A STUDY on MULTIPLE DEGREE-of-FREEDOM FORCE-REFLECTING TELEOPERATION with CONSTANT and VARIABLE TIME DELAYS

This article studies the stability and performance of teleoperation systems under the effect of constant and variable time delays by employing the wave variable method. In particular, the effect of wave variables on the stability of a multi-degree-of-freedom forcereflecting system is demonstrated on a three-axis robot and initial simulation results are presented. Also, the multi-degree-of-freedom teleoperation system model developed in the Matlab environment is described. This model, used in numerical simulations, will also be utilized in real-time implementation of the controller, which is under development. System stability and instability issues are addressed especially when variable time delays are introduced. Finally, in order to insure system stability, the adaptive gain method is described as a potentially effective tool to overcome instability. INTRODUCTION Teleoperation is a robotics application where there is a master and a slave system interacting with each other and with their environment. The master system is often a joystick or a duplicate of the slave system that is driven by the operator. The slave system is the robot that is within a distance from the master system, controlled by the commands sent by the master system and is interacting with the environment that it is working on. There are two main types of teleoperation as unilateral and bilateral teleoperation. In unilateral teleoperation, no feedback is provided from the slave to the master and the slave is driven with the commands sent from the master. In bilateral teleoperation, any kind of feedback from the slave to the master can be sent. This feedback can be visual, force, sound, position, etc. In this study, I considered only the force-feedback bilateral teleoperation, or force-feedback teleoperation. In force-feedback teleoperation, as it was the case in unilateral teleoperation, the slave system is driven with the commands sent from the master system. But this time, slave system sends back the force-feedback information that it produces while interacting with the environment that it is working on, to the master system to make the operator that is in interaction with the master feel the environment that the slave is working on. The common short come of the force-feedback teleoperation is the instability that the system undergoes when it experiences time delay in the communication between the master and the slave. The magnitude of this time delay could be in the order of seconds, minutes, hours or days due to the task of the teleoperation. This problem has been studied by many researchers, but Anderson and Spong were perhaps the first to use the wave variable method to control bilateral controllers [4]. Also, Niemeyer and Slotine [5], and Munir and Book [1, 2] have implemented this method to teleoperation systems. Current studies are on the variable time-delayed teleoperation [6]. Although wave variable technique guarantees stability for the constant time-time delayed teleoperation, the system experiences instability when the time delay varies. This paper is outlined in the following manner: The next section presents a brief description of the wave variable method for single degree-of-freedom systems. Also in this section, the transition to multiple degree-offreedom (DOF) systems is described. The following section introduces the modification made to the wave variable technique to guarantee stability for variable time-delayed teleoperation. The next section presents the modeling of a three degree-of-freedom teleoperation system using Matlab. Descriptions of various Matlab blocks used in the construction of master (joystick) and slave (remote system) sub-systems are provided to orient the reader to Matlab modeling. Subsequently, the implementation of wave variable method to a multi-DOF system is illustrated on a three-DOF teleoperation system in Simulation Results. The legacy of the wave variable method for multi-DOF teleoperation is discussed by presenting the simulation results with and without the wave variable technique for three different time delays. Then it is shown that the teleoperation system goes unstable even though the wave variable technique is used for the variable time delayed teleoeration. Modified version of the wave variable technique is used and the simulation results are presented to overcome this instability introduced because of the variable time delay. Lastly, conclusions and planned future work appear in Section 6.