Reachability Calculations for Vehicle Safety During Manned/Unmanned Vehicle Interaction

This paper describes an approach based on reachability calculations for ensuring robust operation guarantees in flight maneuver sequences performed by unmanned aerial vehicles under supervision of human operators, with applicationstosafety-criticalscenarios.Usingahybridsystemformalismtomodelthemaneuversequence,thepaper devises systematic procedures for designing switching conditions to ensure the properties of safety, target attainability, and invariance, using Hamilton–Jacobi reachability calculations. These calculations lay the foundations for refining or designing protocols for multiple unmanned aerial vehicle and/or manned vehicle interaction. The mathematical foundations necessary are described in order to formulate verification problems on reachabilityandsafetyof flightmaneuvers,includingissuesofcommandlatencyanddisturbance.Anexampleofthis formalism is given in the context of automated aerial refueling, to inform unmanned aerial vehicle decisions that avoid unsafe scenarios while achieving mission objectives.

[1]  Glenn Buell,et al.  Optimal Aircraft Go - Around and Flare Maneuvers , 1973, IEEE Transactions on Aerospace and Electronic Systems.

[2]  P. Souganidis,et al.  Differential Games and Representation Formulas for Solutions of Hamilton-Jacobi-Isaacs Equations. , 1983 .

[3]  Rajeev Alur,et al.  A Theory of Timed Automata , 1994, Theor. Comput. Sci..

[4]  T. Henzinger.  The theory of hybrid automata , 1996, LICS 1996.

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

[6]  Thomas A. Henzinger,et al.  HYTECH: A Model Checker for Hybrid Systems , 1997, CAV.

[7]  Thomas A. Henzinger,et al.  HYTECH: a model checker for hybrid systems , 1997, International Journal on Software Tools for Technology Transfer.

[8]  Thomas A. Henzinger,et al.  Hybrid Systems: Computation and Control , 1998, Lecture Notes in Computer Science.

[9]  Daniel E. Koditschek,et al.  Sequential Composition of Dynamically Dexterous Robot Behaviors , 1999, Int. J. Robotics Res..

[10]  James A. Sethian,et al.  Level Set Methods and Fast Marching Methods , 1999 .

[11]  John Lygeros,et al.  Controllers for reachability specifications for hybrid systems , 1999, Autom..

[12]  J. Lygeros,et al.  A game theoretic approach to controller design for hybrid systems , 2000, Proceedings of the IEEE.

[13]  George J. Pappas,et al.  Discrete abstractions of hybrid systems , 2000, Proceedings of the IEEE.

[14]  Stavros Tripakis,et al.  Verification of Hybrid Systems with Linear Differential Inclusions Using Ellipsoidal Approximations , 2000, HSCC.

[15]  Pravin Varaiya,et al.  Ellipsoidal Techniques for Reachability Analysis , 2000, HSCC.

[16]  Olivier Bournez,et al.  Approximate Reachability Analysis of Piecewise-Linear Dynamical Systems , 2000, HSCC.

[17]  Alberto Bemporad,et al.  Optimization-Based Verification and Stability Characterization of Piecewise Affine and Hybrid Systems , 2000, HSCC.

[18]  Ian M. Mitchell,et al.  Safety verification of conflict resolution manoeuvres , 2001, IEEE Trans. Intell. Transp. Syst..

[19]  Thao Dang,et al.  d/dt: a verification tool for hybrid systems , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[20]  S. Shankar Sastry,et al.  Mode Switching Synthesis for Reachability Specifications , 2001, HSCC.

[21]  Alexandre M. Bayen,et al.  Hybrid verification of an interface for an automatic landing , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[22]  Jean-Pierre Aubin,et al.  Impulse differential inclusions: a viability approach to hybrid systems , 2002, IEEE Trans. Autom. Control..

[23]  John Valasek,et al.  Vision Based Sensor and Navigation System for Autonomous Aerial Refueling , 2002 .

[24]  A. Bayen.  Computational Control of Networks of Dynamical Systems: Application to the National Airspace System , 2003 .

[25]  Prasad,et al.  Envelope Protection in Autonomous Unmanned Aerial Vehicles , 2003 .

[26]  Bruce H. Krogh,et al.  Computational techniques for hybrid system verification , 2003, IEEE Trans. Autom. Control..

[27]  Rodney Teo.  Computing danger zones for provably safe closely spaced parallel approaches: Theory and experiment , 2003 .

[28]  Ronald Fedkiw,et al.  Level set methods and dynamic implicit surfaces , 2002, Applied mathematical sciences.

[29]  Alexandre M. Bayen,et al.  Computational techniques for the verification of hybrid systems , 2003, Proc. IEEE.

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

[31]  C. Tomlin,et al.  Control Strategies in Multi-Player Pursuit and Evasion Game ⁄ , 2005 .

[32]  Ian M. Mitchell,et al.  Online safety calculations for glide-slope recapture , 2005, Innovations in Systems and Software Engineering.

[33]  Alexandre M. Bayen,et al.  A time-dependent Hamilton-Jacobi formulation of reachable sets for continuous dynamic games , 2005, IEEE Transactions on Automatic Control.

[34]  Ian M. Mitchell,et al.  A Toolbox of Hamilton-Jacobi Solvers for Analysis of Nondeterministic Continuous and Hybrid Systems , 2005, HSCC.

[35]  Munther A. Dahleh,et al.  Maneuver-based motion planning for nonlinear systems with symmetries , 2005, IEEE Transactions on Robotics.

[36]  Rodney Teo,et al.  Flight Demonstration of Provably Safe Closely Spaced Parallel Approaches , 2005 .

[37]  Paulo Tabuada,et al.  Bisimulation relations for dynamical, control, and hybrid systems , 2005, Theor. Comput. Sci..

[38]  Wright-Patterson Afb,et al.  Automated Aerial Refueling: Extending the Effectiveness of Unmanned Air Vehicles , 2005 .

[39]  Antoine Girard,et al.  Reachability of Uncertain Linear Systems Using Zonotopes , 2005, HSCC.

[40]  Jianghai Hu,et al.  A stochastic approximation method for reachability computations , 2006 .

[41]  Zhipu Jin,et al.  Scheduling and sequence reshuffle for autonomous aerial refueling of multiple UAVs , 2006, 2006 American Control Conference.

[42]  Antoine Girard,et al.  Approximate simulation Relations for Hybrid Systems , 2006, ADHS.

[43]  B.A. Kish,et al.  Autonomous aerial refueling based on the tanker reference frame , 2006, 2006 IEEE Aerospace Conference.

[44]  Maria Prandini,et al.  Stochastic Reachability: Theory and Numerical Approximation , 2006 .

[45]  B. Krogh,et al.  Reachability analysis of nonlinear systems using trajectory piecewise linearized models , 2006, 2006 American Control Conference.

[46]  Bert G. J. Bakker,et al.  Safety risk simulation of an airborne self separati on concept of operation , 2007 .

[47]  John Hauser,et al.  UAV as a Reliable Wingman: A Flight Demonstration , 2007, IEEE Transactions on Control Systems Technology.

[48]  Mary L. Cummings,et al.  Predicting Controller Capacity in Supervisory Control of Multiple UAVs , 2008, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[49]  Max Mulder,et al.  Haptic Feedback in Uninhabited Aerial Vehicle Teleoperation with Time Delay , 2008 .

[50]  Ian M. Mitchell.  The Flexible, Extensible and Efficient Toolbox of Level Set Methods , 2008, J. Sci. Comput..

[51]  Barbara Savini,et al.  Path Planning for Autonomous Vehicles by Trajectory Smoothing Using Motion Primitives , 2008, IEEE Transactions on Control Systems Technology.

[52]  S. Shankar Sastry,et al.  Reachability calculations for automated aerial refueling , 2008, 2008 47th IEEE Conference on Decision and Control.

[53]  Henk A. P. Blom,et al.  Simulated Safety Risk of an Uncoordinated Airborne Self Separation Concept of Operation , 2009 .

[54]  Jason L. Speyer,et al.  Sensor Fusion Applied to Autonomous Aerial Refueling , 2009 .

[55]  Henk A. P. Blom,et al.  Rare Event Estimation for a Large-Scale Stochastic Hybrid System with Air Traffic Application , 2009, Rare Event Simulation using Monte Carlo Methods.

[56]  Claire J. Tomlin,et al.  Robust reach-avoid controller synthesis for switched nonlinear systems , 2010, 49th IEEE Conference on Decision and Control (CDC).

[57]  H. Blom,et al.  Simulated collision risk of an uncoordinated airborne self separation concept of operation , .