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 Lmin . 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
kc
Number of initial configurations
kc′
Number of kc′ best configurations
no
Number of obstacle configurations
no′
Number of no′ best obstacle configurations
γ
Scaling factor for cost function/metric
nnswp
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 γ=0.1 .
Fig. 7: Original PDF constructed using the Riemannian metric ( γ=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.
Metric
Original Dim.
Reshaped Dim.
1284
414
Memory Footprint (Parameters)
Mean ( μ )
4.36\times1004
7.11\times1003
Std Dev ( σ )
2.25\times1004
1.70\times1003
Min
1.08\times1004
5.28\times1003
Max
6.66\times1004
1.19\times1004
TABLE II: Comparison of TT-Cross memory footprint and execution time for original and reshaped tensor dimensions over 15 trials.
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/.
Ananya Trivedi, Sarvesh Prajapati, Zhexin Xu +3
Northeastern University, Boston, Massachusetts, USA. · University of Maryland, College Park, Maryland, USA. · Northeastern University
Spatiotemporal motion planning, especially in multi-robot settings, requires robots to reason about collision-free regions that change over time, which is challenging in continuous spaces when feasible regions are transient and geometrically constrained. We present an algorithmic framework based on graphs of space-time convex sets (ST-GCSs), where collision-free regions are represented as convex sets in space-time and trajectories correspond to paths on the graph together with continuous motions within the selected sets. We formulate time-optimal planning on ST-GCSs as a graph-search problem over path-indexed states and develop a best-first search solver that evaluates partial paths via continuous trajectory optimization, guided by admissible heuristics and dominance checks. We further present an Exact Convex Decomposition (ECD) scheme to reserve trajectory occupancies in space-time, enabling unified handling of dynamic obstacles and multi-robot interactions. For multi-robot motion planning, we integrate ST-GCS planning and ECD into prioritized planning methods and introduce a windowed coordination scheme to improve efficiency. Extensive experiments on single-robot and multi-robot problems demonstrate substantial speedups over various planners while maintaining high solution quality, particularly in environments with narrow and transient feasible regions. Large-scale demonstrations further show that the proposed multi-robot motion planner can solve instances with up to 100 robots within only a few minutes. Project homepage: https://sites.google.com/view/stgcs
Deep learning methods have vastly expanded the capabilities of motion planning in robotics applications, as learning priors from large-scale data has been shown to be essential in capturing the highly complex behavior required for solving tasks such as manipulation or navigation for autonomous vehicles. At the same time, model-based planning algorithms based on search or optimization remain an essential tool due to their flexibility, efficiency, and the ability to incorporate domain knowledge via expert-designed algorithms and objective functions. We propose a new generative framework to unify these two paradigms. First, we learn an autoencoder with a high compression ratio and a latent space of hierarchically ordered, discrete-valued tokens. Leveraging both the dimensionality reduction and the hierarchical coarse-to-fine structure learned by this autoencoder, we then perform motion planning by directly searching in the latent space of tokens. This search can optimize arbitrary objective functions specified at test time, providing a large degree of flexibility while maintaining efficiency and producing realistic solutions by relying on the generative capabilities of the highly compressed autoencoder. We evaluate our method on nuPlan and the Waymo Open Motion Dataset, showing how latent space search can be used for a variety of guided behavior generation tasks, achieving strong performance for closed-loop motion planning and multi-agent guided scenario synthesis without requiring any task-specific training.