Shortest paths with side sensors

We present a complete characterization of shortest paths to a goal position for a vehicle with unicycle kinematics and a limited range sensor, constantly keeping a given landmark in sight. Previous work on this subject studied the optimal paths in case of a frontal, symmetrically limited Field-Of-View (FOV). In this paper we provide a generalization to the case of arbitrary FOVs, including the case that the direction of motion is not an axis of symmetry for the FOV, and even that it is not contained in the FOV. The provided solution is of particular relevance to applications using side-scanning, such as e.g. in underwater sonar-based surveying and navigation.

[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]  Arthur E. Bryson,et al.  Applied Optimal Control , 1969 .

[3]  Lamberto Cesari,et al.  Optimization-Theory And Applications , 1983 .

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

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

[6]  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 .

[7]  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.

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

[9]  M. Chyba,et al.  Optimality for underwater vehicle's , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

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

[11]  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.

[12]  Nuno Dias,et al.  Manoeuvre based mission control system for Autonomous Surface Vehicle , 2009, OCEANS 2009-EUROPE.

[13]  F. Langner,et al.  Side scan sonar image resolution and automatic object detection, classification and identification , 2009, OCEANS 2009-EUROPE.

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

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

[16]  Devin J. Balkcom,et al.  for Differential-Drive Mobile Robots , 2009 .

[17]  Antonio Bicchi,et al.  Shortest Paths for a Robot With Nonholonomic and Field-of-View Constraints , 2010, IEEE Transactions on Robotics.

[18]  Antonio Bicchi,et al.  Optimal Synthesis for Nonholonomic Vehicles With Constrained Side Sensors , 2011, ArXiv.