous systems and complex manipulation tasks.
Abstract
We present TANGO (Tensor ANd Graph Optimiza- tion), a novel motion planning framework that integrates tensor- based compression with structured graph optimization to enable efficient and scalable trajectory generation. While optimization- based planners such as the Graph of Convex Sets (GCS) offer powerful tools for generating smooth, optimal trajectories, they typically rely on a predefined convex characterization of the high-dimensional configuration space—a requirement that is often intractable for general robotic tasks. TANGO builds further by using Tensor Train decomposition to approximate the feasible configuration space in a compressed form, enabling rapid discovery and estimation of task-relevant regions. These regions are then embedded into a GCS-like structure, allowing for geometry-aware motion planning that respects both system constraints and environmental complexity. By coupling tensor- based compression with structured graph reasoning, TANGO enables efficient, geometry-aware motion planning and lays the groundwork for more expressive and scalable representations of configuration space in future robotic systems. Rigorous simulation studies on planar and real robots reinforce our claims of effective compression and higher quality trajectories.