This paper focuses on the formulation of constraints for hybrid position/force control of robots. Since the noninvariant nature of the classical approach based on orthogonality of some subspaces has recently been demonstrated, alternative methods are proposed in the paper. The geometrical approach is based on the use of an appropriately located compliant frame in which the position and force controlled directions can be clearly identified. Performing the coordinate transformation using sets of curvilinear coordinates is referred to as the analytical approach. The relation between both approaches is described, and their applicability is discussed. It is shown that the analytical approach is more general. The properties of the task space decomposition are analyzed, and the invariant and noninvariant formulations are discussed. The reasons why some previously published approaches produced results with noninvariant terms and some quantities with a misleading physical sense are explained. Two examples illustrate the application of both approaches.

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