## 1 Introduction  
Modern high-precision mechatronic positioning systems use different types of actuators, i.e., electromagnetic, electrostatic, and magnetostrictive. However, most of the actuators are a single degree of freedom devices that generate linear or rotary motion [1]. Usually, in order to induce multiple degrees of freedom motion of the particular type, several actuators are composed into one complex positioning system [2, 3, 4]. Such a design principle makes the overall design and control of the positioning system complex and bulky [5, 6]. Moreover, the synchronization of several actuators is a challenging control task that requires expensive and complex control electronics and software. In addition, synchronization and control of the system consisting of several actuators decrease the accuracy and reliability of positioning systems [7, 8]. Therefore, multi-DOF actuators must be used to simplify control of multi-degree of freedom positioning systems and to reduce the size and complexity of the mechatronic systems. Piezoelectric actuators can induce multi DOF motion of the slider or rotor, have a simple design, self-locking option, short response time, and good controllability [9, 10]. Numerous designs of multi-DOF piezoelectric actuators have been proposed [11, 12, 13, 14]. However, most of them operate only as linear type, rotational type, or can move itself in the plane. In order to combine two types of motion into one piezoelectric system, several piezoelectric actuators must be composed, and the aforementioned disadvantages will be met again [15, 16]. Therefore, the objective of this research is to develop a multi-DOF locomotion type piezoelectric actuator consisting of a single transducer that is able to provide unlimited self-motion in the plane and rotate spherical payload. [PERSON] et al. introduced a piezoelectric robot with the ability to generate bi-directional in-plane motion [17]. The proposed robot has a simple design and operation principle, i.e., the body of the robot is based on a millimeter size glass plate with two piezoelectric patches, while the operation of it is based on the generation of the traveling wave, which is obtained at a frequency that is between frequencies of two bending modes. The authors performed numerical and experimental investigations and found that the proposed robot is able to provide up to 100 mm/s of planar speed while the amplitude of the excitation signal was equal to 65 V\({}_{\text{P-P}}\). On the other hand, the proposed robot is able to provide only one type of motion, i.e., planar, while generation of rotary motion is not foreseen. [PERSON] et al. introduced planar motion quadruped piezoelectric micro-robot [18]. The robot design is based on four piezoelectric legs, which are bonded to a rectangle base. The planar motion of the robot is obtained by the excitation of two perpendicular bending modes of the legs. In order to obtain the elliptical motion trajectory of the legs, two harmonic signals with phase differences were used, and as a result, planar motion is obtained. Numerical and experimental investigations were performed and showed that the proposed robot is able to provide 33.45 mm/s of planar speed and convey up to 200 g of payload. Numerous different designs of piezoelectric robots that can provide planar motion are proposed and investigated [19; 20]. However, most of these piezorobots cannot provide more than three degrees of freedom. On the other hand, several authors introduced 2-DOF rotary--linear piezoelectric actuators that can rotate and provide linear motion of the slider. [PERSON] and [PERSON] reported on a rotary--linear piezoelectric actuator [21]. The actuator consists of a single cubic stator with a cylindrical cavity inside. Dimensions of the actuator can be minimized up to millimeter size. Linear or rotary motion of cylindrical slider can be obtained when the third radial or hybrid vibrations of the first and second extension modes of the stator are excited.