Temporal Logic Motion Planning for Mobile Robots

In this paper, we consider the problem of robot motion planning in order to satisfy formulas expressible in temporal logics. Temporal logics naturally express traditional robot specifications such as reaching a goal or avoiding an obstacle, but also more sophisticated specifications such as sequencing, coverage, or temporal ordering of different tasks. In order to provide computational solutions to this problem, we first construct discrete abstractions of robot motion based on some environmental decomposition. We then generate discrete plans satisfying the temporal logic formula using powerful model checking tools, and finally translate the discrete plans to continuous trajectories using hybrid control. Critical to our approach is providing formal guarantees ensuring that if the discrete plan satisfies the temporal logic formula, then the continuous motion also satisfies the exact same formula.

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

[2]  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).

[3]  Manuela M. Veloso,et al.  OBDD-based Universal Planning: Specifying and Solving Planning Problems for Synchronized Agents in Non-deterministic Domains , 1999, Artificial Intelligence Today.

[4]  George J. Pappas,et al.  Discrete abstractions of hybrid systems , 2000, Proceedings of the IEEE.

[5]  Piergiorgio Bertoli,et al.  MBP: a Model Based Planner , 2001 .

[6]  Steven M. LaValle,et al.  Planning algorithms , 2006 .

[7]  Fahiem Bacchus,et al.  Using temporal logics to express search control knowledge for planning , 2000, Artif. Intell..

[8]  Howie Choset,et al.  Composition of local potential functions for global robot control and navigation , 2003, Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453).

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

[10]  D. Manocha,et al.  Fast Polygon Triangulation Based on Seidel's Algorithm , 1995 .

[11]  Hassan Masum,et al.  Review of Computational Geometry: Algorithms and Applications (2nd ed.) by Mark de Berg, Marc van Kreveld, Mark Overmars, and Otfried Schwarzkopf , 2000, SIGA.

[12]  Daniel E. Koditschek,et al.  Exact robot navigation using artificial potential functions , 1992, IEEE Trans. Robotics Autom..

[13]  Stephan Merz,et al.  Model Checking , 2000 .

[14]  Jan H. van Schuppen,et al.  A control problem for affine dynamical systems on a full-dimensional polytope , 2004, Autom..

[15]  Manuela M. Veloso,et al.  OBDD-based Universal Planning for Synchronized Agents in Non-Deterministic Domains , 2000, J. Artif. Intell. Res..

[16]  C. Belta,et al.  Constructing decidable hybrid systems with velocity bounds , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[17]  Marco Pistore,et al.  NuSMV 2: An OpenSource Tool for Symbolic Model Checking , 2002, CAV.

[18]  Bud Mishra,et al.  Discrete event models+temporal logic=supervisory controller: automatic synthesis of locomotion controllers , 1995, Proceedings of 1995 IEEE International Conference on Robotics and Automation.

[19]  Gerard J. Holzmann,et al.  The SPIN Model Checker - primer and reference manual , 2003 .

[20]  Mark de Berg,et al.  Computational geometry: algorithms and applications , 1997 .

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