A recursive singularity-robust Jacobian generalized inverse

An operator form of a scale-invariant singularity-robust generalized inverse of the Jacobian, J ε R^mxn, for a serial-chain n-link manipulator is developed. This allows the direct computation of a solution to the resolved-rate problem β(0)=Jθ˙ via an O(n) recursive algorithm. There is no restriction on the number of links or the dimension, m⩽6, of the end-effector velocity vector. The generalized inverse requires knowledge of the mass and inertia properties of the manipulator links. However its use is central to the problem of solving closed chain forward dynamics and computing velocity changes due to inelastic collision between a manipulator end-effector and the environment