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Register a new userAn Optimal Algorithm to Solve the Combined Task Allocation and Path Finding Problem
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Added by
Christian Henkel
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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We consider multi-agent transport task problems where, e.g. in a factory setting, items have to be delivered from a given start to a goal pose while the delivering robots need to avoid collisions with each other on the floor. We introduce a Task Conflict-Based Search (TCBS) Algorithm to solve the combined delivery task allocation and multi-agent path planning problem optimally. The problem is known to be NP-hard and the optimal solver cannot scale. However, we introduce it as a baseline to evaluate the sub-optimality of other approaches. We show experimental results that compare our solver with different sub-optimal ones in terms of regret.
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To realize effective heterogeneous multi-robot teams, researchers must leverage individual robots relative strengths and coordinate their individual behaviors. Specifically, heterogeneous multi-robot systems must answer three important questions: textit{who} (task allocation), textit{when} (scheduling), and textit{how} (motion planning). While specific variants of each of these problems are known to be NP-Hard, their interdependence only exacerbates the challenges involved in solving them together. In this paper, we present a novel framework that interleaves task allocation, scheduling, and motion planning. We introduce a search-based approach for trait-based time-extended task allocation named Incremental Task Allocation Graph Search (ITAGS). In contrast to approaches that solve the three problems in sequence, ITAGSs interleaved approach enables efficient search for allocations while simultaneously satisfying scheduling constraints and accounting for the time taken to execute motion plans. To enable effective interleaving, we develop a convex combination of two search heuristics that optimizes the satisfaction of task requirements as well as the makespan of the associated schedule. We demonstrate the efficacy of ITAGS using detailed ablation studies and comparisons against two state-of-the-art algorithms in a simulated emergency response domain.
Efficient utilization of cooperating robots in the assembly of aircraft structures relies on balancing the workload of the robots and ensuring collision-free scheduling. We cast this problem as that of allocating a large number of repetitive assembly tasks, such as drilling holes and installing fasteners, among multiple robots. Such task allocation is often formulated as a Traveling Salesman Problem (TSP), which is NP-hard, implying that computing an exactly optimal solution is computationally prohibitive for real-world applications. The problem complexity is further exacerbated by intermittent robot failures necessitating real-time task reallocation. In this letter, we present an efficient method that exploits workpart geometry and problem structure to initially generate balanced and conflict-free robot schedules under nominal conditions. Subsequently, we deal with the failures by allowing the robots to first complete their nominal schedules and then employing a market-based optimizer to allocate the leftover tasks. Results show an improvement of 11.5% in schedule efficiency as compared to an optimized greedy multi-agent scheduler on a four robot system, which is especially promising for aircraft assembly processes that take many hours to complete. Moreover, the computation times are similar and small, typically hundreds of milliseconds.
We consider the problem of optimal path planning in different homotopy classes in a given environment. Though important in robotics applications, path-planning with reasoning about homotopy classes of trajectories has typically focused on subsets of the Euclidean plane in the robotics literature. The problem of finding optimal trajectories in different homotopy classes in more general configuration spaces (or even characterizing the homotopy classes of such trajectories) can be difficult. In this paper we propose automated solutions to this problem in several general classes of configuration spaces by constructing presentations of fundamental groups and giving algorithms for solving the emph{word problem} in such groups. We present explicit results that apply to knot and link complements in 3-space, discuss how to extend to cylindrically-deleted coordination spaces of arbitrary dimension, and also present results in the coordination space of robots navigating on an Euclidean plane.
The multiple traveling salesman problem (mTSP) is a well-known NP-hard problem with numerous real-world applications. In particular, this work addresses MinMax mTSP, where the objective is to minimize the max tour length (sum of Euclidean distances) among all agents. The mTSP is normally considered as a combinatorial optimization problem, but due to its computational complexity, search-based exact and heuristic algorithms become inefficient as the number of cities increases. Encouraged by the recent developments in deep reinforcement learning (dRL), this work considers the mTSP as a cooperative task and introduces a decentralized attention-based neural network method to solve the MinMax mTSP, named DAN. In DAN, agents learn fully decentralized policies to collaboratively construct a tour, by predicting the future decisions of other agents. Our model relies on the Transformer architecture, and is trained using multi-agent RL with parameter sharing, which provides natural scalability to the numbers of agents and cities. We experimentally demonstrate our model on small- to large-scale mTSP instances, which involve 50 to 1000 cities and 5 to 20 agents, and compare against state-of-the-art baselines. For small-scale problems (fewer than 100 cities), DAN is able to closely match the performance of the best solver available (OR Tools, a meta-heuristic solver) given the same computation time budget. In larger-scale instances, DAN outperforms both conventional and dRL-based solvers, while keeping computation times low, and exhibits enhanced collaboration among agents.
Swarm Intelligence is a metaheuristic optimization approach that has become very predominant over the last few decades. These algorithms are inspired by animals physical behaviors and their evolutionary perceptions. The simplicity of these algorithms allows researchers to simulate different natural phenomena to solve various real-world problems. This paper suggests a novel algorithm called Donkey and Smuggler Optimization Algorithm (DSO). The DSO is inspired by the searching behavior of donkeys. The algorithm imitates transportation behavior such as searching and selecting routes for movement by donkeys in the actual world. Two modes are established for implementing the search behavior and route-selection in this algorithm. These are the Smuggler and Donkeys. In the Smuggler mode, all the possible paths are discovered and the shortest path is then found. In the Donkeys mode, several donkey behaviors are utilized such as Run, Face & Suicide, and Face & Support. Real world data and applications are used to test the algorithm. The experimental results consisted of two parts, firstly, we used the standard benchmark test functions to evaluate the performance of the algorithm in respect to the most popular and the state of the art algorithms. Secondly, the DSO is adapted and implemented on three real-world applications namely; traveling salesman problem, packet routing, and ambulance routing. The experimental results of DSO on these real-world problems are very promising. The results exhibit that the suggested DSO is appropriate to tackle other unfamiliar search spaces and complex problems.
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