Passive haptic rendering and control of Lagrangian virtual proxy

We consider the problem of passive haptic rendering and interfacing of multiple degree-of-freedom (DOF) virtual proxy (VP), which has nonlinear Lagrangian dynamics and interacts with deformable virtual objects. For this, we solve the followings: 1) how to extend our recently-proposed non-iterative passive mechanical integrator (NPMI [1]) to simulate this nonlinear Lagrangian VP haptically-fast and discrete-time passively; 2) how to utilize virtual coupling technique to interface this NPMI-simulated VP and haptic devices while guaranteeing (sampled-data) passivity; and 3) how to passively render the interaction between VP and linear visco-elastic deformable virtual objects, while enhancing passivity at contact-on/off switchings. Some experimental results are also presented to support theory.