Prioritized Multi-agent Path Finding for Differential Drive Robots

Methods for centralized planning of the collision-free trajectories for a fleet of mobile robots typically solve the discretized version of the problem and rely on numerous simplifying assumptions, e.g. moves of uniform duration, cardinal only translations, equal speed and size of the robots etc., thus the resultant plans can not always be directly executed by the real robotic systems. To mitigate this issue we suggest a set of modifications to the prominent prioritized planner -- AA-SIPP(m) -- aimed at lifting the most restrictive assumptions (syncronized translation only moves, equal size and speed of the robots) and at providing robustness to the solutions. We evaluate the suggested algorithm in simulation and on differential drive robots in typical lab environment (indoor polygon with external video-based navigation system). The results of the evaluation provide a clear evidence that the algorithm scales well to large number of robots (up to hundreds in simulation) and is able to produce solutions that are safely executed by the robots prone to imperfect trajectory following. The video of the experiments can be found at https://youtu.be/Fer_irn4BG0.Comment: This is a pre-print version of the paper accepted to ECMR 2019 (https://ieeexplore.ieee.org/document/8870957

Motion Planning for Unlabeled Discs with Optimality Guarantees

We study the problem of path planning for unlabeled (indistinguishable) unit-disc robots in a planar environment cluttered with polygonal obstacles. We introduce an algorithm which minimizes the total path length, i.e., the sum of lengths of the individual paths. Our algorithm is guaranteed to find a solution if one exists, or report that none exists otherwise. It runs in time $\tilde{O}(m^4+m^2n^2)$, where $m$ is the number of robots and $n$ is the total complexity of the workspace. Moreover, the total length of the returned solution is at most $\text{OPT}+4m$, where OPT is the optimal solution cost. To the best of our knowledge this is the first algorithm for the problem that has such guarantees. The algorithm has been implemented in an exact manner and we present experimental results that attest to its efficiency

Pebble Motion on Graphs with Rotations: Efficient Feasibility Tests and Planning Algorithms

We study the problem of planning paths for $p$ distinguishable pebbles (robots) residing on the vertices of an $n$-vertex connected graph with $p \le n$. A pebble may move from a vertex to an adjacent one in a time step provided that it does not collide with other pebbles. When $p = n$, the only collision free moves are synchronous rotations of pebbles on disjoint cycles of the graph. We show that the feasibility of such problems is intrinsically determined by the diameter of a (unique) permutation group induced by the underlying graph. Roughly speaking, the diameter of a group $\mathbf G$ is the minimum length of the generator product required to reach an arbitrary element of $\mathbf G$ from the identity element. Through bounding the diameter of this associated permutation group, which assumes a maximum value of $O(n^2)$, we establish a linear time algorithm for deciding the feasibility of such problems and an $O(n^3)$ algorithm for planning complete paths.Comment: WAFR submissio

Distributed multi-agent pathfinding in horizontal transportation

Horizontal transportation in maritime container terminals plays a crucial role in ensuring safe, efficient, and cost-effective operations. Heavy working machines, such as straddle carriers, trucks, and automated guided vehicles, transport containers between cranes, creating complex routing problems known as multi-agent pathfinding (MAPF) problems. Existing solutions may not adequately address the unique challenges presented by container terminals, necessitating the development of new algorithms. This thesis aims to develop and demonstrate a distributed MAPF algorithm for horizontal transportation in container terminals. The MAPF problem is first formulated as a binary linear programming (BLP) model by expressing the actions in the container terminal using a directed pseudograph. Optimal solutions are obtained using PYOMO, an open-source Python-based optimization software. The Augmented Lagrangian, a graph pathfinding algorithm, and a stochastic element are then employed to create a sub-optimal, distributed algorithm. The developed algorithm is evaluated against an optimal solution and a reference method that prioritizes calculating the path for one agent at a time while taking into account previously calculated paths. A simulator is set up to emulate horizontal transportation in a maritime container terminal, by modeling the terminal as a graph in MATLAB. In the simulator, MAPF algorithms are applied in combination with a high-level coordinator assigning destinations. The experimental part of this thesis investigates the trade-off between solution time (iterations) and solution quality by tuning algorithm parameters and evaluating the performance of the distributed algorithm in comparison to the priority-based method under two different map layouts, particularly addressing the presence of a bottleneck. The results demonstrate the need to adapt the algorithm's parameters and strategies according to specific environments and map layouts, to ensure good performance across various scenarios. The main contribution of this thesis lies in the development of a adaptable, distributed MAPF solution that can ultimately address diverse scenarios and environments. Merikonttiterminaaleissa konttien vaakatasoinen kuljettaminen on keskeinen tekijä turvallisen, tehokkaan ja kustannustehokkaan toiminnan varmistamisessa. Raskaat työkoneet, kuten konttilukit, kuorma-autot ja automaattisti ohjatut ajoneuvot (AGV:t), kuljettavat kontteja nosturien välillä, luoden monimutkaisia reititysongelmia, joita kutsutaan monitoimija-reitinhaku (MAPF) -ongelmiksi. Olemassa olevat ratkaisut eivät riittävästi käsittele konttiterminaaleille asetettuja erityisiä haasteita, mikä edellyttää uusien hajautettujen MAPF-algoritmien kehittämistä. Tämän diplomityön tavoitteena on kehittää ja esitellä hajautettu MAPF-algoritmi vaakasuuntaiseen kuljetukseen konttiterminaaleissa. MAPF-ongelma mallinnetaan ensin binääriseksi lineaariseksi ohjelmointimalliksi (BLP), jossa konttiterminaalissa liikkuminen mallinnetaan suunnattuna pseudograafina. Optimaalisia ratkaisuja tutkitaan käyttämällä PYOMO-ohjelmistoa, joka on avoimen lähdekoodin Python-pohjainen optimointiohjelmisto. Tämän jälkeen laajennettua Lagrangen kertoimien menetelmää, graafin polunetsintä algoritmia ja stokastistista elementtiä käytetään luomaan lähes optimaalinen, hajautettavissa oleva algoritmi. Kehitettyä algoritmia arvioidaan vertaamalla sitä optimaaliseen ratkaisuun ja viite-menetelmään, joka priorisoi polkujen laskemista yhden agentin kerrallaan ottaen huomioon aiemmin lasketut polut. Simulaattori rakennetaan jäljittelemään vaakasuuntaista kuljetusta merikonttiterminaaleissa, mallintamalla terminaali graafina MATLABissa. Simulaattorissa MAPF-algoritmeja sovelletaan yhdessä korkean tason koordinaattorin kanssa, joka määrittelee määränpäät. Diplomityön kokeellisessa osuudessa tarkastellaan ratkaisuajan (iteraatioiden) ja ratkaisun laadun välistä tasapainoa kokeilemalla erilaisia parametreja ja arvioimalla hajautetun algoritmin suorituskykyä verrattuna prioriteettipohjaiseen menetelmään kahden erilaisen karttapohjan päällä, keskittyen erityisesti pullonkaulan lisäämisen tuomiin vaikutuksiin. Tulokset osoittavat, että algoritmin parametrien ja strategioiden mukauttaminen erityisiin ympäristöihin ja karttapohjiin on tarpeen, jos halutaan varmistua tulosten olevan mahdollisimman lähellä optimaalisuutta erilaisissa skenaarioissa. Tämän diplomityön pääasiallinen kontribuutio on joustavan, hajautetun MAPF-ratkaisun kehittäminen, jolla voidaan tulevaisuudessa käsitellä erilaisia tilanteita ja ympäristöjä