Reachable set approach to collision avoidance for UAVs

In this paper, we propose a reachable set based collision avoidance algorithm for unmanned aerial vehicles (UAVs). UAVs have been deployed for agriculture research and management, surveillance and sensor coverage for threat detection and disaster search and rescue operations. It is essential for the aircraft to have on-board collision avoidance capability to guarantee safety. Instead of the traditional approach of collision avoidance between trajectories, we propose a collision avoidance scheme based on reachable sets and tubes. We then formulate the problem as a convex optimization problem seeking suitable control constraint sets for participating aircraft. We have applied the approach on a case study of two quadrotors collision avoidance scenario.

[1]  Matthias Althoff,et al.  Reachability analysis of nonlinear systems with uncertain parameters using conservative linearization , 2008, 2008 47th IEEE Conference on Decision and Control.

[2]  Claire J. Tomlin,et al.  Hierarchical, Hybrid Framework for Collision Avoidance Algorithms in the National Airspace , 2008 .

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

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

[5]  Jur P. van den Berg,et al.  Kinodynamic RRT*: Asymptotically optimal motion planning for robots with linear dynamics , 2013, 2013 IEEE International Conference on Robotics and Automation.

[6]  Naomi Ehrich Leonard,et al.  Virtual leaders, artificial potentials and coordinated control of groups , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

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

[8]  U. Ciniglio,et al.  A Novel 3D Geometric Algorithm for Aircraft Autonomous Collision Avoidance , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[9]  Rogelio Lozano,et al.  Modeling the Quad-Rotor Mini-Rotorcraft , 2013 .

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

[11]  Timothy W. McLain,et al.  Small Unmanned Aircraft: Theory and Practice , 2012 .

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

[13]  Stephen P. Boyd,et al.  Graph Implementations for Nonsmooth Convex Programs , 2008, Recent Advances in Learning and Control.

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

[15]  Yoram Koren,et al.  Potential field methods and their inherent limitations for mobile robot navigation , 1991, Proceedings. 1991 IEEE International Conference on Robotics and Automation.

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

[17]  Antoine Girard,et al.  Efficient Computation of Reachable Sets of Linear Time-Invariant Systems with Inputs , 2006, HSCC.

[18]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[19]  Vijay Kumar,et al.  The GRASP Multiple Micro-UAV Testbed , 2010, IEEE Robotics & Automation Magazine.

[20]  한수철,et al.  비례항법을 이용한 무인 항공기의 최적 충돌 회피 기동 = Proportional navigation-based optimal collision avoidance for UAVs , 2004 .

[21]  Jonathan P. How,et al.  UAV Trajectory Design Using Total Field Collision Avoidance , 2003 .