Guidance using bearing-only measurements with three beacons in the plane

Abstract This paper proposes a bearing-only measurement based guidance algorithm for a mobile agent to navigate in a two-dimensional plane. Based on the bearing vectors and the subtended angles related to three stationary beacons, the proposed algorithm allows the agent to reach its desired location. We show that the agent reaches its desired location globally asymptotically based on Lyapunov stability theory. Under some assumptions, the agent is also proved to reach the desired location exponentially based on Lyapunov's indirect method. Simulations and actual experimental tests on quadrotor system are also provided to verify the effectiveness of the proposed algorithm in outdoor environment.

[1]  Brian D. O. Anderson,et al.  Multi‐target localization and circumnavigation by a single agent using bearing measurements , 2015 .

[2]  Wolfram Burgard,et al.  A Fully Autonomous Indoor Quadrotor , 2012, IEEE Transactions on Robotics.

[3]  Shiyu Zhao,et al.  Bearing-based formation maneuvering , 2015, 2015 IEEE International Symposium on Intelligent Control (ISIC).

[4]  Hyo-Sung Ahn,et al.  A survey of multi-agent formation control , 2015, Autom..

[5]  Vijay Kumar,et al.  Biologically inspired bearing-only navigation and tracking , 2007, 2007 46th IEEE Conference on Decision and Control.

[6]  Huili Yu,et al.  Vision-based Navigation Frame Mapping and Planning for Collision Avoidance for Miniature Air Vehicles , 2010 .

[7]  Roland Siegwart,et al.  Autonomous miniature flying robots: coming soon! - Research, Development, and Results , 2007, IEEE Robotics & Automation Magazine.

[8]  Nathan Michael,et al.  Vision-Based, Distributed Control Laws for Motion Coordination of Nonholonomic Robots , 2009, IEEE Transactions on Robotics.

[9]  Youdan Kim,et al.  UAV guidance using a monocular-vision sensor for aerial target tracking , 2014 .

[10]  Jeffrey M. Sullivan,et al.  Evolution or revolution? the rise of UAVs , 2006, IEEE Technology and Society Magazine.

[11]  Tong Heng Lee,et al.  Distributed control of angle-constrained circular formations using bearing-only measurements , 2012, 2013 9th Asian Control Conference (ASCC).

[12]  Brian D. O. Anderson,et al.  Localization and Circumnavigation of a Slowly Moving Target Using Bearing Measurements , 2014, IEEE Transactions on Automatic Control.

[13]  Rita Cunha,et al.  A nonlinear quadrotor trajectory tracking controller with disturbance rejection , 2014 .

[14]  Tyler H. Summers,et al.  Stabilization of stiff formations with a mix of direction and distance constraints , 2013, 2013 IEEE International Conference on Control Applications (CCA).

[15]  Hugh F. Durrant-Whyte,et al.  Natural landmark-based autonomous vehicle navigation , 2004, Robotics Auton. Syst..

[16]  Antonis A. Argyros,et al.  Angle-based methods for mobile robot navigation: reaching the entire plane , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[17]  Adrian N. Bishop,et al.  Bearing-only triangular formation control on the plane and the sphere , 2010, 18th Mediterranean Conference on Control and Automation, MED'10.

[18]  Kenzo Nonami,et al.  Optic flow-based vision system for autonomous 3D localization and control of small aerial vehicles , 2009, Robotics Auton. Syst..

[19]  Hyo-Sung Ahn,et al.  Nonlinear Control of Quadrotor for Point Tracking: Actual Implementation and Experimental Tests , 2015, IEEE/ASME Transactions on Mechatronics.

[20]  Hamid D. Taghirad,et al.  SLAM Using Single Laser Range Finder , 2008 .

[21]  Camillo J. Taylor,et al.  A vision-based formation control framework , 2002, IEEE Trans. Robotics Autom..

[22]  P.N. Pathirana,et al.  Bearing-Only Localization using Geometrically Constrained Optimization , 2009, IEEE Transactions on Aerospace and Electronic Systems.

[23]  Hyo-Sung Ahn,et al.  Control of a mobile agent using only bearing measurements in triangular region , 2014, the 2014 Seventh IEEE Symposium on Computational Intelligence for Security and Defense Applications (CISDA).

[24]  Roland Siegwart,et al.  Autonomous miniature flying robots , 2007 .

[25]  Shiyu Zhao,et al.  Translational and Scaling Formation Maneuver Control via a Bearing-Based Approach , 2015, IEEE Transactions on Control of Network Systems.

[26]  Philippe Martinet,et al.  Vision-based navigation of unmanned aerial vehicles , 2010 .

[27]  Hugh F. Durrant-Whyte,et al.  A solution to the simultaneous localization and map building (SLAM) problem , 2001, IEEE Trans. Robotics Autom..

[28]  Claire J. Tomlin,et al.  Precision flight control for a multi-vehicle quadrotor helicopter testbed , 2011 .

[29]  Randal W. Beard,et al.  Trajectory tracking for unmanned air vehicles with velocity and heading rate constraints , 2004, IEEE Transactions on Control Systems Technology.

[30]  Hyo-Sung Ahn,et al.  The Fermat-Weber location problem in single integrator dynamics using only local bearing angles , 2015, Autom..

[31]  S. Wiggins.  Introduction to Applied Nonlinear Dynamical Systems and Chaos , 1989 .

[32]  Adrian N. Bishop.  Distributed bearing-only formation control with four agents and a weak control law , 2011, 2011 9th IEEE International Conference on Control and Automation (ICCA).

[33]  Patric Jensfelt,et al.  Distributed control of triangular formations with angle-only constraints , 2010, Syst. Control. Lett..