Informative path planning under temporal logic constraints with performance guarantees

In this work we consider an agent trying to maximize a submodular reward function while moving in a graph environment. Such reward functions can be used to capture a variety of crucial sensing objectives in robotics including, but not limited to, mutual information and entropy. Furthermore, the agent must satisfy a mission specified by temporal logic constraints, which can encode many rich and complex missions such as “visit regions A or B, then visit C, infinitely often. Never visit D before visiting C.” We present an algorithm to maximize a submodular reward function under these constraints and provide an approximation for the performance of the proposed algorithm. The results are validated via simulation.

[1]  Calin Belta,et al.  A receding horizon algorithm for informative path planning with temporal logic constraints , 2013, 2013 IEEE International Conference on Robotics and Automation.

[2]  Orna Kupferman,et al.  Model Checking of Safety Properties , 1999, CAV.

[3]  Robert Fitch,et al.  Online decentralized information gathering with spatial–temporal constraints , 2014, Auton. Robots.

[4]  Andreas Krause,et al.  Efficient Informative Sensing using Multiple Robots , 2014, J. Artif. Intell. Res..

[5]  Christel Baier,et al.  Principles of model checking , 2008 .

[6]  Geoffrey A. Hollinger,et al.  Sampling-based robotic information gathering algorithms , 2014, Int. J. Robotics Res..

[7]  Andreas Krause,et al.  Submodularity and its applications in optimized information gathering , 2011, TIST.

[8]  Alexei Makarenko,et al.  Information based adaptive robotic exploration , 2002, IEEE/RSJ International Conference on Intelligent Robots and Systems.

[9]  Hadas Kress-Gazit,et al.  Temporal-Logic-Based Reactive Mission and Motion Planning , 2009, IEEE Transactions on Robotics.

[10]  Calin Belta,et al.  Distributed Multi-Agent Persistent Surveillance Under Temporal Logic Constraints∗ , 2015 .

[11]  Vijay Kumar,et al.  Approximate representations for multi-robot control policies that maximize mutual information , 2014, Robotics: Science and Systems.

[12]  Calin Belta,et al.  Information-guided persistent monitoring under temporal logic constraints , 2015, 2015 American Control Conference (ACC).

[13]  Stephen L. Smith,et al.  Multi-robot task planning and sequencing using the SAT-TSP language , 2015, 2015 IEEE International Conference on Robotics and Automation (ICRA).

[14]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[15]  Gaurav S. Sukhatme,et al.  Informative path planning for an autonomous underwater vehicle , 2010, 2010 IEEE International Conference on Robotics and Automation.

[16]  Timo Latvala,et al.  Efficient Model Checking of Safety Properties , 2003, SPIN.

[17]  Andreas Krause,et al.  Submodular Function Maximization , 2014, Tractability.

[18]  Andreas Krause,et al.  Nonmyopic Informative Path Planning in Spatio-Temporal Models , 2007, AAAI.

[19]  Calin Belta,et al.  Optimal path planning for surveillance with temporal-logic constraints* , 2011, Int. J. Robotics Res..

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

[21]  Chandra Chekuri,et al.  A recursive greedy algorithm for walks in directed graphs , 2005, 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05).

[22]  Andreas Krause,et al.  Near-optimal Nonmyopic Value of Information in Graphical Models , 2005, UAI.

[23]  Calin Belta,et al.  LTL receding horizon control for finite deterministic systems , 2014, Autom..

[24]  Calin Belta,et al.  Distributed information gathering policies under temporal logic constraints , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[25]  M. L. Fisher,et al.  An analysis of approximations for maximizing submodular set functions—I , 1978, Math. Program..

[26]  Vijay Kumar,et al.  A Multi-robot Control Policy for Information Gathering in the Presence of Unknown Hazards , 2011, ISRR.

[27]  Yevgeniy Vorobeychik,et al.  Submodular Optimization with Routing Constraints , 2016, AAAI.

[28]  Ufuk Topcu,et al.  Receding Horizon Temporal Logic Planning , 2012, IEEE Transactions on Automatic Control.