COMPLETE CONTROLLABILITY CRITERIA FOR CLASSES OF MECHANICAL SYSTEMS WITH BOUNDED CONTROLS

A collection (class) of controllable dynamical systems, each described by Lagrange equations of the second kind, is considered. The class is defined by specifying the bounded domains in which the controls and g eneralized forces may take their respective values. The systems differ from one another both in the expression for the kinetic energy, which may be chosen at will from a set of positive-definite quadratic forms in the velocities (with coefficients, which depend on the coordinates ), and in the generalized forces, which may vary within the same domai n. Necessary and sufficient conditions are established for any such cl ass to be completely controllable (i.e. for any system belonging to th e class to be completely controllable). These conditions have an obvio us physical meaning. In the case, for example, of robot manipulators, the conditions imply that a system is completely controllable if and o nly if the maximum values of the control torques exceed the correspond ing torques of the other forces (weight, resistance, etc.) in absolute value. (C) 1997 Elsevier Science Ltd.