A new method for robot control in singular configurations with motion in any Cartesian direction

A Cartesian control law usually requires the inversion of the Jacobian matrix. In singular configurations, motions along particular directions (degenerate directions) seem to be infeasible. In this paper, the constraints that the reference trajectory must satisfy to be correctly tracked are studied for different types of singularities. For an external singularity, no constraint exists on the path, so a motion along a degenerate direction is possible. For an internal singularity the constraints on the trajectory are stronger, so the tangent to the path at the singular point can not be arbitrary. Then, a method is proposed for computing the control input to obtain a perfect tracking of a given reference trajectory satisfying the constraints described above