10 Pseudoinverse Method and Singularities Discussed Available to Purchase

A manipulator is said to be redundant when more DOF are available than the minimum number required to perform a specific end-effector primary task. For redundant manipulators, as discussed in previous chapters, the inverse kinematic resolution is a fundamental issue in operating the robot systems. The general description of this problem is that, given the desired Cartesian path r_d(t) ∈ ℝ^m for the manipulator’s end-effector to track, how can we generate the corresponding joint trajectory θ(t) ∈ ℝⁿ in real time t? Note that n > m and, thus, there exist multiple or an infinite number of feasible solutions to the inverse-kinematic problem. In this sense, the redundancy of joint motion, together with kinematic and dynamic nonlinearities, complicate the manipulator control problem significantly.