Abstract
Considering an environment containing polygonal obstacles, we address the problem of planning motions for a pair of planar robots connected to one another via a cable of limited length. Much like prior problems with a single robot connected via a cable to a fixed base, straight line-of-sight visibility plays an important role. The present paper shows how the reduced visibility graph provides a natural discretization and captures the essential topological considerations very effectively for the two robot case as well. Unlike the single robot case, however, the bounded cable length introduces considerations around coordination (or equivalently, when viewed from the point of view of a centralized planner, relative timing) that complicates the matter. Indeed, the paper has to introduce a rather more involved formalization than prior single-robot work in order to establish the core theoretical result—a theorem permitting the problem to be cast as one of finding paths rather than trajectories. Once affirmed, the planning problem reduces to a straightforward graph search with an elegant representation of the connecting cable, demanding only a few extra ancillary checks that ensure sufficiency of cable to guarantee feasibility of the solution. We describe our implementation of A\({}^\star \) search, and report experimental results. Lastly, we prescribe an optimal execution for the solutions provided by the algorithm.
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Notes
We find it convenient to use \(\mathfrak {L}\left[ f\right] \) to denote arc length of functions \(f: \mathbb {I}\rightarrow \mathscr {W}\) throughout this work.
Another fact is that checking whether two paths, one for each robot, will satisfy the cable length constraint when executed concurrently depends on the speeds at which they move; hence, that paper ought to have made some such assumption, as done in Sect. 6.
Technically one must consider a manifold with a boundary, and the notion of ‘chart’ here may be closed set; for simplicity throughout we will ignore these nuances.
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Acknowledgements
This work was supported, in part, by the National Science Foundation through awards IIS-1453652 and IIS-1849249. Figure 1, whose author is Cactus26, is used without any further edits under Creative Commons Attribution-Share Alike 3.0 Unported license https://creativecommons.org/licenses/by-sa/3.0/deed.en.
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Teshnizi, R.H., Shell, D.A. Motion planning for a pair of tethered robots. Auton Robot 45, 693–707 (2021). https://doi.org/10.1007/s10514-021-09972-x
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DOI: https://doi.org/10.1007/s10514-021-09972-x