A Disjunctive Programming Approach for Motion Planning of Mobile Router Networks

In this paper we develop a framework based on disjunctive programming for motion planning of robotic networks. Although the methodology presented in this paper can be applied to general motion planning problems we focus on coordinating a team of mobile routers to maintain connectivity between a fixed base station and a mobile user within a walled environment. This connectivity management problem is decomposed into three steps: (i) a feasible line-of-sight path between the base station and the mobile user is computed; (ii) the number of required routers and their goal locations are determined; and (iii) the motion planning with obstacle and inter-vehicle collision avoidance problem is solved. To illustrate the flexibility of the proposed approach we also formulate a novel motion planning algorithm for a team of mobile robots as a disjunctive program. Cell decomposition is used to take into account the size and orientation of the robots. In both cases, connectivity and motion planning, the mixed-integer optimization problems are solve using CPLEX. Moreover, the proposed approach can easily accommodate input and other constraints and mission objectives. Simulation results show the applicability of the proposed strategy.

[1]  Jean-Claude Latombe,et al.  Robot Motion Planning with Uncertainty in Control and Sensing , 1991, Artif. Intell..

[2]  L. Blackmore,et al.  Optimal manipulator path planning with obstacles using disjunctive programming , 2006, 2006 American Control Conference.

[3]  Yasamin Mostofi,et al.  Decentralized Communication-Aware Motion Planning in Mobile Networks: An Information-Gain Approach , 2009, J. Intell. Robotic Syst..

[4]  Eric W. Frew.  Information-Theoretic Integration of Sensing and Communication for Active Robot Networks , 2009, Mob. Networks Appl..

[5]  H. Hashemi,et al.  The indoor radio propagation channel , 1993, Proc. IEEE.

[6]  Karl Henrik Johansson,et al.  Decentralized connectivity maintenance in mobile networks with bounded inputs , 2008, 2008 IEEE International Conference on Robotics and Automation.

[7]  J. Schwartz,et al.  On the “piano movers” problem. II. General techniques for computing topological properties of real algebraic manifolds , 1983 .

[8]  Micha Sharir,et al.  An efficient motion-planning algorithm for a convex polygonal object in two-dimensional polygonal space , 1990, Discret. Comput. Geom..

[9]  Jean-Daniel Boissonnat,et al.  A practical exact motion planning algorithm for polygonal object amidst polygonal obstacles , 1988, Geometry and Robotics.

[10]  Giuseppe Notarstefano,et al.  Maintaining limited-range connectivity among second-order agents , 2006, 2006 American Control Conference.

[11]  George J. Pappas,et al.  Distributed connectivity control of mobile networks , 2007, 2007 46th IEEE Conference on Decision and Control.

[12]  Sven Koenig,et al.  Performance bounds for planning in unknown terrain , 2003, Artif. Intell..

[13]  Hui X. Li,et al.  A probabilistic approach to optimal robust path planning with obstacles , 2006, 2006 American Control Conference.

[14]  Rafael Fierro,et al.  A Geometric Optimization Approach to Detecting and Intercepting Dynamic Targets , 2007, 2007 American Control Conference.

[15]  E. Balas.  Disjunctive programming and a hierarchy of relaxations for discrete optimization problems , 1985 .

[16]  R.M. Murray,et al.  Motion planning with wireless network constraints , 2005, Proceedings of the 2005, American Control Conference, 2005..

[17]  Silvia Ferrari,et al.  Information-Driven Sensor Path Planning by Approximate Cell Decomposition , 2009, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[18]  Abbas Jamalipour,et al.  Wireless communications , 2005, GLOBECOM '05. IEEE Global Telecommunications Conference, 2005..

[19]  Randy A. Freeman,et al.  Distributed Cooperative Active Sensing Using Consensus Filters , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[20]  Douglas W. Gage,et al.  The DARPA LANdroids program , 2009, Defense + Commercial Sensing.

[21]  Yasamin Mostofi,et al.  Communication-aware navigation functions for cooperative target tracking , 2009, 2009 American Control Conference.

[22]  Richard C. Larson,et al.  Model Building in Mathematical Programming , 1979 .

[23]  B. Moor,et al.  Mixed integer programming for multi-vehicle path planning , 2001, 2001 European Control Conference (ECC).

[24]  Rafael Fierro,et al.  Prioritized sensor detection via dynamic Voronoi-based navigation , 2009, 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[25]  R. Fierro,et al.  Decentralized cooperative control - A multivehicle platform for research in networked embedded systems , 2007, IEEE Control Systems.

[26]  I. Grossmann,et al.  New algorithms for nonlinear generalized disjunctive programming , 2000 .

[27]  Patrick Doherty,et al.  Positioning unmanned aerial vehicles as communication relays for surveillance tasks , 2009, Robotics: Science and Systems.

[28]  R. Fierro,et al.  Hierarchical Optimization Strategies for Deployment of Mobile Robots , 2006 .

[29]  Mac Schwager,et al.  Decentralized, Adaptive Coverage Control for Networked Robots , 2009, Int. J. Robotics Res..

[30]  Howie Choset,et al.  Path Planning for Robotic Demining: Robust Sensor-Based Coverage of Unstructured Environments and Probabilistic Methods , 2003, Int. J. Robotics Res..

[31]  Sonia Martínez,et al.  Coverage control for mobile sensing networks , 2002, IEEE Transactions on Robotics and Automation.

[32]  R. Raman,et al.  Modelling and computational techniques for logic based integer programming , 1994 .

[33]  Jean-Claude Latombe,et al.  Robot motion planning , 1970, The Kluwer international series in engineering and computer science.

[34]  Andrea Goldsmith,et al.  Wireless Communications , 2005, 2021 15th International Conference on Advanced Technologies, Systems and Services in Telecommunications (TELSIKS).

[35]  Emilio Frazzoli,et al.  Efficient routing of multiple vehicles with no explicit communications , 2008 .

[36]  Wei Yang,et al.  Robotic Routers: Algorithms and Implementation , 2009, Int. J. Robotics Res..

[37]  M. Ani Hsieh,et al.  An Optimal Approach to Collaborative Target Tracking with Performance Guarantees , 2009, J. Intell. Robotic Syst..

[38]  J. How,et al.  Mixed-integer programming for control , 2005, Proceedings of the 2005, American Control Conference, 2005..

[39]  Vijay Kumar,et al.  Connectivity management in mobile robot teams , 2008, 2008 IEEE International Conference on Robotics and Automation.