Scalable lazy SMT-based motion planning

We present a scalable robot motion planning algorithm for reach-avoid problems. We assume a discrete-time, linear model of the robot dynamics and a workspace described by a set of obstacles and a target region, where both the obstacles and the region are polyhedra. Our goal is to construct a trajectory, and the associated control strategy, that steers the robot from its initial point to the target while avoiding obstacles. Differently from previous approaches, based on the discretization of the continuous state space or uniform discretization of the workspace, our approach, inspired by the lazy satisfiability modulo theory paradigm, decomposes the planning problem into smaller subproblems, which can be efficiently solved using specialized solvers. At each iteration, we use a coarse, obstacle-based discretization of the workspace to obtain candidate high-level, discrete plans that solve a set of Boolean constraints, while completely abstracting the low-level continuous dynamics. The feasibility of the proposed plans is then checked via a convex program, under constraints on both the system dynamics and the control inputs, and new candidate plans are generated until a feasible one is found. To achieve scalability, we show how to generate succinct explanations for the infeasibility of a discrete plan by exploiting a relaxation of the convex program that allows detecting the earliest possible occurrence of an infeasible transition between workspace regions. Simulation results show that our algorithm favorably compares with state-of-the-art techniques and scales well for complex systems, including robot dynamics with up to 50 continuous states.

[1]  Manuel Mazo,et al.  Specification-guided controller synthesis for linear systems and safe linear-time temporal logic , 2013, HSCC '13.

[2]  Alberto L. Sangiovanni-Vincentelli,et al.  A Contract-Based Methodology for Aircraft Electric Power System Design , 2014, IEEE Access.

[3]  Claire J. Tomlin,et al.  Reachability-based synthesis of feedback policies for motion planning under bounded disturbances , 2011, 2011 IEEE International Conference on Robotics and Automation.

[4]  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.

[5]  John Lygeros,et al.  Hamilton–Jacobi Formulation for Reach–Avoid Differential Games , 2009, IEEE Transactions on Automatic Control.

[6]  Ufuk Topcu,et al.  Optimization-based trajectory generation with linear temporal logic specifications , 2014, 2014 IEEE International Conference on Robotics and Automation (ICRA).

[7]  Thomas A. Henzinger,et al.  Counterexample-Guided Control , 2003, ICALP.

[8]  Antonio Bicchi,et al.  Symbolic planning and control of robot motion [Grand Challenges of Robotics] , 2007, IEEE Robotics & Automation Magazine.

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

[10]  Emilio Frazzoli,et al.  Linear temporal logic vehicle routing with applications to multi‐UAV mission planning , 2011 .

[11]  A. Sangiovanni-Vincentelli,et al.  I MHOTEP-SMT : A Satisfiability Modulo Theory Solver For Secure State Estimation ∗ , 2015 .

[12]  Zhengyuan Zhou,et al.  A general, open-loop formulation for reach-avoid games , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[13]  Daniel Le Berre,et al.  The Sat4j library, release 2.2 , 2010, J. Satisf. Boolean Model. Comput..

[14]  Paulo Tabuada,et al.  Secure State Estimation Under Sensor Attacks: A Satisfiability Modulo Theory Approach , 2014, ArXiv.

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

[16]  Fred Kröger,et al.  Temporal Logic of Programs , 1987, EATCS Monographs on Theoretical Computer Science.

[17]  Vijay Kumar,et al.  Automated composition of motion primitives for multi-robot systems from safe LTL specifications , 2014, 2014 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[18]  Ufuk Topcu,et al.  Receding Horizon Temporal Logic Planning , 2012, IEEE Transactions on Automatic Control.

[19]  Alberto L. Sangiovanni-Vincentelli,et al.  CalCS: SMT solving for non-linear convex constraints , 2010, Formal Methods in Computer Aided Design.

[20]  Lydia E. Kavraki,et al.  Sampling-based motion planning with temporal goals , 2010, 2010 IEEE International Conference on Robotics and Automation.

[21]  Viktor Schuppan,et al.  Linear Encodings of Bounded LTL Model Checking , 2006, Log. Methods Comput. Sci..

[22]  Paulo Tabuada,et al.  Linear Time Logic Control of Discrete-Time Linear Systems , 2006, IEEE Transactions on Automatic Control.

[23]  Steven M. LaValle,et al.  Randomized Kinodynamic Planning , 1999, Proceedings 1999 IEEE International Conference on Robotics and Automation (Cat. No.99CH36288C).

[24]  J PappasGeorge,et al.  Temporal logic motion planning for dynamic robots , 2009 .

[25]  Erion Plaku,et al.  Motion planning with temporal-logic specifications: Progress and challenges , 2015, AI Commun..

[26]  Paulo Tabuada,et al.  Secure state reconstruction in differentially flat systems under sensor attacks using satisfiability modulo theory solving , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[27]  Dinesh Manocha,et al.  An efficient retraction-based RRT planner , 2008, 2008 IEEE International Conference on Robotics and Automation.