This paper addresses the problems of designing and analysing a set of stable and robust controls for nonlinear systems whose equations are representative of mechanical systems such as robot manipulators.
When applied to robotics, this theoretical analysis proves that most of the control schemes which are used in practice or proposed in the literature, ranging from the simplest PD control to more complex controls such as adaptive controls or controls based on the so-called 'computed torque method', are liable to perform equally well if the manipulator is perfectly rigid and ideal sensors are used. Consequently, it appears that the main justification for using elaborate schemes is to avoid the need for including large constant control gains when high performance is demanded. At this stage, the analysis suggests the possibility of using more flexible non-linear control gains as a way of improving all schemes.
KEY WORDS Adaptive and robust control of uncertain systems Two-timescale system analysis M(x, X, t)X+E(x, X, t ) x + F ( x , X, t)X+G(x, X, t ) = u * The author is currently on leave from INRIA and is working for the company ITMI, Chemin des Pres, ZIRST, 38240 Meylan, France, as Head of the Robotics Software Department. The author is also with the GRECO-CNRS 'Adaptive Systems'.