This article presents a parameter optimization study for the design
of a highly athletic monopedal robot, known as Skippy, that is
physically capable of performing vertical jumps up to 3m (4m
in later prototypes) and triple somersaults of 2m, and which is
able to stand and balance on one leg. The robot’s design uses
a recently invented transmission mechanism called a ring screw
(http://www.royfeatherstone.org/ringscrew/index.html), which is
largely responsible for its high performance. The use of the ring
screw, an alternative to the widely used ball screw, allows the
robot to achieve higher speeds and greater efficiency.
Even though Skippy has no immediate economic purpose, it
serves to demonstrate the effectiveness of a more systematic
and complete design approach in achieving extreme and
unprecedented behaviors. While this case study focuses on a
one-legged robot, its findings can be generalized to other
types of robots with a properly defined purpose or set of
The main challenge of this study was that the performance
objectives were set very high and the robot already
operates near the limit of what is physically possible
using today’s technology. The objective of the study was
to identify a single design with the highest overall merit
from among all the designs that met all of the desired
objectives. Achieving such an objective is generally not
an easy task because objectives may often conflict with
each other. For example, Skippy-like robots that can jump
very high are usually not very skillful at balancing, and
vice versa. High jumps require a lot of energy, which can
be stored and re-used via springs; balancing, on the other
hand, needs a stiff body, making these two objectives
conflicting. For this reason, we chose a multi-objective
optimization approach for our study.
But what is the point of a one-legged hopping robot? By studying
a highly simplified monopedal robot, we wanted to gain a deeper
understanding of legged locomotion, which we could then
extend to multiple legged versions, and use the mobility offered
by legged locomotion by taking advantage of the symmetry that
characterizes it (think of a human’s legs while running).
The framework of our study consists of a two-layer optimization
scheme. In the first layer, an optimization algorithm searches
the design space for the most athletic design. In the second
layer, each design is tested for its ability to meet each of the
behavior objectives. Each behavior objective is treated as a
separate optimization problem. We define the term ‘behavior’
to describe what the robot does and the term ‘performance
objective’ to describe the outcome of this behavior. An example of
a performance objective, therefore, is for Skippy to landing after a
2m vertical jump and then launch itself back into the air to perform
a 2m triple backward somersault. The conditions at the moment of
landing, plus each of the robot’s actions until the moment it lifts off from the ground, describe a complete behavior. A score that
reflects how close each behavior is to the performance objective
is then awarded for each behavior. This is an example of machine
and behavior co-optimization.
To achieve high performance, highly detailed and realistic models
of the mechanism, its limits and inefficiencies are required.
For example, the motor is subject to speed, torque and thermal
limits, and there are energy losses in the motor, transmission, and
springs, as well as when the robot’s foot hits the ground.
Robot Skippy’s mechanism was modeled with 56 parameters (the
detailed listing of the parameters has been omitted due to its large
size). The schematic diagram is presented in Fig. 1.
The robot has three joints: the ankle, the foot and the hip. The
ankle is a passive joint (it is not directly controlled) and has a
spring attached to it. A second spring is attached in series with the
ring screw nut, which is also connected to the main motor of the
robot. This motor effectively controls the hip via a 4-bar linkage;
both springs are custom made from glass fiber. Finally, Skippy
has a crossbar (controlled by a second motor), which will
be used to achieve 3D balance and steering, which are
not relevant to this study.
We decided that some parameters would be fixed while
others were the result of separate optimization studies
(such as the 4-bar linkage). For the study presented in
this article, we optimized seven parameters: six of these
define the profiles of the two springs while the seventh
defines the position of the center of mass of the upper
link, which has a significant impact on the robot’s
Finally, we developed a simulation environment in
which the mechanism’s performance for each of the
desired performance objectives was tested. A behavior
was defined with 26 parameters of which 13 were independent
variables representing the voltage profile fed to the robot’s motor.
Fig. 2 shows an example of a voltage profile. The simulation was
performed with MATLAB and Simulink.
Fig. 3 - Overall organization of the design optimization process
Fig. 3 illustrates the overall organization of the process has been
arranged into modeFRONTIER, platform for process automation,
optimization and data mining, which, as mentioned previously,
is organized in two layers. The upper layer finds a Pareto front
of optimal designs that meet all of the objectives. The MOGAII
algorithm was used because it allows multiple objectives and
because it is not limited to local exploration, such as gradientbased
algorithms. The latter was important because we were
managing a high dimensional non-linear search space.
The lower layer consists of 12 individual optimization
experiments to find a given mechanism’s best performance for
each performance objective, and a calculation to determine that
mechanism’s balancing ability, which we wanted to maximize. To
summarize, these performance objectives were to:
- perform jumps increasing in height (with no angular
momentum or horizontal velocity) up to 3m from a resting
- return to rest via a series of jumps of decreasing height
- initiate, stop or continue performing travelling hops (with
non-zero horizontal velocity and zero angular momentum)
- perform a 2m triple backward somersault after a 2m vertical
- maximize the physical balancing ability.
MOGA-II was also selected for this stage, with some of the
performance objectives being formulated as multi-objective
Finally, the algorithms were subject to 11 constraints to ensure
the realism and feasibility of the simulations. To name just
a few, these were to: avoid penetrating the ground, avoid selfcollision,
limit the applied current and more. An overview of the
algorithms, which were used in their default configurations, and
their parameters is presented in the following table (Table 1).
Table 1 - Algorithms and parameters used
The Incremental Space Filler technique and a user-defined initial
seed were used to explore the search space. The initial seed is
a mechanism which can nearly perform the desired objectives
and their corresponding behaviors (it was identified via a separate
optimization study using the same framework).
The optimization scheme evaluated 260 designs, of which 46
(~ 18%) passed all the physical performance tests. A design
was considered to be a successful candidate when at least one
valid behavior per objective was discovered, allowing for a small
interval of error.
We discovered mechanisms that were very skillful in one or in
some of the objectives, but that performed poorly in others. The
mechanism that could jump the highest under-performed in the
traveling hops, while the mechanism that excelled in somersaults
had difficulties in performing low hops. A new, more extensive
experiment, to be conducted in future, will seek a deeper
understanding of the physical traits that lead to this natural
inclination for specific behaviors.
In this study, our main objective was to identify a single machine
with the highest overall merit: a machine that displays high
athleticism in all of the performance objectives, is a capable
balancer, and expends the least amount of energy while
performing these behaviors (this was an extra selection criterion
that was not considered for the optimization). By examining the
Pareto front solutions, we identified a design that satisfied all of
the above criteria and this is currently being manufactured to test
the effectiveness of our method.
Fig. 4 presents an sample behavior of our selected design and
shows the stacked energy flows during one of the most demanding
behaviors (the stance phase of a 2m triple backward somersault).
The potential and kinetic energies can be seen as well as energy
losses due to friction in the springs, the motor and the ring screw.
In Fig. 2, we presented the voltage and current profile of the same
stance phase of a 2m triple backward somersault. Notice that the
motor is in saturation (at 31 Volts) for a large part of the stance phase, proving that the mechanism is indeed being driven to its
This study has demonstrated an optimization method for the design
of a robot that meets several highly athletic behavior objectives.
The study focused on the design of a highly athletic mono pod
that can perform jumps of increasing height up to 3m, then jumps
of decreasing height, traveling hops, display a high physical
ability to balance and was selected based on an energy efficiency
criterion. The framework evaluated 260 different designs of which
a single design was selected to be built.
The study was performed in one plane, but is highly realistic
and uses very detailed models and simulations that capture all
the important energy flows. Despite the focus on detail, there
are limitations to our work. We did not simulate our designs on
uneven surfaces and we assumed a constant friction coefficient
with the ground. We plan on investigating these issues, as well as
on varying and introducing additional parameters to our model.
About the Istituto Italiano di Tecnologia (IIT)
The Istituto Italiano di Tecnologia (IIT), based in Genoa, Italy
is a foundation financed by the State to conduct scientific
research in the public interest, for the purpose of technological
development. The IIT aims to promote excellence in basic and
applied research and to promote the development of the national
economy. As at December 2019, the IIT had produced more
than 13000 publications, participated in over 200 European
projects and more than 40 European Research Council (ERC)
projects, made more than 900 active patent applications,
created 22 established start-ups and has more than 40 more
under due diligence. It has a network of 4 hubs in Genoa that
form its Central Research Laboratories, a further 11 research
centres around Italy, and two outstations located in the US at
MIT and Harvard.
Newsletter EnginSoft Year 17 n°1
By Antonios E. Gkikakis and Roy Featherstone | Istituto Italiano di Tecnologia (IIT)
Fig 1 - A schematic diagram illustrating Skippy’s relevant parts
Fig. 2 - Voltage and current profile during a 0.247 second stance phase that results in
a 2m triple backward somersault
Fig. 4 - Stacked energy flow of 0.247 second stance phase that results in a 2m triple backward somersault
Fig. 5 - CAD design of Skippy. Real Skippy is currently being manufactured. Springs,
ring screw nut and electric motor are not displayed.