Analysis on increasing transparency for penalty-based six degree-of-freedom haptic rendering

Virtual coupling is commonly used to maintain stability of penalty-based haptic rendering. However, due to dozens of design parameters involved in the dynamics and force model, to increase transparency while maintaining stability using virtual coupling remains a challenge for 6-Degree-of-Freedom (DOF) haptic rendering. Using an equivalent-angle analysis, we transform 3-DOF rotation into 1-DOF rotation, thereby transforming the 6-DOF dynamics into six 1-DOF dynamics. For each 1-DOF dynamics, a damped vibration model is proposed to analyze the computation of the `graphic tool´. The equilibrium position/angle is defined to analyze the convergence of numerical integration. With this approach, we can improve the transparency of 6-DOF haptic rendering in both free space and constraint space by experimentally determining only two parameters: the integration time step and the number of integrations in each simulation loop. Using this method, we can improve the coupling stiffness to fully exploit the display capability of the haptic device and maintain the stability of the haptic rendering.