Dynamic manipulability of velocity-constrained serial robotic manipulators

This paper presents a new performance metric for serial manipulators with velocity constraints on the chain. These systems arise in several different applications such as serial manipulators in the presence of obstacles and in robotics-assisted minimally invasive surgery. It is important to know how constraints on the chain affect the mobility of the end effector and we therefore present a reformulation of the dynamic manipulability of the end effector for serial manipulators with velocity constraints on the chain. In this paper we propose to use the Constrained Jacobian Matrix, i.e., an analytical mapping between the end-effector and joint velocities that also takes the chain constraints into account. The approach allows us to compare the dynamic manipulability of serial manipulators with and without constraints and we show through a simple planar example how the dynamic manipulability is reduced as a result of the trocar constraint in minimally invasive surgery.