Topological Motion Planning Diffusion: Generative Tangle-Free Path Planning for Tethered Robots in Obstacle-Rich Environments

Yifu Tian; Xinhang Xu; Thien-Minh Nguyen; Muqing Cao

cs.ROMar 16, 2026

Topological Motion Planning Diffusion: Generative Tangle-Free Path Planning for Tethered Robots in Obstacle-Rich Environments

Authors: Yifu Tian, Xinhang Xu, Thien-Minh Nguyen, Muqing Cao

Abstract

In extreme environments such as underwater exploration and post-disaster rescue, tethered robots require continuous navigation while avoiding cable entanglement. Traditional planners struggle in these lifelong planning scenarios due to topological unawareness, while topology-augmented graph-search methods face computational bottlenecks in obstacle-rich environments where the number of candidate topological classes increases. To address these challenges, we propose Topological Motion Planning Diffusion (TMPD), a novel generative planning framework that integrates lifelong topological memory. Instead of relying on sequential graph search, TMPD leverages a diffusion model to propose a multimodal front-end of kinematically feasible trajectory candidates across various homotopy classes. A tether-aware topological back-end then filters and optimizes these candidates by computing generalized winding numbers to evaluate their topological energy against the accumulated tether configuration. Benchmarking in obstacle-rich simulated environments demonstrates that TMPD achieves a collision-free reach of 100% and a tangle-free rate of 97.0%, outperforming traditional topological search and purely kinematic diffusion baselines in both geometric smoothness and computational efficiency. Simulation with realistic cable dynamics further validates the practicality of the proposed approach.

Figures & tables

Fig. 1 : Paths $\tau_{1}$ and $\tau_{2}$ (blue) belong to the same homotopy class as they can be continuously deformed into each other within the obstacle-free space. Path $\tau_{3}$ (orange) represents a distinct homotopy class, circumventing $O_{i}$ from the opposite side. The generalized winding number evaluates the accumulated angle $\int d\theta$ along the path relative to the obstacle center $o_{i}$ .

Fig. 2 : At the $k$ -th step, the robot at $g_{k-1}$ is constrained by the history trajectory $\tau_{hist}^{(k)}$ (blue solid line) anchored at $g_{0}$ . A kinematically feasible but topologically naive segment $\tau^{(k)}$ (red dashed line) heading directly to $g_{k}$ causes the global trajectory $\tau_{global}^{(k)}$ to entangle around obstacle $O_{i}$ , violating the threshold $|W|<W_{th}$ . $\tau^{(k)*}$ (green dashed line) is a valid tangle-free trajectory.

Fig. 3 : The robot currently resides at $g_{k-1}$ , with the dark blue line representing the executed history trajectory $\tau_{hist}^{(k)}$ (i.e., the current physical cable configuration). The diffusion model generates a candidate pool $\mathcal{T}_{cand}$ (red lines) connecting $g_{k-1}$ to the target $g_{k}$ , exploring diverse topological branches ( $\mathcal{H}_{1}\dots\mathcal{H}_{5}$ ). Tthe topological back-end then concatenates a specific candidate—in this case, a trajectory from the $\mathcal{H}_{4}$ branch—with the history. The cyan dashed line illustrates its resulting global taut configuration $\text{Hom}(\tau_{global}^{(k)})$ .

Fig. 4 : While MPD (blue) often produces irregular trajectories that unnecessarily skirt obstacle boundaries, our TMPD (dark red) utilizes topological energy and kinematic penalties to recover optimal, smooth, and safe paths.

Method	Collision-free Reach	Topo-Energy	Length	Smoothness	Time
MPD	100.0%	$3.93\pm 1.54$	$1.68\pm 0.37$	$2544.11\pm 662.21$	$0.56s$
TMPD (Ours)	100.0%	$3.67\pm 1.35$	$1.72\pm 0.41$	$491.76\pm 233.01$	$1.03s$

TABLE I : Results for 100 Trials

Fig. 5 : From left to right: Topo-A*, Topo-RRT, MPD, and our proposed TMPD. The grey circles represent randomly added obstacles, while the red squares denote fixed obstacles used during training. The blue lines indicate the execution history.

Note: TMPD uses $\sigma_{extra}=0.8$ , $\tau_{guide}=0.1$ .
Method	Collision-free Reach ( $\uparrow$ )	Tangle-free ( $\uparrow$ )	Time (s) ( $\downarrow$ )	Topo-Energy ( $\downarrow$ )	Path Length ( $\downarrow$ )	Smoothness ( $\downarrow$ )
Topo-RRT	$90.2\%$	$86.0\%$	$3.68\pm 9.65$	$4.54\pm 2.38$	$1.920\pm 0.37$	$535.46\pm 132.19$
Topo-A*	$98.0\%$	$93.0\%$	$2.01\pm 1.94$	$4.87\pm 2.25$	$1.279\pm 0.18$	$159.907\pm 35.948$
MPD	$96.8\%$	$40.0\%$	$0.93\pm 1.61$	$5.93\pm 2.17$	$1.538\pm 0.19$	$343.87\pm 72.55$
TMPD (Ours)	$\mathbf{100.0\%}$	$97.0\%$	$1.35\pm 0.13$	$4.74\pm 2.44$	$1.660\pm 0.27$	$344.63\pm 76.70$

TABLE II : Comparison of TMPD against Baseline Planners in Lifelong Navigation

Hyperparameter	Value	Tangle-free ( $\uparrow$ )	Time (s) ( $\downarrow$ )	Smoothness ( $\downarrow$ )
Noise Scale ( $\sigma_{extra}$ )	$0.5$	$89.0\%$	$\mathbf{1.54\pm 0.20}$	$56.29\pm 26.82$
	$\mathbf{0.8}$	$\mathbf{95.0\%}$	$1.59\pm 0.18$	$54.66\pm 25.62$
	$1.8$	$92.0\%$	$2.35\pm 0.50$	$42.97\pm 28.33$
	$3.0$	$83.0\%$	$2.27\pm 0.63$	$\mathbf{24.47\pm 27.62}$
Candidate Pool ( $N_{samples}$ )	$30$	$93.0\%$	$\mathbf{1.52\pm 0.11}$	$54.69\pm 26.25$
	$\mathbf{70}$	$\mathbf{97.0\%}$	$1.67\pm 0.21$	$54.87\pm 25.42$

TABLE III : Ablation Study of TMPD Hyperparameters

Fig. 6 : The physical tether (green) is in a semi-enclosed wrapped state. While the generative front-end proposes multiple spatial candidates (white), TMPD identifies the topologically optimal, tangle-free trajectory (yellow) to safely proceed without entanglement.

Motion Planning

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

See all 405 papers

Entanglement-Free Trajectory Planning for Tethered Mobile Robots with a Slack Tether
Aug 10, 2026Gianpietro Battocletti, Dimitris Boskos, Bart De SchutterConstrained Motion Planning Kinodynamic Motion Planning
Delft Center for Systems and Control, Delft University of Technology, Delft, The Netherlands
TAPE: Tether-Aware Path Planning for Autonomous Exploration of Unknown 3D Cavities Using a Tangle-Compatible Tethered Aerial Robot
Jun 29, 2026Louis Petit, Alexis Lussier DesbiensAerial Robotics Mobile Robotics
Createk Design Lab, University of Sherbrooke, Sherbrooke, J1K 2R1, Canada
Tension Tells the Tail: Cable-Obstacle Interaction Sensing for Tethered Mobile Robot Navigation
Oct 17, 2026Ryuki Shimada, Koki Suzuki, Genya IshigamiSafe Robot Navigation Robot Navigation
The authors are with the Space Robotics Group, Department of Mechanical Engineering, Keio University, Yokohama, Kanagawa 223-8522, Japan.

Aug 10, 2026J/K move · Enter open · S save

Entanglement-Free Trajectory Planning for Tethered Mobile Robots with a Slack Tether

Gianpietro Battocletti, Dimitris Boskos, Bart De Schutter

Delft Center for Systems and Control, Delft University of Technology, Delft, The Netherlands

Constrained Motion Planning Kinodynamic Motion Planning Trajectory Generation Safe Motion Planning Robot Motion Planning

Open paper AskPDF arXiv

In motion planning algorithms for tethered mobile robots, the entanglement state of the tether is a critical aspect to consider during the planning phase. This is particularly important in case of a slack tether, where the shape of the tether is not determined solely by the geometry of the environment and the location of the obstacles, but also by the dynamics of the tether, by the trajectory followed by the robot, and possibly by exogenous forces. In this scenario, preventing entanglement requires planning a robot trajectory that accounts for the entanglement definition and for the dynamics of the robot and of the tether. In this work, we propose a motion planning algorithm for tethered mobile robots with a slack tether that computes dynamically feasible entanglement-free trajectories to navigate through an environment with static obstacles. By considering the entanglement state during all the stages of the planning pipeline, we are able to compute safer trajectories that avoid entanglement during the motion of the robot. We achieve this through a three-step pipeline, which includes (i) the construction of a topological model of the entanglement-free configuration space of the tethered robot, (ii) the generation of a set of candidate paths using this model, and (iii) the computation of a dynamically feasible entanglement-free trajectory by solving a homotopy-constrained trajectory generation problem. The resulting trajectory can then be executed to lead the robot to its target location, while maintaining the tether in an entanglement-free configuration. We demonstrate the benefits of this algorithm in simulations, where we show how the planning algorithm avoids violations of the entanglement constraints, resulting in safer and more reliable trajectories.

Abstract

Motion Planning

Explore similar work

Entanglement-Free Trajectory Planning for Tethered Mobile Robots with a Slack Tether

TAPE: Tether-Aware Path Planning for Autonomous Exploration of Unknown 3D Cavities Using a Tangle-Compatible Tethered Aerial Robot

Tension Tells the Tail: Cable-Obstacle Interaction Sensing for Tethered Mobile Robot Navigation