Passive velocity field control (PVFC). Part II. Application to contour following

When the contour following task is represented by a velocity field on the configuration manifold of the system, the coordination aspect of the problem is made explicit. The PVFC scheme developed in the Part I (ibid. vol.29(9) (2001)) can then be applied to track the defined velocity field. However, for some contours, an encoding velocity held on the configuration manifold does not exist or is difficult to define and, as a consequence, the PVFC cannot be directly applied. For systems whose configuration manifolds are compact Lie groups and the desired contour is represented by a parameterized trajectory, a general methodology is developed, using a suspension technique, to define a velocity field on a manifold related to the configuration manifold of the system for which PVFC can be applied. With this strategy, timing along the contour can be naturally varied online by a self-pacing scheme so that the contour tracking performance can be improved. The experimental results for a 2-DOF robot following a Lissajous contour illustrates and verifies the convergence and robustness properties of the PVFC methodology