Coupling Tensor Trains with Graph of Convex Sets: Effective Compression, Exploration, and Planning in the C-Space

We present TANGO (Tensor ANd Graph Optimization), 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.