Robust non linear control of robotic manipulators

This article addresses the problem of controlling robotic manipulators. A preliminary theoretical study is conducted so as to determine a large set of stable and robust controls for non-linear systems whose equations encompass the dynamic equations of any rigid manipulator. Sufficient conditions for obtaining a good tracking of a linear time-invariant model of reference are derived. The local stability of several well known control methods is rigourously established while it is shown that global stability requires the use of non-linear gains in the control expression. An interesting property is that the determination of such gains does not necessarily require an important knowledge of the system; which justifies the use of very simple control schemes in practice. However, a control better conditioned with respect to measurement noises is obtained when a good model of the system is used in the control derivation. Between these two alternatives lies the idea of using adjustable control gains that become large when needed and stay small otherwise. In light of this study, several control schemes proposed in the literature on the subject (including adaptive control schemes) are discussed and conclusions are drawn with a view to future studies.