Piecewise Overactuation of Parallel Mechanisms Following Singular Trajectories: Modeling, Simulation and Control

Abstract

The present approach aims at using the principle of redundant actuation for parallel robotic structures in order to follow complex trajectories in a so-called “mechanically advantageous” way, meaning that for any trajectory configuration the actuators can bear important loads (internal and/or external). Multibody system formalisms using relative coordinates and a robust technique to solve the closed-loop kinematic constraints, which are used for the purpose of modeling, are briefly reviewed. The notion of robot manipulability (and its relation to the velocity and force ellipsoids) is then recalled. As an initial step of the approach developed, suitable locations for the actuators of the non-overactuated system are proposed, the criteria being based on the theoretical concepts mentioned above. Then, according to some possible “customer” requirements, the number of actuators and their location are optimally specified on the basis of a piecewise trajectory planning. Both static and dynamic aspects are treated, depending on the application. Once the number and the locations of the actuators have been determined, a solution for the overdetermined inverse dynamics is proposed. Finally, the approach is validated via two examples of multibody parallel structures that are modeled, simulated and controlled in a suitable environment.