Automated generation of hybrid automata for multi-rigid-body mechanical systems and its application to the falsification of safety properties

ABSTRACT What if we designed a tool to automatically generate a dynamical transition system for the formal specification of mechanical systems subject to multiple impacts, contacts and discontinuous friction? Such a tool would represent an advance in the description and simulation of these complex systems. This is precisely what this paper offers: Dyverse Rigid Body Toolbox (DyverseRBT). This tool requires a sufficiently expressive computational model that can accurately describe the behaviour of the system as it evolves over time. For this purpose, we propose an alternative abstraction of multi-rigid-body (MRB) mechanical systems with multiple contacts as an extended version of the classical hybrid automaton, which we call MRB hybrid automaton. One of the chief characteristics of the MRB hybrid automaton is the inclusion of computation nodes to encode algorithms to calculate the contact forces. The computation nodes consist of a set of non-dynamical discrete locations, discrete transitions and guards between these locations, and resets on transitions. They can account for the energy transfer not explicitly considered within the rigid-body formalism. The proposed modelling framework is well suited for the automated verification of dynamical properties of realistic mechanical systems. We show this by the falsification of safety properties over the transition system generated by DyverseRBT.

[1]  Armin Biere,et al.  Symbolic Model Checking without BDDs , 1999, TACAS.

[2]  Sriram Sankaranarayanan,et al.  S-TaLiRo: A Tool for Temporal Logic Falsification for Hybrid Systems , 2011, TACAS.

[3]  Edward A. Lee,et al.  A component-based approach to modeling and simulating mixed-signal and hybrid systems , 2002, TOMC.

[4]  E. Frazzoli,et al.  Resolution-complete safety falsification of continuous time systems , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[5]  Alberto Griggio,et al.  A Practical Approach to Satisability Modulo Linear Integer Arithmetic , 2012, J. Satisf. Boolean Model. Comput..

[6]  Edward A. Lee,et al.  Taming heterogeneity - the Ptolemy approach , 2003, Proc. IEEE.

[7]  Armin Biere,et al.  A survey of recent advances in SAT-based formal verification , 2005, International Journal on Software Tools for Technology Transfer.

[8]  Vincent Acary,et al.  Numerical Methods for Nonsmooth Dynamical Systems: Applications in Mechanics and Electronics , 2008 .

[9]  R. Sanfelice,et al.  Hybrid dynamical systems , 2009, IEEE Control Systems.

[10]  E. A. Woods,et al.  The Hybrid Phenomena Theory , 1991, IJCAI.

[11]  Benjamin J. Kaipers,et al.  Qualitative Simulation , 1989, Artif. Intell..

[12]  V. Acary,et al.  Projected event-capturing time-stepping schemes for nonsmooth mechanical systems with unilateral contact and Coulomb’s friction , 2013 .

[13]  Sriram Sankaranarayanan,et al.  Falsification of temporal properties of hybrid systems using the cross-entropy method , 2012, HSCC '12.

[14]  J. C. Simo,et al.  An augmented lagrangian treatment of contact problems involving friction , 1992 .

[15]  D. Stewart,et al.  AN IMPLICIT TIME-STEPPING SCHEME FOR RIGID BODY DYNAMICS WITH INELASTIC COLLISIONS AND COULOMB FRICTION , 1996 .

[16]  Thomas A. Henzinger,et al.  The theory of hybrid automata , 1996, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.

[17]  Christoph Glocker,et al.  Solving Normal Cone Inclusion Problems in Contact Mechanics by Iterative Methods , 2007 .

[18]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[19]  Benjamin Kuipers,et al.  Qualitative Simulation , 1986, Artificial Intelligence.

[20]  Bernard Brogliato,et al.  Multiple Impacts in Dissipative Granular Chains , 2013 .

[21]  Dan B. Marghitu,et al.  Rigid Body Collisions of Planar Kinematic Chains With Multiple Contact Points , 1994, Int. J. Robotics Res..

[22]  Vijay Kumar,et al.  Sampling-based Falsification and Verification of Controllers for Continuous Dynamic Systems , 2008, Int. J. Robotics Res..

[23]  Edmund M. Clarke,et al.  dReal: An SMT Solver for Nonlinear Theories over the Reals , 2013, CADE.

[24]  Antoine Girard,et al.  SpaceEx: Scalable Verification of Hybrid Systems , 2011, CAV.

[25]  Pieter J. Mosterman,et al.  A computational model of time for stiff hybrid systems applied to control synthesis , 2012 .

[26]  Friedrich Pfeiffer,et al.  Mechanical System Dynamics , 2008 .

[27]  Edmund M. Clarke,et al.  Satisfiability modulo ODEs , 2013, 2013 Formal Methods in Computer-Aided Design.

[28]  Eva M. Navarro-López,et al.  A Hybrid Automaton for a Class of Multi-Contact Rigid-Body Systems with Friction and Impacts , 2012, ADHS.

[29]  Alessandro Cimatti,et al.  Efficient Scenario Verification for Hybrid Automata , 2011, CAV.

[30]  Stefan Kupferschmid,et al.  Challenges in Constraint-Based Analysis of Hybrid Systems , 2008, CSCLP.

[31]  Paulo Tabuada,et al.  Symbolic Models for Nonlinear Control Systems: Alternating Approximate Bisimulations , 2007, SIAM J. Control. Optim..

[32]  Bernard Brogliato,et al.  The contact problem in Lagrangian systems subject to bilateral and unilateral constraints, with or without sliding Coulomb’s friction: a tutorial , 2016, Multibody System Dynamics.

[33]  Hadas Kress-Gazit.  Robot challenges: Toward development of verification and synthesis techniques [from the Guest Editors] , 2011 .

[34]  Karl Henrik Johansson,et al.  Dynamical properties of hybrid automata , 2003, IEEE Trans. Autom. Control..

[35]  Paulo Tabuada.  An Approximate Simulation Approach to Symbolic Control , 2008, IEEE Transactions on Automatic Control.

[36]  Eva M. Navarro-López,et al.  Hybrid automata: an insight into the discrete abstraction of discontinuous systems , 2011, Int. J. Syst. Sci..

[37]  Andreas Bauer,et al.  Tool-support for the analysis of hybrid systems and models , 2007, 2007 Design, Automation & Test in Europe Conference & Exhibition.

[38]  Eva M. Navarro-López,et al.  Hybrid modelling of a discontinuous dynamical system including switching control , 2009 .

[39]  Sriram Sankaranarayanan,et al.  A trajectory splicing approach to concretizing counterexamples for hybrid systems , 2013, 52nd IEEE Conference on Decision and Control.

[40]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[41]  Johannes Schumacher,et al.  An Introduction to Hybrid Dynamical Systems, Springer Lecture Notes in Control and Information Sciences 251 , 1999 .

[42]  Edward A. Lee,et al.  Demo : CyPhySim — A Cyber-Physical Systems Simulator , 2015 .

[43]  Hilding Elmqvist,et al.  Object-oriented modeling of hybrid systems , 1993 .

[44]  Emilio Frazzoli,et al.  Sampling-Based Resolution-Complete Algorithms for Safety Falsification of Linear Systems , 2008, HSCC.

[45]  Pieter J. Mosterman,et al.  Computer Automated Multi-Paradigm Modeling : An Introduction , 2000 .

[46]  Ufuk Topcu,et al.  Correct, Reactive, High-Level Robot Control , 2011, IEEE Robotics & Automation Magazine.

[47]  Shuji Doshita,et al.  Reasoning about Discontinuous Change , 1987, AAAI.

[48]  R. Ledesma,et al.  Augmented lagrangian and mass-orthogonal projection methods for constrained multibody dynamics , 1996 .

[49]  Lydia E. Kavraki,et al.  Falsification of LTL safety properties in hybrid systems , 2009, International Journal on Software Tools for Technology Transfer.

[50]  Pieter J. Mosterman,et al.  Sliding Mode Model Semantics and Simulation for Hybrid Systems , 1997, Hybrid Systems.

[51]  Marco Bozzano,et al.  Verifying Industrial Hybrid Systems with MathSAT , 2005, BMC@CAV.

[52]  Roger W. Brockett,et al.  On the computer control of movement , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[53]  Lydia E. Kavraki,et al.  Hybrid systems: from verification to falsification by combining motion planning and discrete search , 2007, CAV.

[54]  Pieter J. Mosterman,et al.  A comprehensive methodology for building hybrid models of physical systems , 2000, Artif. Intell..

[55]  Edward A. Lee,et al.  Operational Semantics of Hybrid Systems , 2005, HSCC.

[56]  Kenneth D. Forbus.  Qualitative Process Theory , 1984, Artif. Intell..

[57]  Martin Fränzle,et al.  HySAT: An efficient proof engine for bounded model checking of hybrid systems , 2007, Formal Methods Syst. Des..

[58]  Wei Chen,et al.  dReach: δ-Reachability Analysis for Hybrid Systems , 2015, TACAS.

[59]  Eva M. Navarro-López,et al.  Hybrid-automaton models for simulating systems with sliding motion: still a challenge , 2009, ADHS.

[60]  Ufuk Topcu,et al.  Correct, Reactive, High-Level Robot Control: Mitigating the State Explosion Problem of Temporal Logic Synthesis , 2011 .

[61]  P. Alart,et al.  A mixed formulation for frictional contact problems prone to Newton like solution methods , 1991 .

[62]  Simon Bliudze,et al.  An Operational Semantics for Hybrid Systems Involving Behavioral Abstraction , 2014 .

[63]  Ricardo G. Sanfelice,et al.  Robust Stability and Control for Systems That Combine Continuous-time and Discrete-time Dynamics , 2009 .

[64]  Antoine Girard,et al.  Controller synthesis for safety and reachability via approximate bisimulation , 2010, Autom..

[65]  P. Mosterman,et al.  A theory of discontinuities in physical system models , 1998 .

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

[67]  Armando Tacchella,et al.  Benefits of Bounded Model Checking at an Industrial Setting , 2001, CAV.

[68]  Moshe Y. Vardi,et al.  Motion Planning with Complex Goals , 2011, IEEE Robotics & Automation Magazine.

[69]  Christian Studer,et al.  Numerics of Unilateral Contacts and Friction , 2009 .

[70]  Eva M. Navarro-López,et al.  Hybrid systems neuroscience , 2016 .

[71]  Emilio Frazzoli,et al.  Incremental Search Methods for Reachability Analysis of Continuous and Hybrid Systems , 2004, HSCC.

[72]  Shouchuan Hu.  Differential equations with discontinuous right-hand sides☆ , 1991 .

[73]  M. Egerstedt,et al.  On the regularization of Zeno hybrid automata , 1999 .

[75]  Antoine Girard,et al.  Approximate Simulation Relations for Hybrid Systems , 2008, Discret. Event Dyn. Syst..

[76]  John M. Rushby,et al.  Harnessing Disruptive Innovation in Formal Verification , 2006, Fourth IEEE International Conference on Software Engineering and Formal Methods (SEFM'06).

[77]  Pieter J. Mosterman,et al.  Computation for Humanity - Information Technology to Advance Society , 2013, Computation for Humanity.

[78]  Martin Fränzle,et al.  Efficient Solving of Large Non-linear Arithmetic Constraint Systems with Complex Boolean Structure , 2007, J. Satisf. Boolean Model. Comput..

[79]  Yushan Chen,et al.  Automatic Deployment of Robotic Teams , 2011, IEEE Robotics & Automation Magazine.

[80]  B. Brogliato.  Nonsmooth Mechanics: Models, Dynamics and Control , 1999 .

[81]  Thomas A. Henzinger,et al.  Hybrid Automata: An Algorithmic Approach to the Specification and Verification of Hybrid Systems , 1992, Hybrid Systems.

[82]  N. Wouw,et al.  Stability and Convergence of Mechanical Systems with Unilateral Constraints , 2008 .

[83]  Edward A. Lee,et al.  CyPhySim: a cyber-physical systems simulator , 2015, HSCC.

[84]  Alessandro Cimatti,et al.  Model Checking of Hybrid Systems Using Shallow Synchronization , 2010, FMOODS/FORTE.

[85]  Martin Leucker,et al.  Don’t care in SMT: building flexible yet efficient abstraction/refinement solvers , 2009, International Journal on Software Tools for Technology Transfer.

[86]  Peter A. Fritzson,et al.  Introduction to Modeling and Simulation of Technical and Physical Systems with Modelica , 2011 .

[87]  Jeffrey C. Trinkle,et al.  Complementarity formulations and existence of solutions of dynamic multi-rigid-body contact problems with coulomb friction , 1996, Math. Program..

[88]  Sven Erik Mattsson,et al.  On Object-Oriented Modelling of Relays and Sliding Mode Behaviour , 1996 .

[89]  Emilio Frazzoli,et al.  Sampling-based resolution-complete safety falsification of linear hybrid systems , 2007, 2007 46th IEEE Conference on Decision and Control.