Nonholonomic camera-space manipulation

The method of camera-space manipulation is extended to wheeled systems. A minimum of two cameras is required to place points on end-effectors (or objects in their grasp) of n-degree-of-freedom manipulators relative to other bodies where the nonholonomic degrees of freedom on a mobile manipulator base may be included. The target bodies do not have a precisely known location relative to the environment. The method is illustrated experimentally, though not in real time, using a point placement task. It is then generalized to rigid-body positioning tasks. Although the experimental point placement illustrations make use of a very simple trajectory planning scheme for the wheels of the base, a smoother optimal trajectory planning scheme that makes use of the Pontryagin maximum principle is also developed and illustrated. In a departure from the practice of using time as the independent variable for estimation and optimal trajectory planning algorithms, the present development is time independent and instead introduces the forward rotation of the drive wheel of the base as the independent variable