Position Optimization of a Redundant Haptic Device for Increasing the Simulating Virtual Damping Using Metaheuristic Methods based on Swarm Intelligence

In the present research, a three-degree-of-freedom haptic device was used to simulate a virtual object located on a point on a two-dimensional wall. Two spatial coordinates of the operating point on the wall were arbitrary. Therefore, the robot would have two degrees of freedom redundancy for this task. These two degrees of robot redundancy were specified by the artificial bee colony optimization and crow optimization algorithm in such a way that while ensuring the stability of the robot, the damping coefficient of the simulated virtual object was also maximized. The optimization process was performed in two different ways. In the first case, the stiffness of the robot was assumed to be a constant value in the whole workspace, while in the second case, the stiffness was considered a function of the robot configuration. In each case and at each operating point, first an effective mass, an effective damping coefficient, and an effective stiffness for the robot were obtained, and then using some theoretical relations, a stable operation boundary was obtained. Finally, the optimization methods specify the location of the operating point in such a way that the simulated damping coefficient was maximized. The results show that in the case of constant robot stiffness, both of the mentioned methods were able to simulate the maximum value of 1.825 for the virtual damping coefficient. However, in the case of variable robot stiffness, the crow and bee algorithms reached the values of 2502 and 2498, respectively as the maximum damping coefficient that could be simulated. In addition, although the number of cost function calculations is the same in both methods, the crow optimization algorithm was faster and more repeatable.