Type II singularity evader effect on a singular trajectory encoded with DMP

This video shows the execution of a trajectory generated by Dynamic Movement Primitives (DMP) to avoid Type II singular configurations for the 4-DOF parallel robot. To this end, an initial singular trajectory is encoded by the DMP, which is modified during execution by using coupling actions.

Those coupling actions are activated when either the determinant of the forward Jacobian ||J_D || or the minimum angle between two OTS minΩ_c fall below a threshold. Their values are obtained using a vision system to measure the cartesian pose, and only the two limbs most responsible for the singularity are affected by the coupling action. In this experiment, limbs 3 and 4 are deviated from their original reference (bottom charts) to keep the minΩ_c in the limit (top chart). In the charts, “ref” is the reference of the joint positions, “meas” is the measurement of the signals, and “lim” is the limit for minΩ_c.

A core PD+G controller tracks the modified trajectory free of singularities. The coupling actions are defined through objective controls on the variables ||J_D || and minΩ_c.