Global regulation of flexible joint robots using approximate differentiation

Tomei (1991) presented a globally asymptotically stable PD regulator for robots with flexible joints. A drawback of this scheme is that, as is well known, noise in velocity measurements degrades performance, and numerical differentiation is inaccurate for low and high speeds. On the other hand, approximate differentiation, replacing the derivative operator p by the high pass filter (bp/p+a), is commonly used in applications since it yields good behavior for regulation tasks. In this paper, we show that velocity measurement in Tomei's scheme can be replaced by approximate differentiation preserving global asymptotic stability for all positive values of b and a. Simulations that illustrate our result are also presented.>