arXiv subjects

Tobias Wallner

Publications and source records attributed to Tobias Wallner.

2 recordsLinked to original sources

arXiv2026

Pass the Bucket: Efficient, Robust, Local Load Balancing for Teams of Heterogeneous Robots

We study the problem of decentralized, self-organized task sharing for a swarm of heterogeneous robots that collaborate in transportation or other objectives that require coordinated motion planning. To this end, we present theoretical and practical results for the simple but effective mechanism of \emph{bucket brigades} for load balancing, in which a team of heterogenous robots share a spatial task in a confined, one-dimensional space, while only being able to sense collisions with neighbors or walls. The goal is to optimize throughput of the overall system, without central control or information, aiming at an interval partition proportional to robot velocities. We address possible chaotic system behavior by developing a stabilization mechanism based on simple local aid, a ``token'', that temporarily decelerates robots after an encounter. This purely local change eliminates persistent oscillations, resulting in convergence towards a stable system state. We accelerate system convergence by comparing a single boundary token to ubiquitous two-directional tokens and optimizing the deceleration factor. Event-driven simulations report convergence times and robustness: For a large variety of perturbations (such as robot deletion, position or velocity jittering), the system reliably re-converges. The results suggest a local, practical mechanism for robust load balancing for heterogeneous teams of robots that promises an effective tool as basis for more complex scenarios.

cs.RO↗

arXiv2025

Sliding Squares in Parallel

We consider algorithmic problems motivated by modular robotic reconfiguration in the sliding square model, in which we are given $n$ square-shaped modules in a (labeled or unlabeled) start configuration and need to find a schedule of sliding moves to transform it into a desired goal configuration, maintaining connectivity of the configuration at all times. Recent work has aimed at minimizing the total number of moves, resulting in fully sequential schedules that perform reconfiguration in $\mathcal{O}(nP)$ moves for arrangements of bounding box perimeter size $P$, or a number of moves linear in the sum of module coordinates in the start and target arrangements. We extend the model to leverage the possibility of parallel motion, thereby reducing worst-case makespans by a factor linear in $n$. Our work presents tight results both in terms of complexity and algorithms: We show that deciding the existence of a single parallel reconfiguration step that solves an instance is NP-complete for unlabeled modules, but can be solved efficiently in the labeled setting. Nevertheless, deciding whether a labeled instance can be solved in two parallel steps is NP-complete. Finally, we describe an algorithm to perform in-place reconfiguration in worst-case optimal $\mathcal{O}(P)$ parallel steps for the unlabeled setting. This algorithm has a straight-forward extension to the labeled setting with slight relaxations to either the reconfiguration time or space constraint.

cs.CG↗