Temporal logic motion planning in unknown environments

In this paper, we consider a robot motion planning problem from a specification given as a syntactically co-safe linear temporal logic formula over a set of properties known to be satisfied at the regions of an unknown environment. The robot is assumed to be equipped with deterministic motion and accurate sensing capabilities. The environment is assumed to be partitioned into a finite number of identical square cells. By bringing together tools from formal verification, graph theory, and grid-based exploration, we develop an incremental algorithm that makes progress towards satisfying the specification while the robot discovers the environment using its local sensors. We show that the algorithm is sound and complete. We illustrate the feasibility and effectiveness of our approach through a simulated case study.

[1]  Amir Pnueli,et al.  On the synthesis of a reactive module , 1989, POPL '89.

[2]  Haim Kaplan,et al.  Maximum Flows by Incremental Breadth-First Search , 2011, ESA.

[3]  Calin Belta,et al.  Probabilistic control from time-bounded temporal logic specifications in dynamic environments , 2012, 2012 IEEE International Conference on Robotics and Automation.

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

[5]  Martin Leucker,et al.  Runtime Verification for LTL and TLTL , 2011, TSEM.

[6]  Amir Pnueli,et al.  Synthesis of Reactive(1) designs , 2006, J. Comput. Syst. Sci..

[7]  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.

[8]  Hadas Kress-Gazit,et al.  Guaranteeing High-Level Behaviors while Exploring Partially Known Maps , 2012, Robotics: Science and Systems.

[9]  Joel W. Burdick,et al.  Backtracking temporal logic synthesis for uncertain environments , 2012, 2012 IEEE International Conference on Robotics and Automation.

[10]  Calin Belta,et al.  Temporal Logic Motion Planning and Control With Probabilistic Satisfaction Guarantees , 2012, IEEE Transactions on Robotics.

[11]  Orna Kupferman,et al.  Model Checking of Safety Properties , 1999, Formal Methods Syst. Des..

[12]  Bart Selman,et al.  S. Russell, P. Norvig, Artificial Intelligence: A Modern Approach, Third Edition , 2011, Artif. Intell..

[13]  Steven M. LaValle,et al.  Simple and Efficient Algorithms for Computing Smooth, Collision-free Feedback Laws Over Given Cell Decompositions , 2009, Int. J. Robotics Res..

[14]  Martin Leucker,et al.  The Good, the Bad, and the Ugly, But How Ugly Is Ugly? , 2007, RV.

[15]  Alberto Elfes,et al.  Using occupancy grids for mobile robot perception and navigation , 1989, Computer.

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

[17]  Calin Belta,et al.  Receding horizon temporal logic control for finite deterministic systems , 2012, 2012 American Control Conference (ACC).

[18]  Sebastian Thrun,et al.  Probabilistic robotics , 2002, CACM.

[19]  Erion Plaku.  Planning in Discrete and Continuous Spaces: From LTL Tasks to Robot Motions , 2012, TAROS.

[20]  David Furcy,et al.  Incremental Heuristic Search in AI , 2004, AI Mag..

[21]  Peter Norvig,et al.  Artificial Intelligence: A Modern Approach , 1995 .

[22]  Brian Yamauchi,et al.  Frontier-based exploration using multiple robots , 1998, AGENTS '98.