Proposing a new approach for simplification of haptic device dynamics and studying the realized stability domain accuracy

Haptic devices are the interface between real and virtual environment. Stability of a haptic device is a critical issue to insure human safety. Haptic devices generally have several degrees of freedom and complex dynamics. The complexity of this dynamic is due to the complicated mechanism along with the friction of Coulomb and viscous, which makes it difficult to study their stability in general conditions. These robots can cover a large workspace. While the robot stability during simulating a virtual object is significant, the range of motion of the stylus of the haptic device in this situation is limited. This has led to the use a 1-DoF dynamic to determine the robot's stable boundary. Meanwhile, there is no systematic approach for simplifying the model around the operating point. In this paper, a new method is used to obtain the simplified dynamics of the robot so that the nonlinear dynamics of the multi degrees of freedom haptic device can be simplified to a simple dynamic. Using this method, the stability of a KUKA LWR IV industrial robot (as a six-degree of freedom haptic device) in different configurations has been studied and the accuracy of the proposed method has been evaluated through simulations in MATLAB. In this research, manipulator multi-DOF dynamics is simplified to one-DOF dynamics with constant effective mass, viscous and Coulomb friction around the operational point. While stability and passivity analysis for the main manipulator is complex, the acquired one-DOF dynamics can be employed for these analyses easily. The average relative error realized through this method is less than 18%.