1) Time Domain Analysis:
a) 4CH case: Fig. 6 shows the force and position
tracking responses of the 4CH scheme obtained in the experiments. For the first few seconds, the master is moved back and forth by the user while the slave is in free space. The nonzero values for Fh, even when the slave is in free space, are mainly due to the uncompensated mass of the handle between the force sensor and the operator’s hand. As it can be seen, in free motion, the slave rapidly tracks the master’s motion. Next, the slave makes contact with the environment. The operator pushes against the master, leading to different levels of the slave/environment contact forces. The controller ensures a good agreement between the operator/master and slave/environment forces under contact motion. The environment consists of a sponge with stiffness such as a slight penetration of the slave interface into the environment is possible. However, since this penetration is small for considerable operator forces, we consider this environment to provide a good approximation to a stiff environment; the reason for not using an infinitely stiff environment (e.g., metal) in our experiments lies in trying to avoid force spikes at the onset of the slave/environment contact.