Stability analysis of the operational space control for industrial robots using their own joint velocity PI controllers

Abstract

SUMMARYOperational space control of industrial robots is addressed in this document. We analyze a two-loop hierarchical control with the resolved motion rate controller (RMRC) as outer loop and the joint velocity PI controller as inner loop; the latter is the typical velocity controller used in industrial robots. We prove, by the first time, that these simple controllers make the solutions of the closed-loop system uniformly ultimately bounded. Additionally, we give some simple guidelines for the selection of the control gains so as to ensure an explicit bound of the tracking error.

Motion Control of Industrial Robots in Operational Space: Analysis and Experiments with the PA10 Arm

“…♦ Now, we recall the following theorem in (Camarillo et al, 2008), which is a variation of Theorem 4.18 in (Khalil, 2005). …”

“…▽ The proof of Theorem 1 can be found in (Camarillo et al, 2008). Theorem 1 is the base for the following result: Proposition 1: Consider the overall closed-loop system (27) with the outer-loop kinematic controller…”

“…The stability analysis presented here is taken from (Camarillo et al, 2008). More detail can be found in that reference.…”

“…is considered as a disturbance and, as it is shown in (Camarillo et al, 2008), is upper bounded for all t ≥ t 0 by a quadratic polynomial:…”

“…Industrial robots are suitable for applications where high precision, repeatability and tracking accuracy are required. These facts give a great importance to the analysis of the actual control schemes of industrial robots (Camarillo et al, 2008). It is common to specify the robotic tasks in terms of the pose (position and orientation) of the robot's end-effector.…”