Shortest Dubins Path to a Circle

The Dubins path problem had enormous applications in path planning for autonomous vehicles. In this paper, we consider a generalization of the Dubins path planning problem, which is to find a shortest Dubins path that starts from a given initial position and heading, and ends on a given target circle with the heading in the tangential direction. This problem has direct applications in Dubins neighborhood traveling salesman problem, obstacle avoidance Dubins path planning problem etc. We characterize the length of the four CSC paths as a function of angular position on the target circle, and derive the conditions which to find the shortest Dubins path to the target circle.

[1]  Jean-Daniel Boissonnat,et al.  Accessibility region for a car that only moves forwards along optimal paths , 1993 .

[2]  Parikshit Maini,et al.  Path planning for a UAV with kinematic constraints in the presence of polygonal obstacles , 2016, 2016 International Conference on Unmanned Aircraft Systems (ICUAS).

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

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

[5]  Mario Fernando Montenegro Campos,et al.  An evolutionary approach for the dubins' traveling salesman problem with neighborhoods , 2012, GECCO '12.

[6]  Xavier Goaoc,et al.  Bounded-Curvature Shortest Paths through a Sequence of Points Using Convex Optimization , 2013, SIAM J. Comput..

[7]  Eloy García,et al.  Tightly Bounding the Shortest Dubins Paths Through a Sequence of Points , 2017, Journal of Intelligent & Robotic Systems.

[8]  Vladimir J. Lumelsky,et al.  Classification of the Dubins set , 2001, Robotics Auton. Syst..

[9]  Ravi Vaidyanathan,et al.  UAV Optimal Path Planning Using C-C-C Class Paths for Touring , 2004 .

[10]  Vikram Kapila,et al.  Optimal path planning for unmanned air vehicles with kinematic and tactical constraints , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[11]  Mario Fernando Montenegro Campos,et al.  On the Generation of Trajectories for Multiple UAVs in Environments with Obstacles , 2010, J. Intell. Robotic Syst..

[12]  Jean-Daniel Boissonnat,et al.  A polynomial-time algorithm for computing a shortest path of bounded curvature amidst moderate obstacles (extended abstract) , 1996, SCG '96.

[13]  Joao P. Hespanha,et al.  Algorithms for the traveling Salesman Problem with Neighborhoods involving a dubins vehicle , 2011, Proceedings of the 2011 American Control Conference.

[14]  Sivakumar Rathinam,et al.  On Tightly Bounding the Dubins Traveling Salesman's Optimum , 2015 .

[15]  Craig A. Woolsey,et al.  Minimum-Time Path Planning for Unmanned Aerial Vehicles in Steady Uniform Winds , 2009 .

[16]  Jean-Daniel Boissonnat,et al.  Shortest path synthesis for Dubins non-holonomic robot , 1994, Proceedings of the 1994 IEEE International Conference on Robotics and Automation.

[17]  Pankaj K. Agarwal,et al.  Motion planning for a steering-constrained robot through moderate obstacles , 1995, STOC '95.

[18]  João Pedro Hespanha,et al.  Dubins Traveling Salesman Problem with Neighborhoods: A Graph-Based Approach , 2013, Algorithms.