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

Gerhard Reinerth; Riddhiman Laha; Marcello Romano

cs.ROMar 12, 2026

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

Authors: Gerhard Reinerth, Riddhiman Laha, Marcello Romano

Organizations: Technical University of Munich, Germany · Northeastern University, Boston, USA

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 & tables

Fig. 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.

Fig. 2: Representation of high-dimensional space using TT approximation. Note the decomposition into the different tensor cores.

Fig. 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.

Notation	Corresponding Description
$k_{c}$	Number of initial configurations
$k^{\prime}_{c}$	Number of $k^{\prime}_{c}$ best configurations
$n_{o}$	Number of obstacle configurations
$n^{\prime}_{o}$	Number of $n^{\prime}_{o}$ best obstacle configurations
$\gamma$	Scaling factor for cost function/metric
$n_{nswp}$	Number of TT-Cross iterations

TABLE I: Tunable parameters in TANGO.

Fig. 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.

Fig. 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.

Fig. 6: Original pdf (top) and TT-Cross approximation (bottom) for the Yoshikawa metric. The red points (bottom picture) denote samples taken from the TTD. Regions with a higher probability are sampled more likely. For illustrative and visualization purposes, we fixed the scaling parameter value to $\gamma=0.1$ .

Fig. 7: Original PDF constructed using the Riemannian metric ( $\gamma=1.0$ ). The Riemannian metric results in comparatively more favorable manipulability configurations, whereas the Yoshikawa metric induces a more restricted spatial domain characterized by high-manipulability regions.

Fig. 8: TT-Cross approximation of the PDF. The red points here denote samples taken from the TTD. Regions with a higher probability are sampled more likely.

Fig. 9: Performance evaluation of TANGO and RRT. Execution times of executed trajectories (left), PDF-Score (middle), and number of resulting waypoints (right). The execution times of the generated trajectories are, on average higher for TANGO, while having a better PDF Score (higher values indicate better performance). TANGO requires in general, fewer waypoints, leading to smooth trajectories after further refinement.

Fig. 10: Comparison between a naive RRT and TANGO. The plots show that our Riemannian sampling strategy in TANGO leads to approximate convergence in less time (left) and fewer waypoints (right) for different runs.

Memory Footprint (Parameters)
Metric	Original Dim.	Reshaped Dim.
	$128^{4}$	$4^{14}$
Mean ( $\mu$ )	$4.36\text{\times}{10}^{04}$	$7.11\text{\times}{10}^{03}$
Std Dev ( $\sigma$ )	$2.25\text{\times}{10}^{04}$	$1.70\text{\times}{10}^{03}$
Min	$1.08\text{\times}{10}^{04}$	$5.28\text{\times}{10}^{03}$
Max	$6.66\text{\times}{10}^{04}$	$1.19\text{\times}{10}^{04}$

TABLE II: Comparison of TT-Cross memory footprint and execution time for original and reshaped tensor dimensions over

15

trials.

Motion Planning

Motion planning finds safe, feasible paths and trajectories for robots and vehicles amid geometric, dynamic, and task constraints.

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Motion planning problems such as collision-free navigation and contact-rich manipulation can be naturally formulated as optimization problems that couple discrete decisions with continuous trajectories. The Graphs of Convex Sets (GCS) framework offers a practical solution to these problems. It represents discrete decisions as nodes of a graph and encodes continuous trajectories in the edges connecting them. However, the resulting optimization subproblems can become computationally prohibitive for online replanning. In this work, we propose a learning-based strategy to mitigate this limitation. Specifically, we replace the costly convex relaxation step required by nominal GCS with a single forward pass through a Graph Attention Network that predicts a set of highly probable candidate paths through the graph. A lightweight ranking network then orders these candidates by their estimated trajectory cost. Evaluating them in this order, we terminate our search early while still recovering a near-optimal motion plan. We validate the resulting pipeline across diverse robotic tasks, including collision-free motion planning for a 3D quadrotor and a 7-DoF manipulator, and planning through contact for planar pushing. Across both convex and non-convex cost and constraint settings, our approach yields up to two orders of magnitude speedup over nominal GCS while maintaining a 100% success rate, at the cost of some suboptimality in the recovered solutions. Code implementations and video demonstrations can be found at https://neural-gcs.github.io/.

Abstract

Motion Planning

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