The flexible structure of a robot multi-links manipulator can be either a side effect or, on the contrary, an essential feature. We present a fairly general model to derive the corresponding dynamic equations in quite a systematic and simple way. To this end, we use the Lagrange formulation with strain energy potential and Raleigh (dissipation) functions. The approach can incorporate torsional deformation and aerodynamic friction, and it applies easily to robots working in the sea. The trajectory control appears to be one in the presence of model imprecision, and a slightly modified version of the classical sliding control technique is utilized to design the tracking control of the manipulator. Then we introduce the time-varying inertia link device (carried out by means of sliding masses) which we suggested in earlier work, and we show how it can be used to improve the tracking control scheme above. This paper contributes new ideas concerning flexible multi-links arms and active inertia links.

The author introduced the use of time–varying inertia links to increase the flexibility (or versatility) of manipulators in the sense that they can so achieve more tracking capabilities. Clearly, we then have a pair of control vectors (link inertias and external forces) instead of one control vector only (applied forces). After a careful derivation of the dynamical equations of such manipulators, one shows that their control procedure can be decomposed into two stages, each of them involving sliding control schemes via prescribed dynamics on the error term, that is to say the difference between the desired position and the actual position. This approach provides a good technique to take account of possible constraints on the magnitude of the control, and in addition, it is possible to consider the sliding conditions as an ideal mechanical constraint, therefore the use of the principle of virtual displacements.

This paper is a continuation of the one entitled “Trajector control of manipulators with time–varying inertia links” (Robotica 6, No. 3, 197–202, 1988). It described new techniques to circumvent difficulties arising when the values of the mechanical parameters are not exactly known and when linearization does not apply because of the important deviation. In addition this paper shows that Appel's principle of virtual displacements is more efficient than the Lagrangian parameters for the derivation of the manipulator's dynamic parameters in the presence of mechanical constraints.