Automated composition of motion primitives for multi-robot systems from safe LTL specifications

We present a compositional motion planning framework for multi-robot systems based on an encoding to satisfiability modulo theories (SMT). In our framework, the desired behavior of a group of robots is specified using a set of safe linear temporal logic (LTL) properties. Our method relies on a library of motion primitives, each of which corresponds to a controller that ensures a particular trajectory in a given configuration. Using the closed-loop behavior of the robots under the action of different controllers, we formulate the motion planning problem as an SMT solving problem and use an off-the-shelf SMT solver to generate trajectories for the robots. Our approach can also be extended to synthesize optimal cost trajectories where optimality is defined with respect to the available motion primitives. Experimental results show that our framework can efficiently solve complex motion planning problems in the context of multi-robot systems.

[1]  Ming C. Lin,et al.  Constraint-Based Motion Planning Using Voronoi Diagrams , 2002, WAFR.

[2]  Swarat Chaudhuri,et al.  SMT-based synthesis of integrated task and motion plans from plan outlines , 2014, 2014 IEEE International Conference on Robotics and Automation (ICRA).

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

[4]  R. Murray,et al.  Real‐time trajectory generation for differentially flat systems , 1998 .

[5]  Vijay Kumar,et al.  Minimum snap trajectory generation and control for quadrotors , 2011, 2011 IEEE International Conference on Robotics and Automation.

[6]  Ian R. Manchester,et al.  LQR-trees: Feedback Motion Planning via Sums-of-Squares Verification , 2010, Int. J. Robotics Res..

[7]  Calin Belta,et al.  Optimality and Robustness in Multi-Robot Path Planning with Temporal Logic Constraints , 2013, Int. J. Robotics Res..

[8]  Wolfram Burgard,et al.  A Probabilistic Approach to Collaborative Multi-Robot Localization , 2000, Auton. Robots.

[9]  Nancy M. Amato,et al.  Behavior-based evacuation planning , 2010, 2010 IEEE International Conference on Robotics and Automation.

[10]  Dinesh Manocha,et al.  Constraint‐based motion synthesis for deformable models , 2008, Comput. Animat. Virtual Worlds.

[11]  G. Whelan,et al.  Cooperative search and rescue with a team of mobile robots , 1997, 1997 8th International Conference on Advanced Robotics. Proceedings. ICAR'97.

[12]  Dinesh Manocha,et al.  Multi-robot coordination using generalized social potential fields , 2009, 2009 IEEE International Conference on Robotics and Automation.

[13]  Cesare Tinelli,et al.  Satisfiability Modulo Theories , 2021, Handbook of Satisfiability.

[14]  Wenqi Zhang,et al.  Composition of Motion Description Languages , 2008, HSCC.

[15]  Yushan Chen,et al.  LTL robot motion control based on automata learning of environmental dynamics , 2012, 2012 IEEE International Conference on Robotics and Automation.

[16]  Jean-Claude Latombe,et al.  A general framework for assembly planning: the motion space approach , 1998, SCG '98.

[17]  Nikolaj Bjørner,et al.  Z3: An Efficient SMT Solver , 2008, TACAS.

[18]  Giuseppe De Giacomo,et al.  Linear Temporal Logic and Linear Dynamic Logic on Finite Traces , 2013, IJCAI.

[19]  Lydia E. Kavraki,et al.  Motion planning with hybrid dynamics and temporal goals , 2010, 49th IEEE Conference on Decision and Control (CDC).

[20]  Calin Belta,et al.  Discrete abstractions for robot motion planning and control in polygonal environments , 2005, IEEE Transactions on Robotics.

[21]  Daniel E. Koditschek,et al.  Sequential Composition of Dynamically Dexterous Robot Behaviors , 1999, Int. J. Robotics Res..

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

[23]  Emilio Frazzoli,et al.  Sampling-based motion planning with deterministic μ-calculus specifications , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[24]  Munther A. Dahleh,et al.  Maneuver-based motion planning for nonlinear systems with symmetries , 2005, IEEE Transactions on Robotics.

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

[26]  George J. Pappas,et al.  Sequential composition of robust controller specifications , 2012, 2012 IEEE International Conference on Robotics and Automation.

[27]  Tucker R. Balch,et al.  Behavior-based formation control for multirobot teams , 1998, IEEE Trans. Robotics Autom..

[28]  Bruce Randall Donald,et al.  Moving furniture with teams of autonomous robots , 1995, Proceedings 1995 IEEE/RSJ International Conference on Intelligent Robots and Systems. Human Robot Interaction and Cooperative Robots.

[29]  Hadas Kress-Gazit,et al.  Where's Waldo? Sensor-Based Temporal Logic Motion Planning , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[30]  Peng Gao,et al.  Motion planning with Satisfiability Modulo Theories , 2014, 2014 IEEE International Conference on Robotics and Automation (ICRA).

[31]  James A. Hendler,et al.  Languages, behaviors, hybrid architectures, and motion control , 1998 .

[32]  Vijay Kumar,et al.  Incremental micro-UAV motion replanning for exploring unknown environments , 2013, 2013 IEEE International Conference on Robotics and Automation.