Virtual assembly of complex objects has application in domains ranging from surgery planning to archaeology. In these domains the objective is to plan the restoration of skeletal anatomy or archaeological artifacts to achieve an optimal reconstruction without causing further damage. While graphical modeling plays a central role in virtual assembly, visual feedback alone is often insufficient since object contact and penetration is difficult to discern due to occlusion. Haptics can improve an assembly task by giving feedback when objects collide, but precise fitting of fractured objects guided by delicate haptic cues similar to those present in the physical world requires haptic display transparency beyond the performance of today's systems. We propose a haptic alignment tool that combines a 6 Degrees of Freedom (DOF) attraction force with traditional 6 DOF contact forces to pull a virtual object towards a local stable fit with a fixed object. The object forces are integrated into a virtual coupling framework yielding a stable haptic tool. We demonstrate the use of our system on applications from both cranio-maxillofacial surgery and archaeology, and show that we can achieve haptic rates for fractured surfaces with over 5000 points.

Force-reflecting master arms are explored for use as haptic displays in physical therapy interventions over the internet. Rehabilitation tasks can be constructed in which both the patient and therapist can interact with a common object from distant locations. Each haptic master exerts "forces" on a virtual object which, in response, generates desired velocities for the master arm to track. A novel cooperative control architecture based on wave variables is implemented to counter the destabilizing effect of internet time-delay. The control scheme is validated experimentally using a pair of InMotion2 robots in a virtual beam manipulation task between remote sites.