Motion Planning and Trajectory Tracking on 2-D Manifolds embedded in 3-D Workspaces

In this paper we present a methodology that drives and stabilizes a robotic agent moving in a three dimensional environment, to a 2-dimensional manifold embedded in the workspace. Once the agent reaches the manifold, depending on the application, it performs a motion planning or a trajectory tracking task. Appropriately constructed belt-zone vector fields guarantee that the agent will not depart the 2-D manifold proximity area, while carrying out the motion planning or trajectory tracking task. The derived closed form feedback control law guarantees global convergence and collision avoidance. The properties of the proposed algorithm are verified through non-trivial computer simulations.

[1]  Hao-Chi Chang,et al.  Sliding mode control on electro-mechanical systems , 1999 .

[2]  Aleksej F. Filippov,et al.  Differential Equations with Discontinuous Righthand Sides , 1988, Mathematics and Its Applications.

[3]  D. Koditschek,et al.  Robot navigation functions on manifolds with boundary , 1990 .

[4]  Kostas J. Kyriakopoulos,et al.  Closed loop navigation for multiple non-holonomic vehicles , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[5]  Daniel E. Koditschek,et al.  Exact robot navigation using artificial potential functions , 1992, IEEE Trans. Robotics Autom..

[6]  Howie Choset,et al.  Uniform Coverage of Simple Surfaces Embedded in for Auto-Body Painting , 2004, WAFR.

[7]  Vijay Kumar,et al.  Closed loop motion planning and control for mobile robots in uncertain environments , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[8]  Howie Choset,et al.  Towards optimal coverage of 2-dimensional surfaces embedded in IR/sup 3/: choice of start curve , 2003, Proceedings 2003 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2003) (Cat. No.03CH37453).

[9]  Howie Choset,et al.  Development of deposition models for paint application on surfaces embedded in /spl Ropf//sup 3/ for use in automated path planning , 2002, IEEE/RSJ International Conference on Intelligent Robots and Systems.

[10]  Vadim I. Utkin,et al.  Sliding mode control in electromechanical systems , 1999 .

[11]  Howie Choset,et al.  Uniform Coverage of Automotive Surface Patches , 2005, Int. J. Robotics Res..

[12]  Kostas J. Kyriakopoulos,et al.  Closed loop navigation for multiple holonomic vehicles , 2002, IEEE/RSJ International Conference on Intelligent Robots and Systems.

[13]  W. Boothby.  An introduction to differentiable manifolds and Riemannian geometry , 1975 .

[14]  Kostas J. Kyriakopoulos,et al.  Nonholonomic navigation and control of cooperating mobile manipulators , 2003, IEEE Trans. Robotics Autom..

[15]  Dimos V. Dimarogonas,et al.  Decentralized feedback stabilization of multiple nonholonomic agents , 2004, IEEE International Conference on Robotics and Automation, 2004. Proceedings. ICRA '04. 2004.