Feasible Scaled Region of Teleoperation Based on the Unconditional Stability (2002)

Applications of scaled telemanipulation into micro or nano world that shows many different features from directly human interfaced tools have been increased continuously. Here, we have to consider many aspects of scaling such as force, position, and impedance. For instance, what will be the possible range of force and position scaling with a specific level of performance and stabil- ity? This knowledge of feas ible scaling region can be critical to human operator safety. In this paper, we show the upper bound of the product of force and position scaling and simulation results of 1DOF scaled system by using the Llewellyn's unconditional stability in continuous and discrete domain showing the effect of sampling rate. Recent applications to the micro or nano world like micro- surgery which belongs to a macro -micro bilateral manipula- tion (MMBM) (5)(10)(11) shows the effectiveness of scaled teleoperation. Scaled teleoperation bridges the gap between H.O. (human operator) and task of object to be handled with the capability of scaling in factors such as force, position, im- pedance and power (3). A teleoperation system is composed of several parts such as human operator, master robot or handle, communication channel, slave or remote robot and object. This multi parts involving makes the identification of the fea- sible operation region of scaled teleoperation very difficult due to accumulation of model erro r and time delay in and out of M and S. The operable region is limited by stability and performances (2)(3)(4)(7). Stability problem due to pure com- munication time delay between M (master) and S(slave) which is critical to space operation was solved in some aspect using lossless transmission line analogy (1). Thereafter, this passivity approach has been popular to the researchers. How- ever, this passivity-based control can lower performance down to 50% according to (4). One of the re asons is due to low force reflection gain for the master. It is shown that position-error based force reflection combined with compliance control re- sulted in the best task performance when the set of normal master and big and stiff slave robot was used (9). The overall system stability depends on the both of communication chan- nel time delay, sampling rates and dynamics of M and S. To know the feasible operation region in terms of scaling factors such as position or force can be more helpful to a H.O. as MMBM spreads. So far, there have been few papers showing how feasible operation region depends on position and force scaling factors and sampling rates in nonidentical master and slave robots. In this paper, we derived the upper bound of scaling gain product of position and force based on the unconditional sta- bility. Then we identified the stable or feasible region of scaled teleoperation in terms of force, position scaling and sampling rates based on the characteristic equation when the time delay in each M, S are assumed to be from 0 to three sampling time (Ts). The communication channel delay is i g- nored. To include the time delay from sampling rates we used digital control model.