Book excerpt: "Kinesthetic haptic applications deliver graphics, sound and force feedback to enable the human operator to interact with objects within a virtual world. The force feedback sensation, in particular, is created by a haptic device that displays the forces arising from this interaction. These forces must accurately emulate a real contact interaction, an objective which is commonly referred to as high-fidelity force feedback rendering. Achieving this objective can be quite challenging, for at least two main reasons. The first stems from the very special stability requirements due to the sampled-data nature of a haptic system and the presence of the human in the loop, while the second can be attributed to the difficult nature of modeling contact interaction in mechanics.In this thesis, a special attention has been given to the non-idealities associated with the sampled-data implementation reflected at the energy level, i.e. energy leaks, and their influence on the stability and passivity of the haptic system. It is proposed to avoid the generation of energy leaks, as much as possible, via modified force feedback laws. This novel notion is entitled as energy-consistent rendering, and the smooth-correction leak-dissipation (SCLD) strategy is developed to achieve it. The range of applicability of this method is studied via a renderability analysis framework under different uncertainty assumptions regarding the human influence on the stability of the overall system. Stability charts are constructed in the nondimensionalized stiffness plane for a canonical virtual spring-mass-damper system. This can be considered a generalization of the concepts of Z-width and M-width in relation to virtual walls and virtual masses.For accurate modeling of the interaction, on the other hand, different custom combination of contact representations geared toward haptic rendering are also studied, under different paradigms for connecting the physical domain to the virtual domain. A unified handling of colliding contact and sustained contact via a hybrid penalty-and-impulse-based formulation is developed that leads to a natural transition between contact formulations. This framework is a first step toward looking at contact methods from a unified control-oriented perspective, and is entitled as the generalized contact controller. A haptic billiard game is developed to serve as a detailed case study to show how contact modeling methods can be generalized to the multiple degree-of-freedom case and customized for specific haptic rendering purposes." --