Traveled distance minimization and hierarchical strategies for robotic networks

We study the distance optimal assignment of n mobile robots to an equal number of targets under communication and target-sensing constraints. Extending previous results over uniform distributions, we show that when the robots and targets assume the same but arbitrary distribution over the unit square, a carefully designed distributed hierarchical strategy has expected travel distance that matches the best known upper bound assuming global communication and infinite target-sensing range. In a sense, our result shows that for target assignment problems in robotic networks, local optimality also offers good guarantees on global optimality.

[1]  D. Bertsekas.  The auction algorithm: A distributed relaxation method for the assignment problem , 1988 .

[2]  Feng Xue,et al.  On the connectivity and diameter of small-world networks , 2007, Advances in Applied Probability.

[3]  Vikrant Sharma,et al.  Transfer Time Complexity of Conflict-free Vehicle Routing with no Communications , 2007, Int. J. Robotics Res..

[4]  Richard M. Karp,et al.  Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems , 1972, Combinatorial Optimization.

[5]  Sonia Martínez,et al.  Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions , 2006, IEEE Transactions on Automatic Control.

[6]  Panganamala Ramana Kumar,et al.  Fundamentals of Large Sensor Networks: Connectivity, Capacity, Clocks, and Computation , 2009, Proceedings of the IEEE.

[7]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[8]  Jorge Cortes,et al.  Distributed Control of Robotic Networks: A Mathematical Approach to Motion Coordination Algorithms , 2009 .

[9]  Mauro Dell'Amico,et al.  Assignment Problems , 1998, IFIP Congress: Fundamentals - Foundations of Computer Science.

[10]  Seth Hutchinson,et al.  Path planning for permutation-invariant multirobot formations , 2005, IEEE Transactions on Robotics.

[11]  Pravin M. Vaidya.  Geometry helps in matching , 1988, STOC '88.

[12]  Brian D. O. Anderson,et al.  The Multi-Agent Rendezvous Problem. Part 1: The Synchronous Case , 2007, SIAM J. Control. Optim..

[13]  Pravin M. Vaidya,et al.  Geometry helps in matching , 1989, STOC '88.

[14]  H. Kuhn.  The Hungarian method for the assignment problem , 1955 .

[15]  Brian D. O. Anderson,et al.  The Multi-Agent Rendezvous Problem. Part 2: The Asynchronous Case , 2007, SIAM J. Control. Optim..

[16]  János Komlós,et al.  On optimal matchings , 1984, Comb..

[17]  Emilio Frazzoli,et al.  Asymptotically Optimal Algorithms for One-to-One Pickup and Delivery Problems With Applications to Transportation Systems , 2012, IEEE Transactions on Automatic Control.

[18]  B. Bollobás,et al.  Connectivity of random k-nearest-neighbour graphs , 2005, Advances in Applied Probability.

[19]  Francesco Bullo,et al.  Monotonic Target Assignment for Robotic Networks , 2009, IEEE Transactions on Automatic Control.

[20]  Magnus Egerstedt,et al.  Role-Assignment in Multi-Agent Coordination , 2006 .

[21]  Vijay Kumar,et al.  Goal Assignment and Trajectory Planning for Large Teams of Aerial Robots , 2013, Robotics: Science and Systems.

[22]  Micha Sharir,et al.  Vertical Decomposition of Shallow Levels in 3-Dimensional Arrangements and Its Applications , 1999, SIAM J. Comput..

[23]  Francesco Bullo,et al.  Distributed Control of Robotic Networks , 2009 .

[24]  M. Penrose.  The longest edge of the random minimal spanning tree , 1997 .

[25]  Brian D. O. Anderson,et al.  Connectivity of Large Wireless Networks under A Generic Connection Model , 2012, ArXiv.

[26]  Saptarshi Bandyopadhyay,et al.  Phase synchronization control of complex networks of Lagrangian systems on adaptive digraphs , 2013, Autom..

[27]  George J. Pappas,et al.  Flocking in Fixed and Switching Networks , 2007, IEEE Transactions on Automatic Control.

[28]  Dimitri P. Bertsekas,et al.  Parallel synchronous and asynchronous implementations of the auction algorithm , 1991, Parallel Comput..

[29]  M. Talagrand.  The Ajtai-Komlos-Tusnady Matching Theorem for General Measures , 1992 .

[30]  Steven M. LaValle,et al.  Distance optimal formation control on graphs with a tight convergence time guarantee , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[31]  George J. Pappas,et al.  Dynamic Assignment in Distributed Motion Planning With Local Coordination , 2008, IEEE Transactions on Robotics.

[32]  Soon-Jo Chung,et al.  Distance optimal target assignment in robotic networks under communication and sensing constraints , 2014, 2014 IEEE International Conference on Robotics and Automation (ICRA).

[33]  George J. Pappas,et al.  A distributed auction algorithm for the assignment problem , 2008, 2008 47th IEEE Conference on Decision and Control.

[34]  Mathew D. Penrose,et al.  Random Geometric Graphs , 2003 .

[35]  Panganamala Ramana Kumar,et al.  The Number of Neighbors Needed for Connectivity of Wireless Networks , 2004, Wirel. Networks.