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

Abstract

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.

Figures (10)

• Figure 1: Our algorithm enables a task-specific sampling metric for approximating the feasible configuration space for a system. These approximated regions are then used for discovering a convex structured graph for effective motion planning within the actuator bounds. Note that the larger the size of the node, the larger is the volume of the corresponding convex set.
• Figure 2: Representation of high-dimensional space using TT approximation. Note the decomposition into the different tensor cores.
• Figure 3: An overview of our TANGO algorithm is illustrated as follows. We begin by sampling the configuration space and constructing an inverse probability density function (PDF) using a chosen task metric $L_{min}$. From this distribution, samples are drawn and classified into feasible and infeasible categories. These classifications, along with IRIS, enable the discovery of safe convex regions within the configuration space. Finally, a shortest-path search over the discovered convex sets yields the resulting trajectory from start to goal configuration.
• Figure 4: Executed robot trajectory from start configuration (red sphere) to goal configuration (green sphere) using TANGO. It should be noted that, due to the presence of joint limits, the geodesically shortest path in the configuration space does not necessarily correspond to the shortest path in the task (operational) space.
• Figure 5: Safe convex sets and path planning. The blue convex sets are used for planning with TANGO, and the red convex sets represent obstacles in the configuration space. The final path is shown in white.