The design exploits the use of mechanical standing waves generated on the metal beam and transmitted to its legs to propel the LPMR forward and backward where the vibrations of legs are similar to the bounding gait locomotion of animals. In our proposed design, a forward and backward motion in one dimensional axis is determined by the mechanical design and placement of the legs of the LPMR, and two operating frequencies for both directions are selected by the designer as well. By simple change in the driving frequency, both forward and backward motion can be achieved.

1. https://www.youtube.com/watch?v=2FhDlS0igJk
The locomotion technique shown in this video is known for animals as the bounding
gait locomotion which is a form of legged locomotion generally observed when a
quadruped animal is running at the highest speed.
Legged Robot inspired by the Bounding gait
locomotion of the African Dung Beetles

2. Legged Robot inspired by the Bounding gait
locomotion of the African Dung Beetles
The Legged Robot lands with one leg and brings the other leg in the direction of
motion to achieve one leg step on a half period T/2. Then in the next half period, the
legs switch their roles for the next leg step.

3. Robot Architecture
The robot consists
of one
piezoelectric
patch, a metal
beam, two rigid
legs, and the
various electrical
components as
shown.

4. Locomotion Principle
The locomotion is similar to bounding gait of dung beetle. Forward and Backward
motion is realized by attaching legs at appropriate location along the unimorph
actuator driven at two different modal frequencies.

5. Design Principle
The robot can be designed by identifying zones on the superimposed modal
shapes of the unimorph actuator for legs placement
• Euler Bernoulli Beam Theory
• Natural Frequency
• Mode Shape
f1
f2

6. Design Principle
f1
f2
Design Legs
Location

7. Kinematics of the Legged robot
The trajectory is derived for the case where the legs are
positioned on the left side of the wave antinodes as shown

8. Kinematics of the Legged robot
Steady state response (z-displacement) for the unimorph actuator under a
sinusoidal electrical field
Kinematics equations

9. Experimental verification

10. • http://people.sutd.edu.sg/~hassan_hariri/postdoc-singapore/
• H. H. Hariri, G. S. Soh, S. Foong, and K. Wood, ‘’Locomotion
Study of a Standing Wave Driven Piezoelectric Miniature
Robot for Bi-directional Motion’’, IEEE Transaction on
Robotics, 2017.
• Hassan H. Hariri, Leonardus A. Prasetya, Shaohui Foong,
Gim Song Soh, Kevin N. Otto and Kristin L. Wood ‘‘A Tether-
less Legged Piezoelectric Miniature Robot Using Bounding
Gait Locomotion for Bidirectional Motion’’, International
Conference on Robotics and Automation (ICRA), May 16-21,
2016, Stockholm, Sweden.
• H. Hariri, G. S. Soh, S. H. Foong, K. L. Wood, K. Otto,
‘’Miniature Piezoelectric Mobile Robot driven by Standing
Wave’’, 14th World Congress in Mechanism and Machine
Science, Taipei, Taiwan, 25-30 October, 2015.
References