Damping Design for Robot Manipulators

Abstract

This paper studies the tuning process of controllers for fully actuated manipulators. To this end, we propose a methodology to design the desired damping matrix-alternatively, the derivative gain of a PD controller-of the closed-loop system such that n second-order systems can approximate its behavior with a prescribed damping coefficient, where n denotes the degrees of freedom of the system. The proposed approach is based on the linearization of the closed-loop system around the desired configuration and is suitable for different control approaches, such as PD control plus gravity compensation, impedance control, and passivity-based control. Furthermore, we extensively analyze simulations and experimental results in a cobot.

Interactive Imitation Learning of Bimanual Movement Primitives

“…6 illustrates the employed Cartesian impedance controller in each of the two manipulators, which emulates the behavior of a mass-spring-damper system Λ(q)ẍ = KΔx − D ẋ + f ext (7) where, Λ(q) is the Cartesian inertia matrix of the physical system, K and D are stiffness and damping that symmetric, positive-definite matrices; f ext is the total external force, and Δx = x g − x is the distance between the goal and end-effector poses. The damping matrix can be designed to simulate a critical damping system [34]. In this framework, after computing the orthogonal decomposition of K, i.e., K = R KR T 1 , where K is a diagonal matrix, then D = 2 K1/2 and D = R DR T .…”