Projection-based control of parallel manipulators

This paper presents tracking and set point controllers for parallel mechanism based on the notion of a projection operator. The controller reported here works whether the system is overactuated or not; plus one does not need to derive the minimal-order dynamics model of the system. Since the dimension of projection matrix is fixed, the projection-based controller does not need to change its structure whenever the mechanical system changes its topology or number of degrees of freedom. Moreover, the derivation of the projection-based controller seems to be simpler than the inverse dynamics controller derived using Lagrange-D´Almbert formulation. This is because the structure of the former controller can be obtained from the Jacobian matrix of the constraints, which, in turn, can be deduced from the linkage geometry. The stability of the projection-based controllers are rigourously proved, while the condition for the controllability of parallel manipulators is also derived in detail. Finally, experimental results are appended.