Compliant admittance-coupled DMP without Type II singularity evader

This video shows the execution of a trajectory generated by Dynamic Movement Primitives (DMP) to provide an admittance behavior for the 4-DOF parallel robot. A coupling action is defined as the difference between a reference force and the exerted force, and this coupling action is fed to the DMP to allow the compliant manipulation.

The original reference trajectory is static in position and zero in force, so any external force triggers the movement of the mobile platform. However, in this video, the authors want to emphasize the problem of this kind of scheme in parallel robots: the control of the human upon the robot because of the compliant manipulation may lead the robot to a singular configuration and a subsequent control loss. Indeed, the original trajectory is close to a singularity in the axis of rotation around Z (ψ), so a moment on this axis (bottom-right chart) may cause its movement (bottom-left chart) to enter a singular configuration (which is measured by minΩ_c in the top chart), and the robot eventually responds unpredictably. The solution for this is the incorporation of a Type II singularity evader. In the charts, “ref” is the reference of the rotation around Z, “meas” is the measurement of the signals, and “lim” is the limit for minΩ_c.

The core controller is a PD+G, used to track the trajectory generated by the DMP.