A tracked robot with novel bio-inspired passive “legs”
Sun and Jing Robot. Biomim.
A tracked robot with novel bio-inspired passive “legs”
Bo Sun 1
Xingjian Jing 0 1
0 Hong Kong Polytechnic University Shenzhen Research Institute , Shenzhen , China
1 Department of Mechanical Engineering, Hong Kong Polytechnic University , Hong Kong , China
For track-based robots, an important aspect is the suppression design, which determines the trafficability and comfort of the whole system. The trafficability limits the robot's working capability, and the riding comfort limits the robot's working effectiveness, especially with some sensitive instruments mounted on or operated. To these aims, a trackbased robot equipped with a novel passive bio-inspired suspension is designed and studied systematically in this paper. Animal or insects have very special leg or limb structures which are good for motion control and adaptable to different environments. Inspired by this, a new track-based robot is designed with novel “legs” for connecting the loading wheels to the robot body. Each leg is designed with passive structures and can achieve very high loading capacity but low dynamic stiffness such that the robot can move on rough ground similar to a multi-leg animal or insect. Therefore, the trafficability and riding comfort can be significantly improved without losing loading capacity. The new track-based robot can be well applied to various engineering tasks for providing a stable moving platform of high mobility, better trafficability and excellent loading capacity.
Track-based robots; Mobile robots; Bio-inspired X-shaped structures; Stability control
In the suspension design of track-based robots,
including engineering machinery, most methods are
motivated by tank suspension design. The tank suspension
design is rather complicated, which has shaped various
tracked vehicle designs, including tanks and other
vehicles, conception of which came out in WW1. The idea of
a suspension system to dampen impacts on the chassis
and to decrease the force on the tracks from terrain has
been well known, with many approaches leading to many
effects. Several classic tank suspension designs are briefly
discussed as follows.
Initially, the first tank was designed without suspension
used in WW1 on the British tanks. Later variations had
the tracks on big modules connected to the hull with a
girder, like the Whippet [
]. From the period of WW1
until WW2, the direct coil bogie [
] was adopted which is
a form of suspension, with single or multiple coil springs
carrying a bogie. This was a big improvement, but still
only capable of very minimal travel. Later versions were
invented to allow it to pivot and help with
interconnection, but still limited by the size of the compressed spring
Later on, leaf-sprung bogies are introduced in the tank
suspension design [
]. The system is made of a pair of
wheels carried on leaf sprigs or leaf-sprung arms. When
one wheel is raised like by contacting terrain, the other is
lowered to keep uniform track pressure, which is rather
light, maintenance-friendly, has decent travel length and
keeps the tracks from slipping. Since the friction of the
leaves sliding over each other dampens oscillation, no
shock absorbers are needed. This cheap and effective
system was quickly adopted widely and modified into
various forms [
During the war period, French developed a
standardized system of rubber springs used in their tanks, which
consist of a pair of wheels springing against each other
]. Rubber has a natural dampening property and is not
prone to breaking like steel. But the ability to stand fire
and shell fragment is limited. Similar systems are used
today in vocational trucks and bulldozers. The volute
spring was a very durable system consisted of suspension
arms and coiled strips of metal, which was developed
and used only on US tanks [
]. As the metal layers glided
over each other, it was a strong system and the leverage
of bogie arms provided a decent travel distance. Later
variants used the horizontal volute springs, springing one
wheels off another to interconnect, which contributed to
surprisingly long track life combined with the advanced
and well-insulated American running gear design.
The Horstman bogie is almost like the US suspension
introduced above, but use a coil spring instead of a volute
spring. This system is very comparable to torsion bars,
being a tiny bit stiffer but also having better
interconnection. This system was retained on the Chieftain tank
] and several other vehicles. The Christie system used
a bell crank to transfer arm rotation to spring to allow
that longer springs can be used, which was invented in
American in 1930s. But the Soviets firstly used this
system on the BT and T-34 [
]. This system can provide high
ride quality due to its long spring travel length.
Original Christie tanks also had a chain drive option, so they
could run without their tracks on roads. It also has the
advantages in maintenance and protection of the chassis.
The Bell Crank system is the one with a pair of wheels
on a bell crank, each bogie connected by a short arm and
lever to a central spring running the tank length [
system had too much interconnection but decent travel
length and tended to make the tank sway back and forth
a lot in motion. The single and double Torsion Bar system
is a common modern-type tank suspension and can be
found today on many fast track layers. The original
structure and concept appeared on the German tiger tanks
]. A steel bar runs under the bottom of the tank and
twists with a short trailing arm connected to it and
carrying a wheel. As the wheels hit bumps, the bar twists to
absorb the impact. This system is compact, light, simple
to manufacture and can provide decent travel length.
The hydropneumatic system adopts flexible and soft
gas as a springing medium in cylinders for each wheel to
damp and absorb the shock [
]. The system is actively
controlled by the driver to achieve depression and
elevation and adjusted by the computer to make the chassis
steady while traveling. This is a very complex but effective
and generally light system that promotes track life, crew
comfort, and low mechanical damage due to terrain.
Nowadays, most modern track-based tank designs aim
at high trafficability to achieve stair climbing or
all-terrain mobility. Few suspensions are designed for a more
stable platform during traveling. A benchmark example
is the one developed by DARPA (Fig. 1) which considered
ground vibration and adopted a new arrangement of
suspension design. However, compared to the Christie
suspension, the DARPA design can be regarded as a further
development or optimization and the robot is good only
for heading to one direction.
For mobile robot design, compactness, lightweight,
mobility, stability, loading capacity, and so on are all
needed to be considered. Especially for those intelligent
moving platforms, they are usually expected to carry
sensitive equipment for different tasks, requiring more
riding comfort and stability, etc. Even though many robots
adapted the active vibration isolation approach, its
drawbacks of large size, high energy consumption, expensive
manufacturing costs, and so on limited the development
Therefore, novel suspension systems of high
performance but in passive control manner are highly
relevant to the related areas. To this aim, a novel passive
bio-inspired limb-like suspension system is developed in
this study, which is completely controlled in a purely
passive manner, but can achieve high loading capacity, high
stability, high trafficability on tough ground, similar to a
multi-leg insects or crabs.
The rest of the paper is organized as follows: “The
novel bio-inspired passive suspension structure” and
“Structural modeling and suspension analysis”
sections introduce the bio-inspired suspension design and
its mathematical modeling. “ADAMS model” section
presents some simulation results of the novel suspension
structure. Experiment results are introduced in
“Experiment study” section. A conclusion is drawn thereafter.
The novel bio‑inspired passive suspension structure
Plenty structures and materials in the nature provide
fantastic solutions in vibration isolation and control. It is
noticed that legs or limbs of animals are very easy to
suppress vibration and mitigate shock impact during moving
or jumping due to the very special leg or limb structure.
Inspired by the bird’s leg structure, a new bio-inspired
limb-like or X-shaped anti-vibration structure (Fig. 2)
was proposed and studied recently in [
The X-shaped anti-vibration structure turned out to
be very effective to isolate shock and vibration and keep
the upper platform steady. It has been shown that the
X-shaped structure was proved to be a
quasi-zero-stiffness (QZS) system, which had the characteristic that can
isolate a much broader frequency band of vibration range
than traditional linear isolation systems [
QZS system can be optimized to keep the static stiffness
high and dynamic stiffness low by properly designing the
system parameters, which means the system can remain
a high loading capacity while most of vibrations can be
isolated during motions. These high static stiffness and
low dynamic stiffness properties are exactly needed in
the design of the novel robot suspension.
By applying the bio-inspired X-shaped structure to the
suspension design in the track-based robot, each loading
wheel will be connected to a specially designed X-shaped
structure and then fixed to the robot body. The
singlewheel suspension is shown in Fig. 3, which is constructed
by aluminum rods in a X-shaped form with springs
installed horizontally, in which a central rod provides the
vertical constraint to make the loading wheel only move
vertically from the ground up to 10 cm in height (from
the working position).
By combining all independent bio-inspired
X-structured suspensions together, the whole suspension of the
robot is shown in Fig. 4. Benefited by the single
X-structured suspension, the whole robot can have a decent load
capacity and vibration isolation performance to absorb
the disturbance on road. Also, the long travel distance of
the suspension can ensure the robot easily to overcome a
rather large obstacle on road without losing the stability
of the upper platform.
This would be similar to many multi-leg insects or
animals (Fig. 5). Each leg may not be strong enough to
support the body weight, but all legs together are redundant.
Although one leg is stepped on an obstacle, the other
legs can still maintain the stability of the body.
Importantly, the new suspension design of the robot in Fig. 4 is
totally in a passive control manner. The next section will
provide more understanding about the stiffness
property of the single X-structured suspension and explain
more about why such a passive suspension can
simultaneously achieve high loading capacity but low dynamic
stiffness and therefore lead to an excellent passive vehicle
Structural modeling and suspension analysis
Static stiffness analysis
Referring to Fig. 6 for all structural parameter definitions,
and from Fig. 6 the geometry relationship [
] can be
tan (θ + ϕ) =
2l sin θ + y/3
2l cos θ − x
(2l)2 = 2l sin +y/3 2 + (2l cos θ − x)2
x = 2l cos θ − 2 l2 − l sin θ + y/6 2
Define position a is the equilibrium state and initial force
of the spring F0, then
3 tan θ
When the mass M is moving downwards to the position
b, the restoring force when the mass is at position b is
F = 3(F0 + kl x) tan (ϕ + θ ) − Mg
The force can be presented by y
2 l2 − l sin θ − y/6 2
F = 3 3 Mtang θ + kl −2l cos θ + 2 l2 − l sin θ − y/6 2
2l sin θ − y/3
Thus, the curve of nonlinear restoring force with
different displacement y of the bio-inspired 3 layer leg
suspension structure can be present in the following figure.
From Fig. 7, it can be seen that (a) the equivalent
stiffness of the X-shaped structure is nonlinear and the
nonlinear stiffness is decreased with the compression of the
structure increasing; (b) for the same structure, higher
spring stiffness leads to higher loading capacity but the
equivalent stiffness can all be close to zero after the
structure is compressed to certain distance. As far as we know,
this nonlinear stiffness property is unique in all
existing spring system irrespectively of traditional springs or
pneumatic springs, as most existing spring systems have
obviously increased stiffness during compression. This
beneficial stiffness offers excellent dynamic stiffness of
the robot “legs” when the payload is increased.
To understand the dynamic stiffness of the X-structured
suspension, the dynamic model is studied in this section.
It is supposed that the loading mass is M, the rod length
is l and at equilibrium the assembly angle θ denotes the
angle between the rod and the horizontal line. The spring
stiffness is denoted by kl. The basic parameter for the
3-layer bio-inspired leg suspension model is listed in the
following Table 1.
Moreover, the absolute motion of the loading mass M
is represented by y, the bottom excitation z, the
rotation angle of each connecting rod φ, and the horizontal
motion of the joints at each layer x. The positive direction
of y is upward in the modeling. All motion variables are
listed in Table 2.
The detailed modeling process of the n-layer
symmetric X-shaped structure can be referred to [
Here, it is applied to the 3-layer structure in Fig. 6. For
convenience in discussion and for understanding
dominant dynamic response of the system, the mass of the
connecting rods is not considered. The absolute motion
of the isolation object y is the generalized coordinate.
The kinetic energy can be written as
T = 1 My˙2
V = 2 kl x2
The potential energy is
The Lagrange principle is
dt ∂ y˙
In which L = T − V, and D is the overall damping
effect which is considered as a linear component as
D = c y˙ − z˙ . From Fig. 6, the relative motion between
the mass M and the bottom is ŷ = y–z where y is the
absolute motion of the mass M and z the bottom
excitation, the geometrical relation of variables φ, x and ŷ
can be obtained as
tan (ϕ + θ ) =
2l sin θ + yˆ/3
2l cos θ − x
(2l)2 = 2l sin +yˆ/3 2 + (2l cos θ − x)2
The motion ϕ and x can be expressed as
ϕ = arctan
2l sin θ + yˆ/3
2l cos θ − x
x = 2l cos θ − 2 l2 − l sin θ + yˆ/6 2
By substituting kinetic energy, potential energy, into
the Lagrange principle, the dynamic equation of the
bio-inspired leg suspension can be obtained as
My¨ + (klx)
= −c y˙ − z˙
In which ϕ˙ = ddϕyˆ ddytˆ and x˙ = ddxyˆ ddytˆ due to the geometrical
relations. After some manipulation, the dynamic
equation can be rewritten as
M y¨ˆ + cyˆ˙ + β1 yˆ + β2 yˆ2 + β3 yˆ3 = −Mz¨
where the base excitation z = z0 cosω0t, and
3kl sec4θ sin θ
β3 = kn − 4 kl + 2knl2 cos 2θ sec3θ − 5kl sec5θ
n4 8n4l2 cos θ
The transmissibility curves are shown with different
stiffness in Fig. 8. It can be seen that with smaller k a
smaller resonant frequency can be obtained indicating
a better vibration isolation performance. Compared
with the system of the same stiffness kl but without
using the X-shaped structure, the resonant frequency
is significantly reduced, indicating a much improved
vibration isolation performance (Table 3). This is very
good for robot body stability moving on rough grounds.
Moreover, the structure can also be tuned with
different assembly angle such that a smaller dynamic
stiffness can be obtained. This is discussed in the following
Equivalent stiffness and resonant frequency
The overall spring force of the X-structure is obviously a
nonlinear function, and from the dynamic modeling, the
equivalent linear and nonlinear stiffness coefficients β1,
β2, β3 can be obtained as.
kl tan2 θ
3kl sec4θ sin θ
4kl sec3θ − 5kl sec5θ
648l2 cos θ
The linear stiffness coefficient β1 is a dominant factor to
represent the resonant frequency of the system. To have
a better vibration isolation performance, this coefficient
should as small as possible [
]. The resonant
frequency is (Hz)
This equation reveals very clearly that the resonant
frequency of the single bio-inspired leg suspension can be
tuned to be very small with a smaller kl, a bigger payload
M or a smaller assembly angle θ. When a higher
payload is applied, the spring stiffness kl could be required
to increase. In such case, a smaller assembly angle θ can
be used for a much smaller dynamic stiffness and thus a
much softer single “leg” in moving while maintaining a
higher loading capacity. This is a significant property that
cannot be seen in all existing passive suspension systems.
The loading capacity is determined by the stiffness
of the horizontal spring kl, assembly angle θ, preload
force and strength of structure. Define F0 was the
initial force of the spring and θ2 is the minimum working
angle of the system, when the model is at equilibrium,
3F0 tan θ = Mg. Then, from the assembly angle θ,
compressed to the minimum working angle, the
loading should be applied by 2lkl (tan θ − tan θ2), i.e.,
F0 + 2lkl (tan θ − tan θ2) ≥ 3 tMangθ2.For the 3-layer
bioinspired leg suspension,
With the current design, the maximum loading of the
single bio-inspired leg suspension can be 8 kg. Accordingly,
the overall robot will have the loading capacity up to 80 kg.
The model built in ADAMS is as shown in Fig. 9 and
Fig. 10 which is used to verify the theoretical analysis
With the loading mass M = 5 kg, spring stiffness
kl = 50000 N/m, rod length l = 0.05 m and working angle
at 45°. The transmissibility curve can be achieved by the
simulation in Adams which indicates a resonant
frequency 0.6 Hz (Fig. 10).
As the theory analysis above, the resonant frequency of
the system is
Single 3‑Layer bio‑inspired suspension
For the single 3-Layer bio-inspired suspension, an upper
mass M = 0.5 kg is attached to the top of the bio-inspired
leg as shown in Fig. 11, and the horizontal linear spring’s
stiffness is kl = 4800 N/m. A random vibration signal is
generated with a vibration shaker vertically at the bottom
platform. The experiments will be repeated several times
to guarantee the result.
The acceleration of the upper mass can then be
measured with transmissibility shown in Fig. 12 (3 repeated
times), which show the resonant frequency of the system
is about 5.5 Hz. In theoretical analysis, the resonant
frequency can be represented by
where kl = 4800 N/m, M = 0.5 kg, θ = 45°, then
f0 = 5.2 Hz, which means the theory analysis can match
the experiment results.
Note that for a pure spring-mass system, the
resonant frequency would be around 15.6 Hz. This greatly
validates that the bio-inspired leg can support the same
payload but have much smaller dynamic stiffness and
thus much better vibration isolation performance. This
property will be greatly helpful for stability and comfort
of the upper platform of the robot during moving on
Overall robot with 2‑layer bio‑inspired suspension
In this section, comparative experiments are done to
study the vibration response to road bump with a
developed 2-layer bio-inspired suspension. For comparisons,
the passive bio-inspired suspension can be activated or
locked as shown in Fig. 13. The robot will be controlled
to passive an obstacle about 2–3 cm high on a small
laboratory ground. In such case, any small obstacle could be
observed clearly on the response of the acceleration on
the robot body. Two cases will be considered. The one is
that the robot is to pass the obstacle with only one side of
the wheels, and the other is to pass the obstacle with both
sides of the wheels.
The overall equivalent load of the whole system M = 10 kg,
the speed v = 0.9 m/s, the stiffness of any single horizontal
spring is 3500 N/m in each single “leg.” In such case, the
resonant frequency in the vertical direction of the robot would
be around 4.7 Hz based on theoretical calculation.
Pass obstacles with two tracks
In this section, the robot runs over the obstacle with both
of its tracks. The overall payload of the ten-leg
suspension is Ml = 10 kg, the robot speed is v = 0.9 m/s, and
Fig. 13 Overall robot with 2-layer bio-inspired leg suspension
the stiffness of the horizontal spring was 3500 N/m. The
height of the obstacle is about 3 cm. The time when the
robot touches the obstacle on the ground is between 4
and 5 s.
The acceleration response of the upper platform with
the suspension switched on can be attained by the three
sensors. Compared with the data with the suspension
locked-off, it can be clearly seen that the robot is much
more stable with the bio-inspired suspension system
(Fig. 14). Similar results can also be seen when the robot
passes multi-obstacles with both tracks. Without the
bioinspired suspension, the robot has very strong impulse
response at the upper platform (Fig. 15).
When the bio-inspired suspension is used, the robot
passes the obstacle without any obvious response,
while the robot has obvious vibration without the
Pass obstacles with one track
In this section, the robot runs over the obstacle with
only one track passing on. All parameters are the same as
before (Fig. 16).
The results are shown in Fig. 16 with two trials, both
indicating very good performance during passing the
bump obstacle. The robot with the passive bio-inspired
suspension has almost no response to the bump when
passing on but the robot responded strongly to the bump
without the suspension design. Similar results can also
be seen in Fig. 17 where the robot passes multi-obstacles
with only one track. Very clear shock response can be
seen without the bio-inspired suspension.
These experiments demonstrate clearly that the
bioinspired passive suspension is very helpful for vibration
control of the upper platform of the robot.
Conclusions and discussion
In this study, the track-based mobile robot with a novel
passive bio-inspired leg-like suspension is designed and
demonstrated both with theoretical analysis and
experiments. It is shown that
(1)The bio-inspired X-shaped or leg-like structure has
very good static loading capacity and
simultaneously very excellent quasi-zero dynamic stiffness
properties, which are very good for vibration
control of the robot body in a pure passive manner;
(2)The bio-inspired structure is successfully applied to
the passive suspension design of the track-based
mobile robot such that the robot can maintain
high stability, trafficability, comfort and loading
capacity simultaneously, with only a passive
Due to the advantages above, the track-based robot
with this novel passive bio-inspired suspension can be
extensively used as a universal intelligent platform for
various engineering tasks on rough ground.
It should be noted that the bio-inspired suspension
is very good for vibration control but also creates other
issues in accurate position control of the robot. When
the robot goes through an obstacle, the belt would
be fastened locally around or across the obstacle, the
corresponding motor encoder can record the driving
wheel rotation but actually the robot may not pass the
recorded distance. Therefore, advanced robust tracking
or position control based on multi-sensor information
would be developed for these uncertainties in the further
The authors would like to thank to Mr LI Quankun for his help with
Dr. Jing presented the bio-inspired idea, organized the research and research
results, wrote the paper based on the materials presented by Mr Sun; Mr Sun
completed the design of the robot, conducted the testing and prepared the
draft materials of this paper, under supervision of Dr Jing. All authors read and
approved the final manuscript.
Availability of data and materials
The authors declare that they have no competing interests.
The work is supported by the NSFC project of China (61374041) and the
General Research Fund of Hong Kong RGC with reference number 15206717.
Springer Nature remains neutral with regard to jurisdictional claims in
published maps and institutional affiliations.
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