Shortest Paths for a Robot With Nonholonomic and Field-of-View Constraints

This paper presents a complete characterization of shortest paths to a goal position for a robot with unicycle kinematics and an on-board camera with limited field-of-view (FOV), which must keep a given feature in sight. Previous work on this subject has shown that the search for a shortest path can be limited to simple families of trajectories. In this paper, we provide a complete optimal synthesis for the problem, i.e., a language of optimal control words, and a global partition of the motion plane induced by shortest paths, such that a word in the optimal language is univocally associated with a region and completely describes the shortest path from any starting point in that region to the goal point. An efficient algorithm to determine the region in which the robot is at any time is also provided.

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

[2]  J. Meditch,et al.  Applied optimal control , 1972, IEEE Transactions on Automatic Control.

[3]  J. Ball.  OPTIMIZATION—THEORY AND APPLICATIONS Problems with Ordinary Differential Equations (Applications of Mathematics, 17) , 1984 .

[4]  L. Shepp,et al.  OPTIMAL PATHS FOR A CAR THAT GOES BOTH FORWARDS AND BACKWARDS , 1990 .

[5]  J. Sussmann,et al.  SHORTEST PATHS FOR THE REEDS-SHEPP CAR: A WORKED OUT EXAMPLE OF THE USE OF GEOMETRIC TECHNIQUES IN NONLINEAR OPTIMAL CONTROL. 1 , 1991 .

[6]  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.

[7]  P. Souéres,et al.  Shortest paths synthesis for a car-like robot , 1996, IEEE Trans. Autom. Control..

[8]  Koichiro Deguchi,et al.  Optimal motion control for image-based visual servoing by decoupling translation and rotation , 1998, Proceedings. 1998 IEEE/RSJ International Conference on Intelligent Robots and Systems. Innovations in Theory, Practice and Applications (Cat. No.98CH36190).

[9]  V. Tucker.  The deep fovea, sideways vision and spiral flight paths in raptors. , 2000, The Journal of experimental biology.

[10]  Patrick Gros,et al.  Images interpolation for image-based control under large displacement , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[11]  Devin J. Balkcom,et al.  Time-optimal Trajectories for an Omni-directional Vehicle , 2006, Int. J. Robotics Res..

[12]  Yeung Sam Hung,et al.  Global Path-Planning for Constrained and Optimal Visual Servoing , 2007, IEEE Transactions on Robotics.

[13]  Rafael Murrieta-Cid,et al.  Optimal Paths for Landmark-Based Navigation by Differential-Drive Vehicles With Field-of-View Constraints , 2007, IEEE Transactions on Robotics.

[14]  Antonio Bicchi,et al.  Optimal paths in a constrained image plane for purely image-based parking , 2008, 2008 IEEE/RSJ International Conference on Intelligent Robots and Systems.

[15]  Huifang Wang,et al.  A Geometric Algorithm to Compute Time-Optimal Trajectories for a Bidirectional Steered Robot , 2009, IEEE Transactions on Robotics.

[16]  Devin J. Balkcom,et al.  Minimum Wheel-Rotation Paths for Differential-Drive Mobile Robots , 2009, Int. J. Robotics Res..