Optimal trajectory planning for path convergence in three-dimensional space

This article addresses the problem of determining the shortest path that connects a given initial configuration (position, heading angle, and flight path angle) to a given rectilinear or a circular path in three-dimensional space for a constant speed and turn-rate constrained aerial vehicle. The final path is assumed to be located relatively far from the starting point. Due to its simplicity and low computational requirements the algorithm can be implemented on a fixed-wing type unmanned air vehicle in real time in missions where the final path may change dynamically. As wind has a very significant effect on the flight of small aerial vehicles, the method of optimal path planning is extended to meet the same objective in the presence of wind comparable to the speed of the aerial vehicles. But, if the path to be followed is closer to the initial point, an off-line method based on multiple shooting, in combination with a direct transcription technique, is used to obtain the optimal solution. Optimal paths are generated for a variety of cases to show the efficiency of the algorithm. Simulations are presented to demonstrate tracking results using a 6-degrees-of-freedom model of an unmanned air vehicle.

[1]  Jean-Daniel Boissonnat,et al.  Shortest paths of bounded curvature in the plane , 1994, J. Intell. Robotic Syst..

[2]  Jean-Daniel Boissonnat,et al.  Shortest paths of bounded , 1992 .

[3]  Antonios Tsourdos,et al.  3D Dubins Sets Based Coordinated Path Planning for Swarm of UAVs , 2006 .

[4]  J. Hedrick,et al.  Optimal Path Planning with a Kinematic Airplane Model , 2007 .

[5]  H. Sussmann Shortest 3-dimensional paths with a prescribed curvature bound , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[6]  Salah Sukkarieh,et al.  3D smooth path planning for a UAV in cluttered natural environments , 2008, 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[7]  P. B. Sujit,et al.  Adaptive Optimal Path Following for High Wind Flights , 2011 .

[8]  Y Bestaoui,et al.  Mission plan under uncertainty for an autonomous aircraft , 2010 .

[9]  Timothy W. McLain,et al.  Vector Field Path Following for Miniature Air Vehicles , 2007, IEEE Transactions on Robotics.

[10]  Anil V. Rao,et al.  Practical Methods for Optimal Control Using Nonlinear Programming , 1987 .

[11]  Debasish Ghose,et al.  Reactive collision avoidance of multiple realistic UAVs , 2011 .

[12]  J. Karl Hedrick,et al.  Optimal path planning in a constant wind with a bounded turning rate , 2005 .

[13]  Debasish Ghose,et al.  Optimal path planning for an aerial vehicle in 3D space , 2010, 49th IEEE Conference on Decision and Control (CDC).

[14]  M. Shanmugavel,et al.  3D Path Planning for Multiple UAVs Using Pythagorean Hodograph Curves , 2007 .

[15]  Timothy W. McLain,et al.  Autonomous Vehicle Technologies for Small Fixed Wing UAVs , 2003 .

[16]  Debasish Ghose,et al.  Rectilinear Path Following in 3D Space , 2010, FIRA RoboWorld Congress.

[17]  J. Karl Hedrick,et al.  Linear Tracking for a Fixed-Wing UAV Using Nonlinear Model Predictive Control , 2009, IEEE Transactions on Control Systems Technology.

[18]  L. Dubins On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents , 1957 .

[19]  Yasmina Bestaoui,et al.  Geometry of Translational Trajectories for an Autonomous Aerospace Vehicle with Wind Effect , 2009 .

[20]  Debasish Ghose,et al.  A modified Dubins method for optimal path planning of a Miniature Air Vehicle converging to a straight line path , 2009, 2009 American Control Conference.

[21]  Alfredo Pironti,et al.  Path Generation and Tracking in 3-D for UAVs , 2009, IEEE Transactions on Control Systems Technology.

[22]  Yasmina Bestaoui,et al.  Geometry of Translational Trajectories for an Autonomous Vehicle With Wind Effect , 2009 .

[23]  Christian B Allen,et al.  48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition , 2010 .

[24]  Yasmina Bestaoui,et al.  3D Flight Plan for an Autonomous Aircraft , 2010 .

[25]  A. R. Babaei,et al.  Three-Dimensional Curvature-Constrained Trajectory Planning Based on In-Flight Waypoints , 2010 .