Nonholonomic behavior in redundant robots under kinematic control

We analyze the behavior of redundant robots when the joint motion is generated by inverting task velocity commands through a kinematic control scheme. Depending on the chosen inversion scheme, the robot motion is subject to differential constraints that may or may not be integrable. Accordingly, we give a classification in terms of holonomic, partially nonholonomic, and completely nonholonomic behavior, pointing out also the relationship with the so-called cyclicity property. This general classification is illustrated by means of several examples. When the kinematic control scheme is nonholonomic, the whole configuration space of the robot is accessible by a proper choice of the task input commands. Under this assumption, we address the joint reconfiguration problem, namely the design of end-effector velocity commands that drive the robot to a desired joint configuration. To solve this problem, it is possible to borrow existing methods for motion planning of nonholonomic mechanical systems, such as the sinusoidal steering technique for chainedform systems.