Push Recovery by Stepping for Humanoid Robots with Force
Controlled Joints
Benjamin J. Stephens, Christopher G. Atkeson
Abstract—In order to interact with human environments,
humanoid robots require safe and compliant control which
can be achieved through force-controlled joints. In this paper,
traditional joint trajectory tracking techniques are adapted for
a robot with force-controlled joints by adding model-based
feed-forward controls. Push Recovery Model Predictive Control
(PR-MPC) is presented as a method for generating full-body
step recovery motions after a large disturbance. Results are
presented from experiments on the Sarcos Primus humanoid
robot that uses hydraulic actuators instrumented with force
feedback control.
I. INTRODUCTION
Humanoid robots have the unique potential to operate
in environments already designed for humans. While per-
forming any given task in these complex environments,
robots will encounter uneven ground, dynamic obstacles
and humans. Force controlled robots, as opposed to stiff
position controlled robots, can be compliant to unknown
disturbances, resulting in safer and more robust operation.
We have already presented a general framework for force
control of legged balance with no stepping [1]. For small
disturbances, standing balance is sufficient. However, for
locomotion and large disturbances, the robot needs to step.
The tight coupling between balance control and choice of
footstep location makes this a challenging problem. This
paper presents a method for controlling stepping in a force
controlled robot.
While humanoid robots are very complex systems, the dy-
namics that govern balance are often described using simple
models of the center of mass (COM) [2]. It has been shown
through dynamic simulation that humanoid balance depends
critically on controlling the linear and angular momentum of
the system [3] [4], quantities that can be directly controlled
by manipulating the contact forces.
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) [5]. These trajectories are often
designed using model predictive control that optimizes over
a receding horizon into the future [6] [7]. For unknown en-
vironments or small disturbances, the inverse kinematics can
be modified to directly control the contact forces using force
feedback [8]. However, this requires force-measurement at
the point of contact, and the high impedance of the system
limits the bandwidth at which it can comply.
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. The controller presented in this paper allows a humanoid robot
to recover from large perturbation by stepping. It is applied to the Sarcos
Primus hydraulic humanoid robot pictured.
For compliant robots with low impedance joints, there are
a number of ways that contact force control can be achieved.
Virtual model control (VMC) [9] is a simple method that only
uses a kinematic model. Desired contact forces are converted
into joint torques assuming static loading using a Jacobian-
transpose mapping, i.e.  = JTF. It has been shown that
under quasistatic assumptions and proper damping of internal
motions the desired forces can be achieved [10]. In contrast,
given a full constrained rigid-body dynamics model, desired
joint accelerations can be converted into joint torques using
inverse dynamics for improved tracking performance [11].
Stepping strategies have been considered by several au-
thors. Simple models have been used to define stable footstep
locations, known as Capture Points [12]. Robots with stiff
position control that expect small disturbances often solve
footstep planning separately [13]. For situations when desired
footstep locations cannot be known in advance, such as in the
presence of large disturbances, motion and footstep planning
can be performed simultaneously [14].
In this paper, the technique of planning stepping motions
is extended to robots with force controlled joints, such as
the Sarcos humanoid robot shown in Figure 1. Planning
is performed by a linear model predictive controller called
Push Recovery Model Predictive Control (PR-MPC). This
is accomplished using a simple model presented in Section