# A Robust \(H_{\infty}\) Application for Motor-Link Control Systems of Industrial Manipulators
## 1 Introduction  
In recent years, thanks to the persistent growth of automation, the employment of industrial robots in different applications keeps increasing. Moreover, the demands on their performances are beginning to be much more accurate and meticulous. In addition, there is also the desire of reducing costs, improving safety, and reaching high-speed and precision in movements. This incessant progress confers to the control research area a remarkable focus, it having a direct responsibility of the manipulator's behavior. The robots of the latest generation have lower weight and lower mechanical stiffness, and hence they may suffer more frequently from significant vibration problems, especially when operating at high-speed conditions. Vibrations in mechanical structures constitute a common criticality in the robotic field, which must be robustly handled by the control system. The control system can easily counteract the effects of vibrations on the mechanical arm if some measures of them are included in the closed-loop architecture as additional inputs. This happens if some further sensor, for example, a link gyroscope, is added to the system, capturing these events and feeding the back to the controller. Some solutions have been recently proposed in literature exploiting the usage of additional sensors, such as in [1], where a robust \(H_{\infty}\) control scheme is developed and applied to the base joints of an industrial KUKA robot, equipped with secondary encoders, and in [2], where vibration control is addressed by means of multi-modal, time-varying input shaping based on the identification of the dynamic map of the robot using accelerometers. The drawback of these solutions is that such additional sensors are not generally available for all the industrialrobots. In most cases, the measurements come from sensors installed on the motor that do not give information about the end-effector behavior. Here, the action of the control system is much more complex, since it has to balance out possible link excitations without directly knowing them. Our main goal, then, will just be to guarantee satisfying responses from both the motor and link by only having motor measures available. Through the years, many types of robot-control systems have been exploited. The state-of-the-art recognizes the following control systems among the most important ones: the computed-torque control and the joint-space control, including PD control, PID control, Inverse Dynamics control, and Lyapunov-based control. However, since the dynamics of robots are highly non-linear and contain uncertain parameters, high performance is not often achieved by means of this class of algorithms. In particular, PI or PID controls have issues in parameter tuning, and because of their simple structure, the attainment of proper achievements is usually a slow process that can involve many iterations, especially for several Degrees of Freedom (DOFs) manipulators comprising high non-linearities and couplings. Because of this, industries are particularly interested in investigating the application of control methodologies assuring robust properties in front of nonlinear and complex behaviors in the presence of possible vibration problems at high velocity, possibly avoiding too complex or too specific approaches. In the literature, the interested reader can find various _ad-hoc_ solutions to address the vibration suppression problem, for example, through preshaping input trajectories, as in [3], or by means of an online real-time path compensation system based on a laser tracker, as in [4]. In this context, \(H_{\infty}\) control finds space. The problem is that, despite its relevance in control literature, currently, its application appears to be still limited in the manufacturing world. In order to overcome application difficulties, over time, many researchers have investigated this topic by presenting various types of control implementations.