ZMP Preview Control Based Compliance Control for a
Walking Quadruped Robot
Jiaqi Xu, Ligang Ge, Jian Wang, Qing Wei, Hongxu Ma
College of Mechatronics Engineering and Automation,
National University of Defense Technology
E-mail: xujiaqi0426@sina.cn
Abstract - In this paper, a compliance control strategy based
on ZMP preview control for quadruped walking gait locomotion
under unperceived disturbances is proposed. The preview control
is designed to plan the CoM trajectory to realize the desired ZMP.
When the robot suffers from interference of environmental
disturbances, we introduce an adjusted expected ZMP to
suppress the change of the ZMP. The force distribution module
calculate desired contact force by eliminating interaction force
between the stance legs and the force controller make the contact
force track the desired force. Simulation results demonstrate the
effectiveness of our compliance control strategy based on ZMP
preview control as the quadruped robot successfully walking
under unperceived disturbances.
Keywords—quadruped robot; walking gait; preview control;
compliance control; ZMP
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 and dexterous locomotion capabilities in a compliant
manner and show their strong environmental adaptability.
Quadruped robots have difficulty in traveling through
rough terrain because the unexpected collisions with the
ground of the large impact and the disturbances to the trunk of
the robot will cause the robot posture instability. So an
appropriate compliance control is necessary for quadruped
robots to achieve stable locomotion in complicated
environment. Raibert used spring loaded inverted pendulum
model (SLIP) achieve the stability of a hopping monopod
control, and promoted the concept of virtual leg to the
quadruped robots [1]. The control of BigDog who has good
adaptability to the environment is developed on the basis of
the model and demonstrates the compliance and robustness
[2]. The LittleDog quadruped robot, manufactured by Boston
Dynamics achieves traveling through a wide variety of rough
terrain of varying difficulty levels by using floating-base
inverse dynamics control and predictive force control [3-4].
HyQ’s virtual model control method is used to maintain the
stability of the body. Each leg of HyQ is simplified into a
linear spring damping to realize the active compliance control
[5-6]. Jaehwan designed a variable impedance control strategy,
aiming at changing the impedance parameters in different
stages [7-8].
There are various methods for obtaining CoM (Center of
Mass) references from ZMP (Zero Moment Point) references.
Fourier series approach [9], Laplace transformation [10] 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. working on ZMP preview control [11]. Wieber proposed
a method of generating walking patterns for the given ZMP
region by applying a quadratic program approach [12].
In view of the compliance problem of quadruped robots’
walking gait, this paper proposes a compliance control method
based on ZMP preview control. As shown in Fig1, 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
eliminating the interaction force of diagonal stance legs, 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. Simulation results show
that the compliance control strategy based on ZMP preview
control allows for the quadruped robot walking under
disturbances in a robust and compliant manner.
The rest of this document is organized as follows: 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 and show a contact
force controller. Section V shows results of simulations and we
conclude our remarks in the Section VI.
This work is supported by National Nature Science Foundation of China
and National Hi-tech Research and Development
Program of China (Grant NO. 2015AA042202).