Modeling and Control of Elastic Joint Robots

Abstract

In this paper we study the modeling and control of robot manipulators with elastic joints. We first derive a simple model to represent the dynamics of elastic joint manipulators. The model is derived under two assumptions regarding dynamic coupling between the actuators and the links, and is useful for cases where the elasticity in the joints is of greater significance than gyroscopic interactions between the motors and links. In the limit as the joint stiffness tends to infinity, our model reduces to the usual rigid model found in the literature, showing the reasonableness of our modeling assumptions. We show that our model is significantly more tractable with regard to controller design than previous nonlinear models that have been used to model elastic joint manipulators. Specifically, the nonlinear equations of motion that we derive are shown to be globally linearizable by diffeomorphic coordinate transformation and nonlinear static state feedback, a result that does not hold for previously derived models of elastic joint manipulators. We also detail an alternate approach to nonlinear control based on a singular perturbation formulation of the equations of motion and the concept of integral manifold. We show that by a suitable nonlinear feedback, the manifold in state space which describes the dynamics of the rigid manipulator, that is, the manipulator without joint elasticity, can be made invariant under solutions of the elastic joint system. The implications of this result for the control of elastic joint robots are discussed.

Observer analysis and synthesis for Lipschitz nonlinear systems under discrete time-varying measurements

“…Let us consider the model (1) of a flexible joint described by [Spong (1987)], and considered by [Raff (2007), Raff (2008), Chen (2013) The trajectory of the observation error along the sampling sequence is given in Fig. 2, where after a transient the observer converge to the true state.…”

ILC applied to a flexible two-link robot model using sensor-fusion-based estimates

“…The Toeplitz matrices F ij , F r,ij are described similarly to (17), noting that the systems F ij , F r,ij are non-causal. This results in the ILC update (23) on matrix form,…”

“…In many publications the subject of estimation and control of flexible robots are discussed, see for example [17]. In [10] the states for a robot with flexible joints are estimated using an observer based on only the motor angles.…”

Cartesian Impedance Control of Flexible Joint Robots: A Decoupling Approach

“…In this work the so-called reduced model of a robot with n flexible joints is considered as proposed by (Spong, 1987): (7) …”

“…The stability theory for cascaded control systems (Seibert & Suarez, 1990;Loria, 2001) can be applied to analyze the closed-loop system. When dealing with a robot model with flexible joints, the maybe most obvious approach for the design of an impedance controller is the singular perturbation approach (Spong, 1987;De Luca, 1996;Ott et al, 2002). Therein the fast subsystem, which is in our case the torque dynamics, is considered as a perturbation of the rigid body model.…”