A mixed integer programming model for timed deliveries in multirobot systems

We present a solution that enables robots to operate in long-duration missions with minimal interruption for recharging or refreshing other resources. Consider a set of deployed “task robots” that request resources (e.g. batteries) from a distribution center, which can deploy “delivery robots” to fulfill those requests. We address the scheduling problem with multiple incoming time-bound requests from the task robots. Our proposed framework incorporates priorities on working robots that can be adjusted by a human operator during scheduling, since mission priorities can change over time. The framework allows a relaxed delivery schedule when available resources are scant and permits dynamic re-routing of delivery robots. The problem is posed as a variant of the Vehicle Routing Problem with Time Windows, and solved as a Mixed Integer Quadratic Program using a branch and bound based solver. We present the specific case of a battery distribution system and validate the results in simulation.

[1]  Panos M. Pardalos,et al.  Quadratic programming with one negative eigenvalue is NP-hard , 1991, J. Glob. Optim..

[2]  Gaurav S. Sukhatme,et al.  Staying alive: a docking station for autonomous robot recharging , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[3]  Y. Edan,et al.  Vision-Based Autonomous Robot Self-Docking and Recharging , 2006, 2006 World Automation Congress.

[4]  Henrik Schiøler,et al.  Potentially Distributable Energy: Towards Energy Autonomy in Large Population of Mobile Robots , 2007, 2007 International Symposium on Computational Intelligence in Robotics and Automation.

[5]  Emilio Frazzoli,et al.  Dynamic vehicle routing with heterogeneous demands , 2008, 2008 47th IEEE Conference on Decision and Control.

[6]  Joao P. Hespanha,et al.  Dynamic vehicle routing with moving demands - Part I: Low speed demands and high arrival rates , 2009, 2009 American Control Conference.

[7]  Joao P. Hespanha,et al.  Dynamic vehicle routing with moving demands - Part II: High speed demands or low arrival rates , 2009, 2009 American Control Conference.

[8]  Tobias Achterberg,et al.  SCIP: solving constraint integer programs , 2009, Math. Program. Comput..

[9]  Richard T. Vaughan,et al.  Adaptive mobile charging stations for multi-robot systems , 2009, 2009 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[10]  Emilio Frazzoli,et al.  Dynamic Vehicle Routing with Priority Classes of Stochastic Demands , 2009, SIAM J. Control. Optim..

[11]  Vijay Kumar,et al.  Energy-aware coverage control with docking for robot teams , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[12]  Nathan Michael,et al.  Multi-robot persistent surveillance planning as a Vehicle Routing Problem , 2011, 2011 IEEE International Conference on Automation Science and Engineering.

[13]  Mac Schwager,et al.  Persistent monitoring of changing environments using a robot with limited range sensing , 2011, 2011 IEEE International Conference on Robotics and Automation.

[14]  James R. Morrison,et al.  UAV Consumable Replenishment: Design Concepts for Automated Service Stations , 2011, J. Intell. Robotic Syst..

[15]  Jonathan P. How,et al.  Automated Battery Swap and Recharge to Enable Persistent UAV Missions , 2011 .

[16]  Emilio Frazzoli,et al.  Linear temporal logic vehicle routing with applications to multi‐UAV mission planning , 2011 .

[17]  James R. Morrison,et al.  Automatic Battery Replacement System for UAVs: Analysis and Design , 2011, Journal of Intelligent & Robotic Systems.

[18]  Steven Lake Waslander,et al.  A graph-based approach to multi-robot rendezvous for recharging in persistent tasks , 2013, 2013 IEEE International Conference on Robotics and Automation.

[19]  James R. Morrison,et al.  On the Concerted Design and Scheduling of Multiple Resources for Persistent UAV Operations , 2013, 2013 International Conference on Unmanned Aircraft Systems (ICUAS).

[20]  David Hyunchul Shim,et al.  Persistent UAV Service: An Improved Scheduling Formulation and Prototypes of System Components , 2013, 2013 International Conference on Unmanned Aircraft Systems (ICUAS).

[21]  M. Bernardine Dias,et al.  The Autonomous Recharging Problem: Formulation and a market-based solution , 2013, 2013 IEEE International Conference on Robotics and Automation.

[22]  Francesco Bullo,et al.  On Dynamic Vehicle Routing With Time Constraints , 2014, IEEE Transactions on Robotics.

[23]  Steven Lake Waslander,et al.  Optimal Path Planning in Cooperative Heterogeneous Multi-robot Delivery Systems , 2014, WAFR.

[24]  Hrvoje Gold,et al.  Vehicle Routing Problem , 2008, Encyclopedia of GIS.