*Article* **Motion of a Legged Bidirectional Miniature Piezoelectric Robot Based on Traveling Wave Generation**

#### **Jorge Hernando-García \*, Jose Luis García-Caraballo, Víctor Ruiz-Díez and Jose Luis Sánchez-Rojas**

Microsystems, Actuators and Sensors Group, Universidad de Castilla-La Mancha, E-13071 Ciudad Real, Spain; JoseLuis.GCaraballo@uclm.es (J.L.G.-C.); Victor.Ruiz@uclm.es (V.R.-D.); JoseLuis.SAldavero@uclm.es (J.L.S.-R.) **\*** Correspondence: jorge.hernando@uclm.es; Tel.:+34-926-295-300

Received: 21 February 2020; Accepted: 19 March 2020; Published: 20 March 2020

**Abstract:** This article reports on the locomotion performance of a miniature robot that features 3D-printed rigid legs driven by linear traveling waves (TWs). The robot structure was a millimeter-sized rectangular glass plate with two piezoelectric patches attached, which allowed for traveling wave generation at a frequency between the resonant frequencies of two contiguous flexural modes. As a first goal, the location and size of the piezoelectric patches were calculated to maximize the structural displacement while preserving a standing wave ratio close to 1 (cancellation of wave reflections from the boundaries). The design guidelines were supported by an analytical 1D model of the structure and could be related to the second derivative of the modal shapes without the need to rely on more complex numerical simulations. Additionally, legs were bonded to the glass plate to facilitate the locomotion of the structure; these were fabricated using 3D stereolithography printing, with a range of lengths from 0.5 mm to 1.5 mm. The optimal location of the legs was deduced from the profile of the traveling wave envelope. As a result of integrating both the optimal patch length and the legs, the speed of the robot reached as high as 100 mm/s, equivalent to 5 body lengths per second (BL/s), at a voltage of 65 Vpp and a frequency of 168 kHz. The blocking force was also measured and results showed the expected increase with the mass loading. Furthermore, the robot could carry a load that was 40 times its weight, opening the potential for an autonomous version with power and circuits on board for communication, control, sensing, or other applications.

**Keywords:** robot; piezoelectric; miniature; traveling wave; leg
