## 1 Introduction
Moreover, the ability to identify obstacles when controlled with a tracking device depends on the perception and position of the operator's hand [33]. An overlooked problem when controlling manipulators using a tracking device is the size ratio [26] between the movement of the operator's hand and the displacement of the manipulator effector, which has a direct impact on the value of its velocity. This problem does not seem to be so important when controlling surgical manipulators. This is due to the small-scale ratio, for which the effector makes less movement in relation to the operator's hand [29; 34]. The velocity of the movements in this case is of little importance. The basic problem is to ensure the accuracy of the effector's movement of the controlled manipulator. It is confirmed in the research of hydraulic excavators [35], describing the efficiency of conventional control system and tracking devices. During the research, the effort of the operators was also compared using a survey NASA-TLX. On its basis, the problem of the operator's psychophysical load due to the oscillations of the excavator's bucket was noticed. They resulted from small, uncontrolled movements of the operator's hand during control with the tracking device. The amplified vibration of the operator's hand by the manipulator control system limited the efficiency of operation. On this basis, it was found that the scale ratio may have a significant impact on the efficiency of operation for manipulators with a large working area, such as foundry manipulators, EOD robot manipulators, arms of hydraulic excavators, or demolition equipment. These conclusions are confirmed by the research presented in the paper [36]. The authors compare a conventional control system of the excavator with two tracking devices using position control and rate control. They found that both systems based on a tracking device improve the velocity and accuracy of task realization more than twice as compared to the conventional type of control. However, according to the subjective assessments of the test participant, the use of the position control system is more intuitive in operation in relation to the rate control system, although the implementation of long movements may cause early stress on the user's arm and then increase his frustration. To limit the impact of the operator's hand vibration on the efficiency of the manipulator, a hybrid control method was proposed [26]. Rate control was used for the rotation of the excavator swing and position control was for the positioning of the working equipment. In this way, the intuitive control of the working equipment was maintained and the problem with the control of the excavator swing, whose range of movement is 360\({}^{\circ}\), was eliminated. The research [31] shows that the direction of the operator's hand movement has no significant effect on the velocity. However, there are significant differences in the maximum values of the operator's hand velocity during reaching movements (average maximum speed 1 m/s) and precision movements (average maximum speed 0.5 m/s). The research results so far take into account the accuracy and velocity of task execution using intuitive tracking control systems. The discussed issues concern the impact of haptic feedback on the effectiveness of control and adjusting the control using the tracking device to the operator's hand. Most of the research on the HMI device relates to the control of manipulators with a small working area, where the size ratio does not affect their work efficiency. Manipulators with a large working area need other solutions. Based on subjective assessments, the impact size ratio on the efficiency of work with these manipulators was found, but this information is vague and omitted in further analyses. There is also no information on the velocity of the effectors of manipulators with a large working area depending on the size ratio and the perception of the operator.