Stability of haptic rendering for deformable objects

Stable and robust point-based haptic rendering interaction and sliding with and on various types of deformable elastic objects, ranging from low-stiffness (soft) to high-stiffness (rigid), is one of the main technical challenges in the field of virtual environments and force feedback haptic displays. The methods proposed in this work offer a high-fidelity 3D force reflecting haptic model to guarantee a stable interaction and sliding of deformable objects. Consequently, one is able to maintain a continuous force feedback field over the surface of polygonal-based deformable bodies with different normal stiffnesses in each polygonal mesh. Several control strategies are developed and investigated for maintaining and improving on the stability margins and achievable performances for haptic rendering intended for interacting with virtual deformable objects. Two specific classes of control strategies are investigated in this thesis. The first is a Lead-Lag compensator design based on classical control theory and the second scheme is a Linear-Quadratic-Gaussian (LQG) controller designed according to modern control theory. A detailed comparative evaluation of the proposed control strategies are presented to illustrate the performance of the resulting controlled haptic display when applied to deformable objects.