A computational preprint reports that its robot-planning variants delivered the lowest mean path cost on 15 of 21 MotionBenchMaker manipulation problems within a 60-second budget. The same work found that the fixed-budget, random-restart version covered the highest average number of homotopy classes—different route types—in tests on street-view maps. The design separates that fixed-budget policy from a second approach that grows its budget and uses informed expansion.
A broader search over possible routes
The method generalizes GTMP so that edges between adjacent layers of its search graph can be realized by any black-box local planner. The authors list interpolation, splines, sampling-based planning, trajectory optimization and generative sampling among the possible choices, allowing the global search to work with different local planning tools.
Two policies govern the search. Anytime-GTMP uses fixed budgets and random restarts, while AO-GTMP uses monotonically growing budgets with informed expansion. After coverage, the layered-graph search returns a minimum-cost chain in every route class that has been realized.
Promises that depend on assumptions
The formal claims are conditional. Under the stated assumptions, the theory gives high-probability coverage of each class meeting its clearance condition and simultaneous coverage of bounded-length classes. It also says that the chance of missing a class drops exponentially as the number of samples per layer rises, while the number of layers needed falls sublinearly as the local planner becomes stronger.
For Anytime-GTMP, a separate theorem says that if each stage has a positive chance of covering a target class, that class enters the archive almost surely—meaning with probability one in the model. The expected waiting bound is at most 1/pcov stages, and the result is stated simultaneously for every δ-clear class. The guarantee depends on fresh independent stages and a finite family of target classes.
AO-GTMP has a different asymptotic promise. Under its local-planner, sampling-region, clearance and fresh-sample schedule assumptions, the best path length converges almost surely to the optimum. That does not establish finite-budget optimality within a 60-second benchmark; it describes the behavior of the search as the process continues.
What the benchmarks found
On MotionBenchMaker, the evaluation used seven problems for each of three robots—Panda, UR5 and Fetch—and ran 100 trials for every planner–problem pair. The manipulation problems involved robots described as having six to eight degrees of freedom, and the reported cost summary used a 60-second evaluation window.
Across the full time budget, Anytime-GTMP with straight-line collision checking matched FCIT’s final success rate at approximately 85%.
On the common solved set, AO-GTMP had the lowest mean cost on five of seven Panda problems, all seven UR5 problems and five of seven Fetch problems. Anytime-GTMP led on four of seven, three of seven and one of seven respectively; AORRTC led on six of seven Panda problems, three of seven UR5 problems and three of seven Fetch problems. These comparisons exclude trials not solved by every reference planner in the relevant column, so they describe a narrower set than the overall success-rate comparison.
Diversity and cost pull in different directions
The 2D evaluation used street-view maps and a 60-second budget. Every explored start-to-goal path was recorded as an event, assigned a homotopy-invariant label, and pre-clustered with Dynamic Time Warping. The study notes that this clustering procedure is not itself a homotopy invariant, so the result is an observed comparison of route diversity rather than proof that every route class was preserved by the clustering step.
Anytime-GTMP covered the highest average number of homotopy classes on those maps. On the Sydney map, AO-GTMP with RRTC and FCIT each identified one class. The finding is an average observed result, not a claim that every class was found on every map, and it does not establish topological coverage for the higher-degree-of-freedom manipulation problems.
The tests also exposed a budget trade-off inside the planner. Path cost improved until roughly 400 to 600 RRT-Connect iterations and then flattened. Under a fixed overall planning budget, moderate local effort paired with more global sampling dominated heavier local effort in the reported comparison.
AO-GTMP showed a separate trade-off between exploration and concentration. New-sample diversity reached 0.6 just after the first feasible solution, then declined as the informed cost bound tightened. This was a descriptive measure of search behavior, not a direct measure of task performance.
The results remain conditional
Taken together, the study presents a search design that can retain multiple realized route classes while pursuing lower-cost paths, but its guarantees rely on clearance, bounded-length, sampling, local-planner and fresh-sample conditions. The class-aware search also requires labels that compose along concatenated paths and identify homotopy classes.
The authors released the implementation as open-source code. The supplied document is an arXiv version 1 preprint dated 26 Aug 2026, so the evidence reported here remains the stated theory and computational benchmark results.
Paper data and sources
Original title: Anytime Global Tensor Motion Planning
Authors: Sai Coumar, An T. Le, Zachary Kingston
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-26
DOI: Not available
Original paper · Full text