Article
A Bio-Inspired Compliance Planning and Implementation
Method for Hydraulically Actuated Quadruped Robots with
Consideration of Ground Stiffness
Xiaoxing Zhang , Haoyuan Yi, Junjun Liu, Qi Li and Xin Luo *
Citation: Zhang, X.; Yi, H.; Liu, J.; Li,
Q.; Luo, X. A Bio-Inspired
Compliance Planning and
Implementation Method for
Hydraulically Actuated Quadruped
Robots with Consideration of Ground
Stiffness. Sensors 2021, 21, 2838.
https://doi.org/10.3390/s21082838
Academic Editors: Abolfazl Zaraki,
Biswanath Samanta and Hamed
Rahimi Nohooji
Received: 1 March 2021
Accepted: 15 April 2021
Published: 17 April 2021
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4.0/).
State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and
Technology, Wuhan 430074, China; xiaoxingzhang@hust.edu.cn (X.Z.); yihaoyuan@hust.edu.cn (H.Y.);
liujunjun@hust.edu.cn (J.L.); qili@hust.edu.cn (Q.L.)
* Correspondence: mexinluo@mail.hust.edu.cn; Tel.: +86-27-8755-6594
Abstract:
There has been a rising interest in compliant legged locomotion to improve the adaptability
and energy efficiency of robots. However, few approaches can be generalized to soft ground due to the
lack of consideration of the ground surface. When a robot locomotes on soft ground, the elastic robot
legs and compressible ground surface are connected in series. The combined compliance of the leg and
surface determines the natural dynamics of the whole system and affects the stability and efficiency of
the robot. This paper proposes a bio-inspired leg compliance planning and implementation method
with consideration of the ground surface. The ground stiffness is estimated based on analysis of
ground reaction forces in the frequency domain, and the leg compliance is actively regulated during
locomotion, adapting them to achieve harmonic oscillation. The leg compliance is planned on the
condition of resonant movement which agrees with natural dynamics and facilitates rhythmicity
and efficiency. The proposed method has been implemented on a hydraulic quadruped robot. The
simulations and experimental results verified the effectiveness of our method.
Keywords:
active compliance control; stiffness control; compliance planning; quadruped robots;
harmonic locomotion
1. Introduction
Legged robots have superior mobility and maneuverability in complex unstructured
environments, benefitting from the ability afforded by their morphology and varied
gaits [
1
]. Recent years have witnessed significant achievements in the research area of
legged robots. Versatile high-performance robots, such as BigDog, Spot, and Atlas de-
veloped by Boston Dynamics [
2
], the MIT cheetah series [
3
–
7
], the HyQ [
8
,
9
] and the
ANYmal [
10
,
11
] developed by IIT and ETH Zurich, the Aliengo [
12
] from the Unitree
Robotics, and the Jueying robots [
13
,
14
] developed by the DeepRobotics and Zhejiang
University, have brought prospective practical applications. Nevertheless, despite consid-
erable performance improvements in the past 20 years in mechatronics and control, the
locomotion efficiency of the state-of-the-art robots lags far behind that of their biological
counterparts [
15
]. The evolutionary process of thousands of years has endowed legged
animals with an exquisite dynamic mechanism and achieved excellent motion performance.
Learning the dynamic mechanism from legged animals is the inevitable way to further
improve the performance of legged robots.
An essential property of animal locomotion is the alternative foot-ground contact
in the swing and support phases of a locomotor cycle based on their inherent dynamics,
roughly defining the locomotion’s rhythmicity [
16
,
17
]. Elastic structures and spring-like
leg behavior have been widely found in the locomotion of animals, and the spring-loaded
inverted pendulum (SLIP) model has been abstracted into a template to resolve the redun-
dancy of multiple legs and joints [18,19]. The inherent parameters of the dynamic system,
namely the body mass and the compliance of the leg, determine the rhythmicity of legged
Sensors 2021, 21, 2838. https://doi.org/10.3390/s21082838 https://www.mdpi.com/journal/sensors
