Haptic simulations aim to create an immersive, interactive computer generated environment, using haptic devices to render forces to the user based on interactions in the virtual world. In many applications, these simulations must be capable of handling interactions between multiple users, multiple hands, and complex virtual tools. In particular, consider the example of simulating two-handed robotic surgery, where each hand independently directs its own surgical robot to manipulate a tool.

Traditionally only quasi-static, point-like proxies are used to represent the human in virtual environments. In previous works, we proposed dynamic proxies to improve upon this notion. Giving the proxy first order, velocity based dynamics makes it massless but capable of producing crisp dynamic interaction forces. With this paper, we generalize the proxy concept to the case of independent, multiple degree-of-freedom virtual manipulators, by giving the proxy not only first-order dynamics, but its own kinematic properties as well. Like real robots, the virtual manipulators' tips track the user and master motion while generating force feedback. Interactions between the virtual arms and with other objects are implemented as geometric constraints on the tip velocities, and solved in a linearly constrained least-squares minimization. A stability proof is given in terms of passivity. The approach is demonstrated on an actual two-handed haptic console, running a real-time simulation of a pair of six degree-of-freedom virtual manipulators with cylindrical links.

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