On Local Active Compliance Control Strategy for a Redundant
Prototype Leg of Hydraulic-Driving Quadruped Robot
Pengpeng Zeng, Honglei An, Jian Wang, Hongxu Ma and Qing Wei
College of Mechatronic Engineering and Automation, National University of Defense Technology, Changsha 410073, P. R. China
E-mail: mieer20113660@163.com
Abstract: The leg control on foot trajectory planning and contact forces is the most crucial problem for a hydraulic quadruped
robot. In contrast with a non-redundant leg, the redundant one generally has larger foot workspace and more agility for leg
motion control in rough terrain, however, this redundant joint obviously adds complexities and difficulties to the control system.
This work aims to avoid those disadvantages but not apparently affect the designed performance indices of the redundant leg.
Thus, based on the control problems of a redundant prototype leg, a novel local active compliance control strategy is proposed
for the first time ever. Works presented in this paper mainly includes modeling for a planar redundant leg, selecting desired joint
on a redundant leg by solving optimization model, designing local active compliance controller and discussing the constraints on
implementing the proposed control strategy. Final experiments prove the proposed strategy feasible and effective.
Key Words: Hydraulic-driving, Quadruped robot, Redundant leg, Local active compliance
1 Introduction
Recently, mobile robot particularly for the quadruped
robot have become a hot research field. Based on bionic-
s research on mammals, quadruped robots’ stability, speed,
load capacity and the adaptability to unstructured environ-
ments have been rapidly improved and wildly utilized in the
fields such as military equipment, resource exploration, dis-
aster rescue and so on. The BigDog[1] is one of the most
representative robots, as shown in Figure 1.
Fig. 1: BigDog walking in snow.
Legs’ trajectory planning and contact forces control-
ling are the most crucial part to achieve a stable gait for
quadruped robot system. Problems can be totally differen-
t for different configurations of the leg. At present, there
are two main types of leg configuration: the redundant leg
which has 4 joints (lateral and anterior hip joint, keen join-
t and ankle joint) and the non-redundant one having only 3
joints. Quadruped Robots such as LS3[2], HyQ[3] and S-
calf[4] have four non-redundant legs; however, legs of Big-
Dog, MIT Cheetah[5] and the NUTD’s quadruped robot[6]
are redundant mainly in the consideration of that the redun-
dant leg has an optimal DOF and broader workspace to be
more agile on complex terrain, such as avoiding obstacles
and climbing stairs.
As for a hydraulic-driving quadruped robot, no matter
This work is supported by National Natural Science Foundation of Chi-
na(NNSF) under Grant No.61473304 and National Hi-tech Research and
Development Program of China under Grant No.2015AA042202.
which kind of leg configuration it has, the compliance is vital
because legs directly interact with the ground when the robot
is walking or running. Particularly the high-speed gaits in-
cluding galloping or bounding, the foot regularly bears great
impacts resulted from the high stiffness of the hydraulic ac-
tuators and instantaneously touch with ground. The GRF-
s (Ground Reaction Forces), on the one hand, can always
cause mechanical damage or destroy force sensor fixed on
the foot; on the other hand, produce great disturbance and
finally affect the stability of the control system. Fortunately,
these problems can be perfectly solved by adding compli-
ance to the leg, such as using real elastic components, this
kind of compliance is called passive compliance. Early in
the 1980s, MIT’s Raibert[7] studied the one-legged hopping
robot which has a pneumatic cylinder. This leg is springy be-
cause air trapped in the leg actuator compresses when the leg
is touching the ground and shortens; Another kind is active
compliance which can be acquired and tuned by program-
ming instead of using elastic elements. IIT’s Boaventura[8]
proved that the prototype leg of HyQ can acquire the same
active compliance as that acquired by using a real spring;
The Spot[9] can still show high compliance without any e-
lastic elements on its leg. Although there are none papers
accessible for researchers, it’s commonly believed that cer-
tain active compliance control strategy is implemented in
this robot system. And the active compliance control algo-
rithms are wildly used by researchers to control the contact
forces for quadruped robots.
Naturally, the NUTD’s quadruped robot is expected to u-
tilize those advantages of its redundant legs and achieve de-
sired leg compliance. However, in most cases, the redundant
leg obviously adds complexities and difficulties to the con-
trol system, such as the inverse kinematics solving problem,
more energy consumption, design on control algorithms and
so on. Conversely, a non-redundant leg could show more
advantages over a redundant one for the same tasks under
certain conditions. Thus, as for motion control on redundant
leg, it’s expected to avoid the unfavorable factors caused by
the redundant joint and implement active compliance at the
same time. One possible solution is that controlling the re-