Maintaining visibility of a moving holonomic target at a fixed distance with a non-holonomic robot

In this paper we consider the problem of maintaining surveillance of a moving the target by a nonholonomic mobile observer. The observer's goal is to maintain visibility of the target from a predefined, fixed distance, l. The target escapes if (a) it moves behind an obstacle to occlude the observer's view, (b) it causes the observer to collide with an obstacle, or (c) it exploits the nonholonomic constraints on the observer motion to increase its distance from the observer beyond the surveillance distance l. We deal specifically with the situation in which the only constraint on the target's velocity is a bound on speed (i.e., there are no nonholonomic constraints on the target's motion), and the observer is a nonholonomic, differential drive system having bounded speed. We develop the system model, from which we derive a lower bound for the required observer speed. Finally, we consider the effect of obstacles on the observer's ability to successfully track the target.

[1]  Masafumi Yamashita,et al.  Searching for a Mobile Intruder in a Polygonal Region , 1992, SIAM J. Comput..

[2]  S. Sastry,et al.  Probabilistic pursuit-evasion games: a one-step Nash approach , 2000, Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No.00CH37187).

[3]  Steven M. LaValle,et al.  Visibility-Based Pursuit-Evasion in an Unknown Planar Environment , 2004, Int. J. Robotics Res..

[4]  Jean-Claude Latombe,et al.  Robot motion planning , 1970, The Kluwer international series in engineering and computer science.

[5]  T. D. Parsons,et al.  Pursuit-evasion in a graph , 1978 .

[6]  P. Varaiya,et al.  Differential games , 1971 .

[7]  J. Schwartz,et al.  On the “piano movers'” problem I. The case of a two‐dimensional rigid polygonal body moving amidst polygonal barriers , 1983 .

[8]  Alejandro Sarmiento,et al.  Maintaining visibility of a moving target at a fixed distance: the case of observer bounded speed , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.

[9]  Héctor H. González-Baños,et al.  Motion strategies for maintaining visibility of a moving target , 1997, Proceedings of International Conference on Robotics and Automation.

[10]  Héctor H. González-Baños,et al.  A reactive motion planner to maintain visibility of unpredictable targets , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[11]  Alejandro Sarmiento,et al.  On the existence of a strategy to maintain a moving target within the sensing range of an observer reacting with delay , 2003, Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453).

[12]  Craig Becker,et al.  An Intelligent Observer , 1995, ISER.

[13]  Bernard Bayle,et al.  Nonholonomic Mobile Manipulators: Kinematics, Velocities and Redundancies , 2003, J. Intell. Robotic Syst..

[14]  Richard M. Murray,et al.  A motion planner for nonholonomic mobile robots , 1994, IEEE Trans. Robotics Autom..

[15]  Héctor H. González-Baños,et al.  Real-time combinatorial tracking of a target moving unpredictably among obstacles , 2002, Proceedings 2002 IEEE International Conference on Robotics and Automation (Cat. No.02CH37292).

[16]  Leonidas J. Guibas,et al.  Visibility-Based Pursuit-Evasion in a Polygonal Environment , 1997, WADS.

[17]  David J. Kriegman,et al.  Computing exact aspect graphs of curved objects: Algebraic surfaces , 1990, International Journal of Computer Vision.

[18]  T. Başar,et al.  Dynamic Noncooperative Game Theory , 1982 .

[19]  Zexiang Li,et al.  Motion of two rigid bodies with rolling constraint , 1990, IEEE Trans. Robotics Autom..

[20]  H. Sussmann,et al.  Limits of highly oscillatory controls and the approximation of general paths by admissible trajectories , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[21]  S. Shankar Sastry,et al.  Probabilistic pursuit-evasion games: theory, implementation, and experimental evaluation , 2002, IEEE Trans. Robotics Autom..

[22]  Rufus Isaacs,et al.  Differential Games , 1965 .

[23]  S. Sastry,et al.  Nonholonomic motion planning: steering using sinusoids , 1993, IEEE Trans. Autom. Control..

[24]  Jean-Paul Laumond,et al.  Robot Motion Planning and Control , 1998 .

[25]  Devin J. Balkcom.  Geometric Construction of Time Optimal Trajectories for Differential Drive Robots , 2000 .

[26]  Rafael Murrieta-Cid,et al.  Optimal Motion Strategies Based on Critical Events to Maintain Visibility of a Moving Target , 2005, Proceedings of the 2005 IEEE International Conference on Robotics and Automation.