Humanoid Push Recovery
Benjamin Stephens
Robotics Institute
Carnegie Mellon University
Pittsburgh, Pennsylvania 15213
Email: bstephens@cmu.edu
http://www.cs.cmu.edu/∼bstephe1
Abstract—We extend simple models previously developed for
humanoids to large push recovery. Using these simple models, we
develop analytic decision surfaces that are functions of reference
points, such as the center of mass and center of pressure, that
predict whether or not a fall is inevitable. We explore three
strategies for recovery: 1) using ankle torques, 2) moving internal
joints, and 3) taking a step. These models can be used in robot
controllers or in analysis of human balance and locomotion.
Index Terms—Dynamics, Robots, Robot dynamics
I. INTRODUCTION
We study humanoids as a way to understand humans.
Any technology that is applied to aid humanoid motion
can potentially be applied to help elderly or persons with
disabilities walk with more stability and confidence. We want
to understand what causes humanoids to fall, and what can
be done to avoid it. Disturbances and modeling error are
possible contributors to falling. For small disturbances, simply
behaving like an inverted pendulum and applying a compen-
sating torque at the ankle can be enough. As the disturbance
increases, however, more of the body has to be used. Bending
the hips or swinging the arms creates an additional restoring
torque. Finally, if the disturbance is too large, the only way to
stop from falling is to take a step.
In this paper, we unify simple models used previously by
biomechanists and roboticists to explain humanoid balance and
control. In Section I-A, we discuss previous work in detail
and in Section I-B we summarize our models and balance
strategies. Section II describes the simplest balance strategy
for small disturbances, using only ankle torques to stabilize.
Section III employs an expanded model to allow use of the
rest of the body. Finally, in Section IV, we discuss the choice
of step location when balance strategies fail.
The main contributions of this paper are the unification
of models and strategies used for humanoid balance and
the development of decision surfaces that define when each
strategy is necessary and successful at preventing a fall. These
decision surfaces are defined as functions of reference points,
such as the center of mass and center of pressure, that can
be measured or calculated easily for both robots and humans.
We assume that both ankle and internal joint actuation are
available and used in balance recovery.
A. Related Work
The problem of postural stability in humanoids has been a
subject for many years. Vukobratovic, et.al. was the first to
Fig. 1. The three basic balancing strategies. The green dot represents the
center of mass, the magenta dot represents the center of pressure, and the
blue arrow represents the ground reaction force. 1. CoP Balancing (“Ankle
Strategy”) 2. CMP Balancing (“Hip Strategy”) 3. Step-out
apply the concept of the ZMP, or zero moment point, to biped
balance [1]. Feedback linearizing control of a simple double-
inverted pendulum model using ankle and hip torques was used
by Hemami, et.al. [2]. Stepping to avoid fall was also studied
by Goddard, et.al. [3], using feedback control of computed
constraint forces derived from Lagrangian dynamics.
Modern bipedal locomotion research has been heavily in-
fluenced by Kajita, et.al. and their Linear Inverted Pendu-
lum Model (LIPM) [4]. It is linearized about vertical and
constrained to a horizontal plane, so it is a one-dimensional
linear dynamic system representing humanoid motion. When
considering ankle torques and the constraints on the location of
the ZMP, or zero moment point, it has also been referred to as
the “cart-on-a-table” model. An extension to the LIPM is the
AMPM, or Angular Momentum inducing inverted Pendulum
Model [5], which generates momentum by applying a non-
centroidal torque to the center of mass (CoM).
Hofmann [6] studied humanoid control during walking and
balancing tasks in his thesis. He argues that the key to
balancing is controlling the horizontal motion of the CoM,
and there are three strategies for accomplishing this. For small
disturbances, simply shifting the center of pressure (CoP)
changes the tangential ground reaction force (GRF), which
directly affects the motion of the CoM. Because the location of
the CoP is limited to be under the feet, a second strategy is to
create a moment about the CoM, creating a momentarily larger
tangential GRF. This leads to a new point, an effective CoP,
called the centroidal moment point (CMP). The third strategy