Integral Control of Humanoid Balance
Benjamin Stephens
The Robotics Institute
Carnegie Mellon University
Pittsburgh, PA 15213, USA
bstephens@cmu.edu
http://www.cs.cmu.edu/∼bstephe1
Abstract—This paper presents a balance controller that
allows a humanoid to recover from large disturbances and still
maintain an upright posture. Balance is achieved by integral
control, which decouples the dynamics and produces smooth
torque signals. Simulation shows the controller performs better
than other simple balance controllers. Because the controller
is inspired by human balance strategies, we compare human
motion capture and force plate data to simulation. A model
tracking controller is also presented, making it possible to
control complex robots using this simple control.
I. INTRODUCTION
A fundamental control problem for humanoids is balanc-
ing, which is related to the control of unstable systems such
as inverted pendulums. We believe that balance is achieved
by a set of decoupled controls that regulate the center of pres-
sure and simultaneously ensure that the humanoid balances
upright. In human balance experiments, it has been observed
that people use a mixture of strategies for dealing with these
disturbances. The ankle strategy fixes all joints except the
ankle, and balances like a single inverted pendulum. The
hip strategy is characterized by a large bending at the hips,
which results in a repositioning of the center of mass [1].
These two strategies are illustrated in Fig. 1.
In Section II, we present a controller that is inspired by
these human balance strategies and accounts for the limits
on the location of the center of pressure to ensure that the
robot can stand with its feet flat on the ground and withstand
large disturbances. We begin by ignoring the presence of
the feet and pretend there are no constraints on the joint
torques. The torques generated by the balance controller
determine the ideal positioning of the center of pressure. This
information is fed into an integral controller which maintains
the constraints on the center of pressure and keeps the robot
standing upright. Our controller is simulated on a double
inverted pendulum, which is subjected to a large external
disturbance force and results are presented in Section III. The
performance is compared to other controllers and to human
balance experiment data.
Since humans behave like double inverted pendulums, we
want our humanoid robots to also behave as such. For this
reason, we present a model tracking control algorithm in
Section IV. The algorithm makes use of operational points
to define a relationship between the simple model system
(e.g. the double inverted pendulum) and the more complex
Fig. 1. The two strategies mimicked by our balance controller. The ankle
strategy causes the robot to behave like a single inverted pendulum while
the hip strategy allows the robot to use the gravitational force to help it
balance
robot (e.g. a humanoid). We apply this algorithm to a 3-link
planar biped robot in the sagittal plane and simulation results
are presented in Section V.
A. Related Work
Humanoid robot researchers often describe balance and
motion using simple models. Early work on balance and
stability of dynamic bipeds was done by Vukobratovic, et.
al. [2], followed by Golliday, et. al. [3] and Hemami, et.
al. [4]. In these studies, the biped was usually represented
by a planar double inverted pendulum with the base joint
representing the stance foot and ankle joint.
The center of pressure (CoP) is used as a measure of
stability in bipeds. It represents the location of an equivalent
force, equal to the integral of the pressure distribution under
the foot, that is a measure of the tendency for the feet to
rotate and come off the ground. The use of ground reference
points, such as the CoP, has been present in almost every
humanoid project. While the definition and usefulness of the
CoP has been questioned [5] [6], it is still the dominant
measure of stability used by many robots, including the
highly successful Honda Asimo [7].
The constraints imposed on the ankle joint make hu-
manoids behave like the acrobot [8], which consists of a
series of inverted pendulums with all but the base joint
actuated. By definition, the CoP of the acrobot is always
fixed below the base joint, yet it can still balance itself. In
humanoids, the location of the CoP is roughly proportional to
the magnitude of the torque at the ankle. If the ankle torque