Optimal Control with Weighted Average Costs and Temporal Logic Specifications

We consider optimal control for a system subject to temporal logic constraints. We minimize a weighted average cost function that generalizes the commonly used average cost function from discrete-time optimal control. Dynamic programming algorithms are used to construct an optimal trajectory for the system that minimizes the cost function while satisfying a temporal logic specification. Constructing an optimal trajectory takes only polynomially more time than constructing a feasible trajectory. We demonstrate our methods on simulations of autonomous driving and robotic surveillance tasks.

[1]  Jan H. van Schuppen,et al.  Reachability and control synthesis for piecewise-affine hybrid systems on simplices , 2006, IEEE Transactions on Automatic Control.

[2]  G. Dantzig,et al.  FINDING A CYCLE IN A GRAPH WITH MINIMUM COST TO TIME RATIO WITH APPLICATION TO A SHIP ROUTING PROBLEM , 1966 .

[3]  Krishnendu Chatterjee,et al.  Mean-payoff parity games , 2005, 20th Annual IEEE Symposium on Logic in Computer Science (LICS' 05).

[4]  Richard M. Karp,et al.  A characterization of the minimum cycle mean in a digraph , 1978, Discret. Math..

[5]  B. Faverjon,et al.  Probabilistic Roadmaps for Path Planning in High-Dimensional Con(cid:12)guration Spaces , 1996 .

[6]  Calin Belta,et al.  A Fully Automated Framework for Control of Linear Systems from Temporal Logic Specifications , 2008, IEEE Transactions on Automatic Control.

[7]  Dimitri P. Bertsekas,et al.  Dynamic Programming and Optimal Control, Two Volume Set , 1995 .

[8]  Thomas H. Cormen,et al.  Introduction to algorithms [2nd ed.] , 2001 .

[9]  Calin Belta,et al.  Optimal path planning for surveillance with temporal-logic constraints* , 2011, Int. J. Robotics Res..

[10]  Rajesh K. Gupta,et al.  Faster maximum and minimum mean cycle algorithms for system-performance analysis , 1998, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

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

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

[13]  James B. Orlin,et al.  Finding minimum cost to time ratio cycles with small integral transit times , 1993, Networks.

[14]  Pierre Wolper,et al.  An Automata-Theoretic Approach to Automatic Program Verification (Preliminary Report) , 1986, LICS.

[15]  Paolo Toth,et al.  The Vehicle Routing Problem , 2002, SIAM monographs on discrete mathematics and applications.

[16]  Ufuk Topcu,et al.  Receding horizon control for temporal logic specifications , 2010, HSCC '10.

[17]  S. LaValle,et al.  Randomized Kinodynamic Planning , 2001 .

[18]  Christel Baier,et al.  Principles of model checking , 2008 .

[19]  C. Belta,et al.  Controlling a class of non-linear systems on rectangles , 2006 .

[20]  Richard M. Karp,et al.  Parametric shortest path algorithms with an application to cyclic staffing , 1981, Discret. Appl. Math..

[21]  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.

[22]  Ricardo G. Sanfelice,et al.  Optimal control of Mixed Logical Dynamical systems with Linear Temporal Logic specifications , 2008, 2008 47th IEEE Conference on Decision and Control.

[23]  Xin-She Yang,et al.  Introduction to Algorithms , 2021, Nature-Inspired Optimization Algorithms.

[24]  Lydia E. Kavraki,et al.  Motion Planning With Dynamics by a Synergistic Combination of Layers of Planning , 2010, IEEE Transactions on Robotics.