Dynamic Balance Force Control for Compliant Humanoid Robots
Benjamin J. Stephens, Christopher G. Atkeson
Abstract—This paper presents a model-based method, called
Dynamic Balance Force Control (DBFC), for determining full
body joint torques based on desired COM motion and contact
forces for compliant humanoid robots. The center of mass
(COM) dynamics are affected directly through contact force
control to achieve stable balance. This idea is used to formulate
DBFC considering the full rigid-body dynamics of the robot to
produce desired contact forces. To achieve generic force control
tasks, a virtual model controller, DBFC-VMC, is presented.
Examples using this control are presented as results from
simulation and experiments on a force-controlled humanoid
robot.
I. INTRODUCTION
Humanoid robots must operate in complex environments
while interacting closely with people and performing a wide
variety of tasks. Many tasks involve the regulation of forces,
requiring compliant mechanisms and controllers that are
stable but also safe and robust to unknown disturbances. This
paper describes a simple method of control for full body
balance and other tasks that is suitable for compliant force-
controlled humanoid robots.
While humanoid robots are very complex systems, the
dynamics that govern balance are often described using
simple models of the center of mass (COM) [1]. It has been
shown through dynamic simulation that humanoid balance
depends critically on controlling the linear and angular
momentum of the system [2], quantities that can be directly
controlled by contact forces. This suggests that balance is a
fundamentally low-dimensional problem that can be solved
by contact force control. This idea is the inspiration for the
controller presented in this paper.
Given a robot with stiff joint position control and a
known environment, the most common approach to balance
is to generate a stable trajectory of the COM and then
track it using inverse kinematics (IK) [3]. For environments
with small uncertainty or small disturbances, the inverse
kinematics can be modified to directly control the contact
forces using force feedback [4]. Position-based controllers
generally exhibit high impedance, and the speed at which
they will comply to an unknown force is limited. Robots
with low impedance joints can comply faster. This is useful,
but also makes balance control more important and more
difficult.
For compliant robots, there are a number of ways that
contact force control can be achieved. Virtual model control
(VMC) [5] is the simplest method that only uses a kinematic
B. J. Stephens and C. G. Atkeson are with the
Robotics Institute, Carnegie Mellon University, 5000 Forbes
Ave, Pittsburgh, PA, USA. bstephens@cmu.edu,
http://www.cs.cmu.edu/˜bstephe1
Fig. 1. Block diagram of full control algorithm including DBFC.
model. Desired contact forces are converted into joint torques
assuming static loading using a Jacobian-transpose mapping.
It has been shown that under quasistatic assumptions and
proper damping of internal motions the desired forces can
be achieved [6]. In contrast, given the full constrained rigid-
body dynamics model, desired joint accelerations can be
converted into joint torques using inverse dynamics for
improved tracking performance [7].
This paper presents another method, called Dynamic
Balance Force Control (DBFC), which is summarized in
Figure 1. Like [7], the full dynamic model is used and
no quasistatic assumptions are made. However, like [5] and
[6], the input is desired contact forces. Contact forces are
computed independent of the full robot model based on a
simple COM dynamics model and external forces. Because
of force-based nature of this controller, it can be modified
for the compensation of non-contact forces using VMC-
like controls. This modification, called DBFC-VMC, can be
used to perform generic tasks such as posture control and
manipulation. The output of the DBFC(-VMC) is full body
joint torques. Figure 2 offers a comparison these various
control methods.
This paper is organized as follows. In Section II, desired
contact forces are calculated from a simplified model based
on COM dynamics. In Section III, it is shown how full body