## 1 Introduction  
Nowadays, piezoelectric devices are very common in a wide range commercial and industrial areas. Piezoelectric devices are used in optomechanical systems, micromanipulators, and robotics [1, 2]. Typically, piezoelectric actuators are of small size, simple design, and generate micrometer-scale mechanical displacement (from 0.5 \(\upmu\)m to 150 \(\upmu\)m). Because of the small size and mass, the inertia force of the device is low, and therefore, the response time is short. These features of the piezoelectric actuator allow to achieve good performance and power/volume ratio. It is worth mentioning that the piezoelectric actuator is made from non-magnetic materials and can be used where strong magnetic fields are undesirable to any equipment and should be protected from the additional magnetic noise. Piezoelectric actuators are able to reach extremely high precision with micro- or even nano-resolution and are driven at high-frequency modes that can generate unlimited linear or rotary motion. These features allow to integrate them into a wide variety of applications. Simple design and uncomplicated working principles allow using piezoelectric devices in industries such as space, satellite communication, and navigation. Specifications for the devices which may be used for space application are rigorous, i.e., small mass and volume, easy integration, and high reliability are only a few of those requirements. Piezoelectric actuators and devices are good candidates for such tasks and may be used for space applications. However, the majority of piezoelectric actuators and motors are the single degree of freedom (DOF) devices, while there are many applications where several DOF systems are required. Those systems can be assembled using several actuators, but the systems become complicated, and it is challenging to manage errors while combining several single DOF actuators. Moreover, such behavior is not acceptable for the tasks, where the size and weight of the mechanism are limited, and high precision becomes an issue. Oppositely, building a large system requires separate units because of the size limitations of piezoelectric actuators [3]. However, in this approach, the size of the motor must be designed in a way when a minimum number of elements are needed. Multi-DOF ultrasonic motors are devices that can set orientation and positioning of the object in any direction. 3 DOF piezoelectric actuator, which consists a cylindrical stator and the round-shaped rotor, was designed and developed by [PERSON] et al. This actuator actuates the longitudinal and bending vibrations when the harmonic driven signal is applied to the piezoelectric rings [4]. [PERSON] et al. [5] designed and investigated a novel pyramidal-shaped three DOF positioning mechanism. This mechanism is made from aluminum alloy, and three piezoelectric actuators are inserted at every 120\({}^{\circ}\) angle. Such a mechanism can deliver 3D elliptical movements of the contacting points in space. There are more studies on the investigation of ultrasonic motor (USM) capability to generate a rotational movement of the spherical rotor. Analytical studies of linear piezoelectric unimorph model were described by [PERSON] et al. [PERSON] and [PERSON] modified and improved this analytical model. [PERSON] et al. proposed 3D electromechanical analysis of a piezoelectric unimorph [6]. [PERSON] et.al. proposed a new design of 3 DOF piezoelectric actuator developed to rotate the spherical rotor about three axes [7]. The rotor is placed on the square shape vibrating frame that is excited by four piezostacks. The elliptical motion of four driving tips is transferred to the rotation of the rotor. The rotation direction of the rotor is controlled by changing the amplitude and phase of the harmonic electric signal of the different piezo stacks. [PERSON] et.al. proposed 3D hybrid piezo electrical drive with spherical rotor which is made using permanent magnetic semi-spheres [8]. These semi-spheres are hollow and connected together. This sphere is the rotor of the drive.