An Optimal Algorithm to Solve the Combined Task Allocation and Path Finding Problem

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 multiagent 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.

[1]  Alexander Zelinsky,et al.  A mobile robot exploration algorithm , 1992, IEEE Trans. Robotics Autom..

[2]  Illah R. Nourbakhsh,et al.  Heterogeneous Multirobot Coordination with Spatial and Temporal Constraints , 2005, AAAI.

[3]  Nathan R. Sturtevant,et al.  Conflict-based search for optimal multi-agent pathfinding , 2012, Artif. Intell..

[4]  Nidhi Kalra,et al.  Market-Based Multirobot Coordination: A Survey and Analysis , 2006, Proceedings of the IEEE.

[5]  Peter Norvig,et al.  Artificial Intelligence: A Modern Approach , 1995 .

[6]  Enrico Pagello,et al.  Advanced approaches for multi-robot coordination in logistic scenarios , 2017, Robotics Auton. Syst..

[7]  Gary B. Lamont,et al.  A genetic algorithm for unmanned aerial vehicle routing , 2005, GECCO '05.

[8]  Richard F. Hartl,et al.  A survey on pickup and delivery problems , 2008 .

[9]  Harold W. Kuhn,et al.  The Hungarian method for the assignment problem , 1955, 50 Years of Integer Programming.

[10]  M. Sol.  The general pickup and delivery problem , 2010 .

[11]  Lynne E. Parker,et al.  ALLIANCE: an architecture for fault tolerant multirobot cooperation , 1998, IEEE Trans. Robotics Autom..

[12]  Sven Koenig,et al.  Optimal Target Assignment and Path Finding for Teams of Agents , 2016, AAMAS.

[13]  Michal Pechoucek,et al.  Multi-agent RRT: sampling-based cooperative pathfinding , 2013, AAMAS.

[14]  Jesfis Peral,et al.  Heuristics -- intelligent search strategies for computer problem solving , 1984 .

[15]  Stuart J. Russell,et al.  Combined Task and Motion Planning for Mobile Manipulation , 2010, ICAPS.

[16]  Eiichi Taniguchi,et al.  Optimal size and location planning of public logistics terminals , 1999 .

[17]  Prithviraj Dasgupta,et al.  Multirobot Task Allocation with Real-Time Path Planning , 2013, FLAIRS.

[18]  Emilio Frazzoli,et al.  Provably safe and deadlock-free execution of multi-robot plans under delaying disturbances , 2016, 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS).

[19]  Sophie N. Parragh,et al.  A survey on pickup and delivery problems Part I : Transportation between customers and depot , 2007 .

[20]  Roni Stern,et al.  The Increasing Cost Tree Search for Optimal Multi-Agent Pathfinding , 2011, IJCAI.

[21]  Refael Hassin,et al.  Multi-Color Pebble Motion on Graphs , 2009, Algorithmica.

[22]  Sven Koenig,et al.  Lifelong Multi-Agent Path Finding for Online Pickup and Delivery Tasks , 2017, AAMAS.

[23]  Gérard Cornuéjols,et al.  An algorithmic framework for convex mixed integer nonlinear programs , 2008, Discret. Optim..

[24]  David G. Lowe,et al.  Scalable Nearest Neighbor Algorithms for High Dimensional Data , 2014, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[25]  Felipe Garcia Lopez,et al.  Cloud-based cooperative navigation for mobile service robots in dynamic industrial environments , 2017, SAC.

[26]  J. Tanchoco,et al.  Intersection graph method for AGV flow path design , 1991 .

[27]  Ronald Kube,et al.  Cooperative transport by ants and robotsC , 1998 .

[28]  Torsten Schaub,et al.  Generalized Target Assignment and Path Finding Using Answer Set Programming , 2017, IJCAI.

[29]  David Silver,et al.  Cooperative Pathfinding , 2005, AIIDE.

[30]  A. Kleiner,et al.  ARMO: Adaptive road map optimization for large robot teams , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[31]  Steven M. LaValle,et al.  Structure and Intractability of Optimal Multi-Robot Path Planning on Graphs , 2013, AAAI.

[32]  Hoong Chuin Lau,et al.  Pickup and Delivery with Time Windows: Algorithms and Test Case Generation , 2002, Int. J. Artif. Intell. Tools.