Compliance Control Based for a Quadruped Robot
Walking over Rough Terrain
Jiaqi Xu, Lin Lang, Honglei An and Hongxu Ma
College of Mechatronics Engineering and Automation,
National University of Defense Technology
Changsha, China
E-mail: xujiaqi0426@sina.cn
Kaiying Zhu
PLA Special Operations University
Guangzhou, China
E-mail: zkylydia@163.com
Abstract—It is well-known that the walking gait for
quadruped robots has great potential to travel over rough terrain
because of its higher flexibility and better environment
adaptability. This paper presents a control framework for a
quadruped robot walking over rough terrain, which includes
such features: First, a preview controller is designed to create an
appropriate body trajectory to realize the desired ZMP; Second,
a new optimal force distribution is presented by minimizing the
sum of the weighted torque efforts of the robot; Third, a contact
force based compliance controller is designed to increase
robustness in face of unknown and unanticipated disturbances.
Simulations were performed with no four feet supporting period,
the robot model successfully fast walking over rough terrain and
going upstairs and downstairs. Then in the experiments, the
quadruped robot achieved going upstairs with a stair of 0.15m.
Simulations and experiments demonstrate the effectiveness of our
compliance control strategy.
Keywords—quadruped robot; walking gait; preview control;
compliance control; force distribution
I. INTRODUCTION
Quadruped robots appear to possess great potentials to be
used in cluttered environments for performing outdoor tasks,
such as military transportation, scientific exploration and
disaster rescue. They can be stable and efficient when move
through rough terrain with obstacles such as rocks, sands and
steep slopes. In performing such tasks, these robots exhibit
agile locomotion capabilities in a compliant manner and show
their strong environmental adaptability. The BigDog
quadruped developed by Boston Dynamics achieved walking
through rough terrain freely with high adaptability [1-2]. The
LittleDog quadruped robot, manufactured by Boston Dynamics
achieved traveling fast through a wide variety of rough terrain
of varying difficulty levels by using floating-base inverse
dynamics control and predictive force control [3-4]. The SILO-
4 quadruped robot used active compliance with stability-
compensation controller to improve the walking gait [5].
For walking robots, each leg supporting the robot applies a
certain force on the support point, which can balance together
the external disturbance using (equal and opposite) reaction
forces of the ground [6]. The distributed force represents the
distributed component of the external forces and moments
applied on that leg. Since the physical constraints producing
the contact forces are only inequalities, the mathematical
solution is not unique. Therefore, the optimization of the force
for the legs is required [7].
There are various methods for obtaining CoM (Center of
Mass) references from ZMP (Zero Moment Point) references.
Fourier series approach [8], Laplace transformation [9] and
preview control are among methods. Preview control is a
general control scheme specifically designed to deal with
dynamical systems and generate online motions that need to be
realized, with the potential ability to react efficiently to a wider
range of situations. It globally amounts to solving online a
sequence of Optimal Control problems. ZMP preview control
has been widely employed for biped walking robots. Safe biped
walking has indeed encountered several improvements in the
early 2000s with a noticeable breakthrough from Kajita et al
[10]. working on ZMP preview control. Wieber proposed a
method of generating walking patterns for the given ZMP
region by applying a quadratic program approach [11].
In view of the compliance problem of quadruped robots’
walking gait, this paper proposes a compliance control method.
As shown in Fig.1, there are three levels in this control diagram:
The external loop is the high level control of the robot. A
preview controller is designed to plan the CoM trajectory to
realize the desired ZMP. The middle loop using a position
controller to control body’s position and posture to avoid
interference of environmental disturbance and unknown model
characters. By minimizing the sum of the weighted torque
efforts of the robot, a force distribution module is used to
calculate desired contact force. The internal loop is the low
level control of the robot, using the force controller make the
foot contact force track the desired force to realize the foot soft
contact with the ground and reduce the impact to the body.
Simulations and experiments show the compliance control
strategy allows for the quadruped robot walking over rough
terrain in a robust and compliant manner.
The rest of this document is organized as following:
Section II details the dynamics model of the quadruped robot.
We present the ZMP preview control in section III. In section
IV we discuss the force distribution strategy. Then section V
shows a control law of floating-base inverse dynamics. Section
VI and VII respectively show the results of simulations and
experiments. Finally, we conclude our remarks in the
SectionVIII.
This work is supported by National Nature Science Foundation of China
(Grant NO. 61473304) and National Hi-tech Research and Development
Program of China (Grant NO. 2015AA042202).