Global regulation of flexible joint robots using approximate differentiation

Abstract

In a recent paper Tomei presented a globally asymptotically stable PD regulator for robots with flexible joints. A drawback of this scheme is that noise in velocity measurements degrades performance. In this paper we show that velocity measurement in Tomei's scheme can be replaced by approximate differentiation preserving global asymptotic stability. Simulations that illustrate our result are also presented'. 2 Main Result Propositioii 1. Consider the n degree of freedom flexible joints robot model (1) in closed-loop with the following controller: where ai and bi are positive constants, and l i p , K D are constant diagonal positive definite matrices. Assume I\ ' and K p satisfy min{A,i,(K), &,,in(#p)} > p6. Under these conditions, the closed loop system has * T T . T , $ t ' T = an unique equilibrium point: [qT, q1 , q2 , q2 [qTd,O, qTd, 0, OIT which is GAS. ] 1 U.S. Government work not protected by U.S. copyright 617

A dynamic output feedback control law for elastic joint robots via feedback-passivity approach

“…Compared to the previous results e.g. [8,10], the proposed condition lowers the bound of minimum eigenvalue of stiffness matrix so that a larger class of systems can be incorporated. Next, instead of using the velocity measurements, we design an input-dimensional dynamic system and consider a temporary parallel connection with the additional system.…”

“…This model is slightly more general than that of [9][10][11][12] where B 2 ¼ C 2 ¼ 0: An important structural property of Eq. (1) is that the matrix ð ' B À 2CÞ is skew-symmetric.…”

“…The need to measure the rotor speed has been removed by using a suitable linear filter (e.g. [10,14]) or by observer-based controllers (e.g. [9,15]).…”

Velocity-free saturated PD controller for asymptotic stabilization of spacecraft

“…Note that in the derivation of (19) we have utilized the fact s that the eigenvalues of I + σ σ T are 1 + σ T σ , 1 and 1.…”

“…Note that Tanh(·) function serves as a saturation function and other saturation functions can be freely chosen to replace in the proposed controllers. Note also that the filter given by (29) and (30) are borrowed from [5,19].…”