This thesis discusses the application of manifold stabilization to industrial robots with a focus on human-robot collaboration. Manifold stabilization aims at stabilizing submanifolds defined in the output space of a dynamical system without any a priori time parametrization. A robot is typically operating in a three-dimensional Euclidean space and thus the stabilization of the end-effector on a path or a surface are of particular interest. This special types of manifold stabilization are denoted as path following control (PFC) and surface following control (SFC), respectively. Novel PFC and SFC approaches for fully actuated manipulators and elastic joint robots in three-dimensional space are proposed, which are based on input-output linearization. The controllers transform the nonlinear robot dynamics into a linear system with decoupled dynamics in tangential and transversal direction with respect to a path or surface. A parallel transport frame is used for the design of the PFC, which not only allows to directly cope with paths having zero curvature, but also drastically simplifies the PFC law compared to existing approaches. These properties of the PFC and SFC approaches make them highly suitable for industrial robotic applications. In particular a combination of PFC and SFC strategies with compliance control opens up new possibilities for the systematic design of robot operation in contact with the environment and for human-robot collaboration. Moreover, it is shown that a large number of virtual fixtures can be systematically generated with the proposed approaches. Virtual fixtures denote control algorithms that restrict the workspace of a manipulator in physical human-robot interaction tasks, e.g., hand-guiding operation.weiterlesen