Composition of Safety Constraints With Applications to Decentralized Fixed-Wing Collision Avoidance

In this paper we discuss how to construct a barrier certificate for a control affine system subject to actuator constraints and motivate this discussion by examining collision avoidance for fixed-wing unmanned aerial vehicles (UAVs). In particular, the theoretical development in this paper is used to create a barrier certificate that ensures that two UAVs will not collide for all future times assuming the vehicles start in a safe starting configuration. We then extend this development by discussing how to ensure that multiple safety constraints are simultaneously satisfied in a decentralized manner (e.g., ensure robot distances are above some threshold for all pairwise combinations of UAVs for all future times) while ensuring output actuator commands are within specified limits. We validate the theoretical developments of this paper in the simulator SCRIMMAGE with a simulation of 20 UAVs that maintain safe distances from each other even though their nominal paths would otherwise cause a collision.

[1]  Stephen Prajna.  Barrier certificates for nonlinear model validation , 2006, Autom..

[2]  Marcus Johnson,et al.  Unmanned Aircraft System Traffic Management (UTM) Concept of Operations , 2016 .

[3]  Li Wang,et al.  Multi-objective compositions for collision-free connectivity maintenance in teams of mobile robots , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[4]  Ivan Petrovic,et al.  Dynamic window based approach to mobile robot motion control in the presence of moving obstacles , 2007, Proceedings 2007 IEEE International Conference on Robotics and Automation.

[5]  Michael Day,et al.  Simulating Collaborative Robots in a Massive Multi-agent Game Environment (SCRIMMAGE) , 2018, DARS.

[6]  Kostas E. Bekris,et al.  Using minimal communication to improve decentralized conflict resolution for non-holonomic vehicles , 2011, 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[7]  Michael Defoort,et al.  Motion planning for cooperative unicycle-type mobile robots with limited sensing ranges: A distributed receding horizon approach , 2009, Robotics Auton. Syst..

[8]  S. Shankar Sastry,et al.  Conflict resolution for air traffic management: a study in multiagent hybrid systems , 1998, IEEE Trans. Autom. Control..

[9]  Antonio Bicchi,et al.  Decentralized Cooperative Policy for Conflict Resolution in Multivehicle Systems , 2007, IEEE Transactions on Robotics.

[10]  Leslie Pack Kaelbling,et al.  Collision Avoidance for Unmanned Aircraft using Markov Decision Processes , 2010 .

[11]  Magnus Egerstedt,et al.  Safe certificate-based maneuvers for teams of quadrotors using differential flatness , 2017, 2017 IEEE International Conference on Robotics and Automation (ICRA).

[12]  Pablo A. Parrilo,et al.  Semidefinite programming relaxations for semialgebraic problems , 2003, Math. Program..

[13]  Paulo Tabuada,et al.  Correctness Guarantees for the Composition of Lane Keeping and Adaptive Cruise Control , 2016, IEEE Transactions on Automation Science and Engineering.

[14]  Paulo Tabuada,et al.  Realizing simultaneous lane keeping and adaptive speed regulation on accessible mobile robot testbeds , 2017, 2017 IEEE Conference on Control Technology and Applications (CCTA).

[15]  K.A. Morgansen,et al.  Decentralized reactive collision avoidance for multiple unicycle-type vehicles , 2008, 2008 American Control Conference.

[16]  T. Sideris.  Ordinary Differential Equations and Dynamical Systems , 2013 .

[17]  Mykel J. Kochenderfer,et al.  Aircraft Collision Avoidance Using Monte Carlo Real-Time Belief Space Search , 2011, J. Intell. Robotic Syst..

[18]  Li Wang,et al.  Control Barrier Certificates for Safe Swarm Behavior , 2015, ADHS.

[19]  Aaron D. Ames,et al.  Sufficient conditions for the Lipschitz continuity of QP-based multi-objective control of humanoid robots , 2013, 52nd IEEE Conference on Decision and Control.

[20]  Aaron D. Ames,et al.  Control barrier function based quadratic programs with application to bipedal robotic walking , 2015, 2015 American Control Conference (ACC).

[21]  S. Saripalli,et al.  Path planning using 3D Dubins Curve for Unmanned Aerial Vehicles , 2014, 2014 International Conference on Unmanned Aircraft Systems (ICUAS).

[22]  Koushil Sreenath,et al.  Safety-Critical Control for Dynamical Bipedal Walking with Precise Footstep Placement , 2015, ADHS.

[23]  Paulo Tabuada,et al.  Control Barrier Function Based Quadratic Programs for Safety Critical Systems , 2016, IEEE Transactions on Automatic Control.

[24]  Magnus Egerstedt,et al.  Nonsmooth Barrier Functions With Applications to Multi-Robot Systems , 2017, IEEE Control Systems Letters.

[25]  Peter Thomas,et al.  On-board trajectory generation for collision avoidance in unmanned aerial vehicles , 2011, 2011 Aerospace Conference.

[26]  Bin Di,et al.  Potential field based receding horizon motion planning for centrality-aware multiple UAV cooperative surveillance , 2015 .

[27]  Xiangru Xu,et al.  Constrained control of input-output linearizable systems using control sharing barrier functions , 2018, Autom..

[28]  Wolfram Burgard,et al.  The dynamic window approach to collision avoidance , 1997, IEEE Robotics Autom. Mag..

[29]  Erick J. Rodríguez-Seda.  Decentralized trajectory tracking with collision avoidance control for teams of unmanned vehicles with constant speed , 2014, 2014 American Control Conference.

[30]  Stephen P. Boyd,et al.  OSQP: an operator splitting solver for quadratic programs , 2017, 2018 UKACC 12th International Conference on Control (CONTROL).

[31]  R. Olfati-Saber.  Near-identity diffeomorphisms and exponential /spl epsi/-tracking and /spl epsi/-stabilization of first-order nonholonomic SE(2) vehicles , 2002, Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301).

[32]  Srikanth Saripalli,et al.  Collision avoidance for UAVs using reachable sets , 2015, 2015 International Conference on Unmanned Aircraft Systems (ICUAS).

[33]  P Panyakeow,et al.  Decentralized deconfliction algorithms for unicycle UAVs , 2010, Proceedings of the 2010 American Control Conference.

[34]  Li Wang,et al.  Permissive Barrier Certificates for Safe Stabilization Using Sum-of-squares , 2018, 2018 Annual American Control Conference (ACC).

[35]  Koushil Sreenath,et al.  Exponential Control Barrier Functions for enforcing high relative-degree safety-critical constraints , 2016, 2016 American Control Conference (ACC).

[36]  Dusan M. Stipanovic,et al.  Formation Control and Collision Avoidance for Multi-agent Non-holonomic Systems: Theory and Experiments , 2008, Int. J. Robotics Res..

[37]  H. Jin Kim,et al.  Nonlinear Model Predictive Formation Flight , 2009, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.

[38]  Paulo Tabuada,et al.  Robustness of Control Barrier Functions for Safety Critical Control , 2016, ADHS.

[39]  Ali Jadbabaie,et al.  Safety Verification of Hybrid Systems Using Barrier Certificates , 2004, HSCC.

[40]  Magnus Egerstedt,et al.  Constructive Barrier Certificates with Applications to Fixed-Wing Aircraft Collision Avoidance , 2018, 2018 IEEE Conference on Control Technology and Applications (CCTA).