Highly Dynamic Quadruped Locomotion via
Whole-Body Impulse Control and Model Predictive Control
Donghyun Kim
1
, Jared Di Carlo
2
, Benjamin Katz
1
, Gerardo Bledt
1
, and Sangbae Kim
1
Abstract— Dynamic legged locomotion is a challenging topic
because of the lack of established control schemes which can
handle aerial phases, short stance times, and high-speed leg
swings. In this paper, we propose a controller combining whole-
body control (WBC) and model predictive control (MPC). In
our framework, MPC finds an optimal reaction force profile
over a longer time horizon with a simple model, and WBC
computes joint torque, position, and velocity commands based
on the reaction forces computed from MPC. Unlike existing
WBCs, which attempt to track commanded body trajectories,
our controller is focused more on the reaction force command,
which allows it to accomplish high speed dynamic locomotion
with aerial phases. The newly devised WBC is integrated
with MPC and tested on the Mini-Cheetah quadruped robot.
To demonstrate the robustness and versatility, the controller
is tested on six different gaits in a number of different
environments, including outdoors and on a treadmill, reaching
a top speed of 3.7 m/s.
I. INTRODUCTION
To fully exploit the hardware capability of legged systems,
we need a controller that can address the challenging issues
related to dynamic locomotion, such as body control during
short stance periods, aerial phases, and high speed swing leg
motion control. Several successful cases for both running
bipeds [1], [2] and quadrupeds [3] have been presented, but
they are either difficult to scale up to high degree-of-freedom
systems [1] or heavily rely on specific system dynamics [2]
or are undocumented [3]. Whole-body control (WBC) is a
strong candidate as a dynamic motion controller because of
its dynamically consistent formulation and general frame-
work, which makes it easy to extend to various systems and
tasks. However, existing WBCs focus on how to follow the
given trajectory by manipulating contact forces, which makes
it nontrivial to address motion involving frequent non-contact
phases such as high speed running.
To tackle the issue, we formulate WBC to follow both
the reaction force and body trajectory commands. The idea
of reaction force tracking originates from the impulse plan-
ning used in Cheetah 2 [4], which demonstrates successful
dynamic bounding and jumping. The underlying idea of [4]
is to plan reaction forces, which are impulses, rather than
CoM trajectory, which is not practical to follow when the
locomotion is extremely dynamic and has significant periods
of under-actuation. In this paper, we embrace the impulse
planning idea in WBC and formulate whole-body impulse
Authors are with the
1
Department of Mechanical Engineering at the
Massachusetts Institute of Technology, and the
2
Department of Elec-
trical Engineering and Computer Science at the Massachusetts Institute
of Technology, Cambridge, MA, 02139, USA. Corresponding Author:
robot.dhkim@gmail.com
Simplified model
Full body dynamics
Actual robot (Mini-Cheetah)
MPC (0.04kHz)
WBC (0.5kHz)
Fig. 1. Control Architecture. The proposed control architecture consists
of two parts: Model predictive control and whole-body control. The reaction
forces computed by MPC are modified by WBC to incorporate body
stabilization and swing leg control. The final commands found in WBC
are sent to the robot to perform dynamic locomotion.
control (WBIC) that can incorporate both body posture stabi-
lization and reaction force execution. In terms of formulation,
WBIC is not significantly different from the existing whole-
body controllers [5]–[7], but the additional feature, which is
an incorporation of pre-computed reaction forces by relaxing
the floating base control, plays an important role in dynamic
locomotion control. In our formulation, the WBIC is mostly
used to track the ground reaction force profile rather than a
body trajectory.
To find the reaction force command, we utilize model
predictive control (MPC). In our previous work, we demon-
strated that convex MPC can perform various dynamic gaits
at high speed on both Cheetah 3 [8] and Mini-Cheetah [9].
Utilization of MPC enhances the versatility of locomotion,
enabling us to switch between various gaits by simply
changing the contact sequence. However, using MPC with
a simple model has a fundamental limitation in position
control because of its low update frequency (40 Hz in our
implementations) and model simplifications. WBC provides
a solution to the MPC’s limitation by running a high-
frequency feedback loop while still accounting for full-body
dynamics with contact.
On the other hand, the prediction horizon of MPC com-
pliments the WBC perfectly to fill in the WBC’s limita-
tion that it cannot consider more than a single time step
ahead. This limited time horizon issue has been addressed
in [10], [11] which developed an MPC formulation using
full-body dynamics. However, even their highly optimized
solvers barely fit into a 200 Hz update frequency and the
arXiv:1909.06586v1 [cs.RO] 14 Sep 2019