Temporal Logic Planning and Control of Robotic Swarms by Hierarchical Abstractions

We develop a hierarchical framework for planning and control of arbitrarily large groups (swarms) of fully actuated robots with polyhedral velocity bounds moving in polygonal environments with polygonal obstacles. At the first level of hierarchy, we aggregate the high-dimensional control system of the swarm into a small-dimensional control system capturing its essential features. These features describe the position of the swarm in the world and its size. At the second level, we reduce the problem of controlling the essential features of the swarm to a model-checking problem. In the obtained hierarchical framework, high-level specifications given in natural language, such as linear temporal logic formulas over linear predicates in the essential features, are automatically mapped to provably correct robot control laws. For the particular case of an abstraction based on centroid and variance, we show that swarm cohesion, interrobot collision avoidance, and environment containment can also be specified and automatically guaranteed in our framework. The obtained communication architecture is centralized

[1]  V. Weispfenning.  A New Approach to Quantifier Elimination for Real Algebra , 1998 .

[2]  Paulo Tabuada,et al.  Hierarchical trajectory refinement for a class of nonlinear systems , 2005, Autom..

[3]  Vijay R. Kumar,et al.  Optimal Motion Generation for Groups of Robots: A Geometric Approach , 2004 .

[4]  Vijay Kumar,et al.  Modeling and control of formations of nonholonomic mobile robots , 2001, IEEE Trans. Robotics Autom..

[5]  Volker Weispfenning,et al.  The Complexity of Linear Problems in Fields , 1988, Journal of symbolic computation.

[6]  S. LaValle,et al.  Motion Planning , 2008, Springer Handbook of Robotics.

[7]  E. Allen Emerson,et al.  Temporal and Modal Logic , 1991, Handbook of Theoretical Computer Science, Volume B: Formal Models and Sematics.

[8]  K.J. Kyriakopoulos,et al.  Automatic synthesis of multi-agent motion tasks based on LTL specifications , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[9]  Fumin Zhang,et al.  Control of small formations using shape coordinates , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[10]  Calin Belta,et al.  Abstraction and control for Groups of robots , 2004, IEEE Transactions on Robotics.

[11]  Paul Gastin,et al.  Fast LTL to Büchi Automata Translation , 2001, CAV.

[12]  Peter N. Belhumeur,et al.  Closing ranks in vehicle formations based on rigidity , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[13]  Xiaoming Hu,et al.  Formation constrained multi-agent control , 2001, Proceedings 2001 ICRA. IEEE International Conference on Robotics and Automation (Cat. No.01CH37164).

[14]  L.C.G.J.M. Habets,et al.  Control of Rectangular Multi-Affine Hybrid Systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[15]  Littlejohn,et al.  Internal or shape coordinates in the n-body problem. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[16]  Petter Ögren,et al.  Formations with a Mission: Stable Coordination of Vehicle Group Maneuvers , 2002 .

[17]  Calin Belta,et al.  A Fully Automated Framework for Control of Linear Systems from LTL Specifications , 2006, HSCC.

[18]  G. Swaminathan.  Robot Motion Planning , 2006 .

[19]  M. Broucke.  A geometric approach to bisimulation and verification of hybrid systems , 1998, Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171).

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

[21]  George J. Pappas,et al.  Consistent abstractions of affine control systems , 2002, IEEE Trans. Autom. Control..

[22]  Robin Milner,et al.  Communication and concurrency , 1989, PHI Series in computer science.

[23]  Paulo Tabuada,et al.  Bisimilar control affine systems , 2004, Syst. Control. Lett..

[24]  Thomas Bak,et al.  Multi-Robot Motion Planning: A Timed Automata Approach , 2004 .

[25]  Hadas Kress-Gazit,et al.  Temporal Logic Motion Planning for Mobile Robots , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.

[26]  Paulo Tabuada,et al.  Hierarchical trajectory generation for a class of nonlinear systems , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[27]  E. W. Justh,et al.  Steering laws and continuum models for planar formations , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[28]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[29]  Petter Ögren,et al.  Cooperative control of mobile sensor networks:Adaptive gradient climbing in a distributed environment , 2004, IEEE Transactions on Automatic Control.

[30]  Thomas Bak,et al.  Planning : A Timed Automata Approach , 2004 .

[31]  Paulo Tabuada,et al.  Model Checking LTL over Controllable Linear Systems Is Decidable , 2003, HSCC.

[32]  M. Spivak.  A comprehensive introduction to differential geometry , 1979 .