N.H. Getz,
and J.E. Marsden, "Joint-Space Tracking
of Workspace Trajectories in Continuous Time",
34th IEEE Conference on Decision and Control, December 1995 New Orleans.
The current state of workspace tracking control for robotic manipulators consists of two classes of controllers. In one class the manipulator dynamics is transformed into workspace coordinates allowing continuous-time tracking of workspace trajectories via control gains posed in the workspace. In the second class one chooses a sequence of via points along the workspace trajectory, applies an inverse kinematics algorithm to get a sequence of points in the configuration space, splines these configuration space points together, and then tracks the time-parameterized spline. In this paper a third class of controllers is offered. A recently introduced technique for inverting nonlinear maps using continuous time dynamics is incorporated into a tracking controller. The controller provides exponential convergence to a desired end-effector trajectory using gains specified in configuration space. This is accomplished without appeal to the use of discrete inverse-kinematics algorithms, allowing the controller to be posed entirely in continuous time.