# Effect of End-Effector Compliance on Collisions in Robotic Teleoperation
## 1 Introduction  
Since its introduction, teleoperation has been extensively studied by control theoreticians with the aim of achieving the goals of stability and telepresence [1, 2].  
Stability is the ability of a system to remain stable independently of an operator and environment behavior.  
Telepresence, also called transparency, is the ability of a system to accurately render the environment to the operator, which means that the position and the force of the slave closely follow the position and the force of the master.  
Unfortunately, a delay in the communication channel affects both these goals, and several solutions have been proposed in the past decades to mitigate this problem. As can be inferred from the literature, most of the proposed solutions have focused on the improvement of the control system (wave variables [3], adaptive [4] and model predictive algorithms [5]).  
In contrast, in this paper, a completely mechanical approach is adopted. Specifically, the research is focused on improving the use of teleoperation with industrial robots. The aim is to control industrial robots in order to achieve planar movements, such as those needed for smoothing out piles or handling objects.  
In this context, the teleoperation is improved by means of an innovative tool design. This tool is able to reduce the transferred momentum to the object during impacts, obtaining a sort of absorption of the impact itself. Consequently, not only are the delay effects reduced, but also the approach velocity can be incremented, allowing faster movements and minimizing task duration. Therefore, the overall quality of the teleoperation can be improved.  
It is worth noting that the method used in this paper can be applied to all kinds of system in which a delayed/absorbed impact is targeted. For example, the designed tool can be applied in tasks in which the environment is unknown, and a vision system, which has been extensively used in this context [6], cannot be used or is difficult to implement. In this case, the robot can move blindly in a certain direction, and when an impact occurs, the robot can feel this via sensors on the tool or via the torque sensor of the robot (if present). Thanks to the design of the tool, the robot has enough time to elaborate the signals from the sensors and respond to the impact, without the risk of shooting away the objects.  
It is important to underline that the tool requires very small modifications when dealing with objects of different sizes and masses. Accordingly, this study can be considered to correspond to the field of flexible and adaptive tools [6; 7; 8; 9].  
In this paper, the planar movement of a tool mounted on a typical six-degree of freedom (DOF) industrial robot with a spherical wrist is considered. A mono-dimensional model of the collision is implemented, which is enough to characterize the movement of the end-effector along the approach direction. Consequently, the six-DOF robot model has been reduced to a a one-DOF mass-spring-damper system, and the effects of the compliance and the inertia of the robot in the impact are taken into account. The properties of the tool are investigated and optimized in order to reduce the momentum transferred during impacts. Finally, a non-linear system is developed, obtaining a tool that, in simulations, is able to delay the moment in which it actively pushes the objects, giving time to the robot and the operator to detect and respond to the impact.