Synthesis of output feedback control for motion planning based on LTL specifications

In the paper, we study the motion planning problem of a mobile robot in the plane. The goal is to design output feedback control such that the resulting path of a mobile robot satisfies desired linear temporal logic (LTL) specifications. Our control strategy is divided into a local output feedback control problem and a supervisory control for LTL specifications. For the former one, we design output feedback control laws to ensure that output trajectories either remain in a simplex, or leave the simplex and enter an adjacent simplex in finite time. For the latter, we construct a transition system based on reachability and search for feasible paths that satisfy the LTL specifications. In this way, a piecewise affine output feedback control is obtained to solve the motion planning problem. A simulation result is presented to illustrate our approach.

[1]  Antoine Girard,et al.  Hybridization methods for the analysis of nonlinear systems , 2007, Acta Informatica.

[2]  Gerardo Lafferriere,et al.  A Differential Geometric Approach to Motion Planning , 1993 .

[3]  Daniel E. Koditschek.  The Control of Natural Motion in Mechanical Systems , 1991 .

[4]  J. Van Leeuwen,et al.  Handbook of theoretical computer science - Part A: Algorithms and complexity; Part B: Formal models and semantics , 1990 .

[5]  A. Astolfi.  Discontinuous control of nonholonomic systems , 1996 .

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

[7]  Carl A. Gunter,et al.  In handbook of theoretical computer science , 1990 .

[8]  Eduardo Sontag.  Nonlinear regulation: The piecewise linear approach , 1981 .

[9]  Valentin Goranko,et al.  Logic in Computer Science: Modelling and Reasoning About Systems , 2007, J. Log. Lang. Inf..

[10]  Mireille E. Broucke,et al.  Necessary and Sufficient Conditions for Reachability on a Simplex , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

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

[12]  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.

[13]  Eduardo Sontag.  From linear to nonlinear: some complexity comparisons , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[14]  J. Canny,et al.  Nonholonomic Motion Planning , 1992 .

[15]  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).

[16]  Eduardo D. Sontag,et al.  Interconnected Automata and Linear Systems: A Theoretical Framework in Discrete-Time , 1996, Hybrid Systems.

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

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

[19]  George J. Pappas,et al.  Translating Temporal Logic to Controller Specifications , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[20]  Michael Huth,et al.  Logic in computer science - modelling and reasoning about systems , 2000 .

[21]  Antoine Girard,et al.  Motion planning for nonlinear systems using hybridizations and robust controllers on simplices , 2008, 2008 47th IEEE Conference on Decision and Control.

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