Singularity-consistent dynamic path tracking under torque limits

We develop further our singularity-consistent approach to arrive at a parameterized form of the dynamics of a nonredundant robotic mechanism tracking a desired path in Cartesian space. It is shown that this form is suitable for incorporating joint torque limits, which is an important issue for practical applications. We propose a closed-loop controller which behaves as a “conventional” resolved-acceleration type controller at regular points of the kinematic function. Around any singularity and at so-called instantaneous self-motion singularities the controller is able to truck the direction of the specified path exactly. The limit on the torque norm results in some position error, without deteriorating, however, the direction tracking ability. It is shown also that motion through the bifurcation type singularity can be easily controlled in practice as well