A Controller for Avoiding Dynamic Model Degeneracy of Parallel Robots During Type 2 Singularity Crossing

Abstract

Parallel robots presents singular configurations that divide the operational workspace into several aspects. It was proven that such singularities can be crossed under the constraint of a dynamic criterion. However, the development of a controller able to track such trajectories is up to now limited by a restrictive criterion, which decreases the total number of possible trajectories for crossing a singularity. In this paper, by finding a solution to the inverse dynamic model at the singularity locus, we were able to implement a controller in Cartesian space and track a trajectory that crosses a Type 2 singularity.

A Controller Avoiding Dynamic Model Degeneracy of Parallel Robots During Singularity Crossing

“…Since the matrix J T T 2 is not full rank, its kernel is not empty, and so there is an infinite number of solutions to the inverse dynamic model including (18). An illustration is given Fig.…”

“…with ν a n do f -dimensional arbitrary vector called the overconstraint. Among the possible solutions to the inverse dynamic model, the solution minimizing the input torques, given by equation (18), will be retained. Note also that, out of a singularity, the following equality is obtained J T T 2…”

“…Based on the assumption that the criterion is respected in the neighborhood of the singularity, a projection of the desired wrench in the dynamic model is performed. The design of the error inhibitor is given in this section for a Type 2 singularity from equation (18). The design of a similar inhibitor for a LPJTS singularity can be obtained from equation (24).…”

“…Unfortunately, the computation of the inverse dynamic model in such controller require the inversion of matrices that become singular in Type 2 or LPJTS singularities. This issue was partially solved in [17] and [18]. However, both solutions are limited to Type 2 singularities.…”

“…However, both solutions are limited to Type 2 singularities. Also the solution in [17] requires a restrictive trajectories and the solution in [18] is limited to a control of the Cartesian coordinates of the robot tool, which are rarely available on industrial robots. This paper proposes a global solution allowing the crossing of Type 2 and LPJTS singularities with a computedtorque control, valid for any trajectory that crosses the singularity, as long as the dynamic criterion established in [5,16] is respected.…”