Type Design and Behavior Control for Six Legged Robots
Fang and Gao Chin. J. Mech. Eng.
Type Design and Behavior Control for Six Legged Robots
Ling Fang 0
Feng Gao 0
0 State Key Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University , Shanghai 200240 , China
The research on legged robots attracted much attention both from the academia and industry. Legged robots are multi-input multi-output with multiple end-effector systems. Therefore, the mechanical design and control framework are challenging issues. This paper reviews the development of type synthesis and behavior control on legged robots; introduces the hexapod robots developed in our research group based on the proposed type synthesis method. The control framework for legged robots includes data driven layer, robot behavior layer and robot execution layer. Each layer consists several components which are explained in details. Finally, various experiments were conducted on several hexapod robots. The summarization of the type synthesis and behavior control design constructed in this paper would provide a unified platform for communications and references for future advancement for legged robots.
Legged robot; Type synthesis; Human robot interaction; Control framework
Since the last decade, research on legged robots has
gained much attention, with its development represents
the state of art technology in both industry and research
]. The evolvement of legged robots has progressed
rapidly. Many companies and universities designed
various type of autonomous robots. One of the outstanding
organizations is Boston Dynamics, which created two
and four legged robots, including BigDog, Atlas and LS3
]. In addition, six legged robots were developed, such
as Athlete (NASA), Whegs (Quinn) and Octopus (SJTU)
]. With mainstream media converges on BigDog,
SpotMini, Handle, etc., people are demanded for legged
robots that can operate in unstructured environment and
accomplish tasks to assist human.
Unlike industry arm robots which are multi-input
multi-output system with single end-effector, legged
robots are multi-input multi-output with multiple
endeffector systems with nonlinear mapping between input
and output [
]. Therefore, legged robots are much more
challenging and complicated to design and control.
One of the major advantages of legged robot is their
flexibility in adapting to complicated environments.
Hence, they are commonly applied in unstructured
settings. These robots can even overcome terrains with
considerable variations and spatial constraints [
Moreover, legged robots are often capable of integrating
walking and operational tasks because of high degree of
freedoms (DoF) on their body frame .
Despite of many prototypes of legged robots are
designed, very few are utilized to facilitate human daily
life or mass industry operations [
]. There are two main
reasons which cause this drawback. Firstly, given a
specific task or application requirement to the robots, the
design of the legged robots is not mathematically
associated with the demand [
]. Secondly, the control system
is very complicated with little high-level guidance [
Because of these two challenges, this paper focuses on
the following two questions: How to design the
mechanisms of legged robots according to certain application
requirements? How to design the control system of the
legged robots to achieve autonomy?
In this paper, the development of type synthesis
and behavior control system are firstly reviewed. The
mechanical design on various type synthesis model are
demonstrated. With each type synthesis model, a design
prototype of a six-legged robot is provided. Three layers,
including data driven layer, robot behavior layer and
robot execution layer of the control framework, are
introduced. Each layer consists of several components. Finally,
various complicated tasks conducted by several hexapod
robots are introduced and discussed.
2 Review on Type Synthesis and Control
Framework of Legged Robots
The design of mechanical system consists of structure
and mechanism components [
]. The mechanism design
contains three important aspects: characteristic
evaluation, dimension synthesis and type synthesis. Among
these three, type synthesis is the most original and
inventive one [
]. Various mathematical tools were used in
the type synthesis to solve the problem of setting up type
criteria with classifications of design objectives [
Type criteria is not just the extension of the dimensions
or description of end-effector motion. It has to express
the end-effector characteristics completely and precisely,
with concern on the succession of motions and the
interactions between different motion attributes .
As the theoretical foundation of type synthesis, the
mathematical theory is the tool to establish type criteria
at the same time to classify and describe mechanisms.
Appropriate mathematical tools can systemize the
complicated synthesis process. The integrity of type criteria
determines the integrity of mechanisms classifications
and the correctness of the type synthesis results. At
present, several kinds of mathematical tools are utilized in
different methodologies, such as the screw theory [
the theory of differential geometry including the Lie
group and differential manifolds [
], the theory of
linear transformation and the set theory [
]. A number of
researchers, including Mruthyunjaya [
], Huang et al.
5, 25, 26
], Herv [
], Gogu [
], Jin et al. , Shen
et al. [
], Meng et al. [
], Gao et al. [
et al. , and Bi et al. [
], contributed much to the
development of the type synthesis of parallel and serial
The screw is composed of two vectors, expressing the
direction and the position of the screw axis, respectively.
The motion and the constraint screw systems are
reciprocal systems, which are useful to replace the complex
intersection operation of screws with the simple union
]. The motion system of a limb can be
transformed into the corresponding constraint system. The
union of all limbs’ constraint systems is the constraint
system of the parallel mechanism’s mobile platform,
of which reciprocal system is the motion system of the
mobile platform [
]. The screw theory is an effective
tool to analyze the instantaneous motions of mechanisms
Based on the theory of differential geometry, the
concepts of differential manifolds, displacement
submanifolds, Lie groups and displacement subgroups are utilized
to derive type synthesis [
]. The motion characteristics,
which fulfill the algebra structures of the Lie group, are
represented by twelve kinds of displacement subgroups.
Those subgroups are not influenced by the succession
of motions. Other motion characteristics, which do not
fulfill the algebra structures of the Lie group, are
represented by displacement submanifolds. Those
submanifolds are sensitive to the succession of motions. The Lie
groups and differential manifolds provided precise
mathematical descriptions for the motion characteristics of
kinematic pairs and chains, laying the foundation for
kinematic analysis and type synthesis [
Position and orientation characteristic (POC) sets were
proposed upon the output translational and rotational
velocities of mechanical end-effectors [
]. POC sets
contain fifteen separate kinds and they are breakthrough
by focusing on the characteristics of end-effectors rather
than separate kinematic pairs .
The generalized function (GF) sets are the special sets
of motion elements of mechanical end-effectors [
Taking the succession and the interaction of motion
characteristics into account, the GF sets represent the motion
ability of end-effectors. The type synthesis approach
based on the GF sets is developed by combining the
intersection algorithms and the number synthesis formulas
A considerable number of researchers developed
distinct methodologies for the type synthesis problem. As a
result, this field is undergoing significant progress, which
can be ascertained from the considerable amount of
publications on various journals and conference
proceedings. However, type synthesis for legged robots are not
the same as parallel or serial system. Hence, the methods
mentioned above cannot be utilized directly for
designing legged robots. Unlike parallel or serial mechanisms,
which usually have single end-effector (manipulator),
legged robots normally possess multiple end-effectors,
including body (main output), legs and hands. A type
synthesis method that can describe the motion of the legs
and the body for legged robots is still in need. How to
express and classify the output of end-effectors are
challenging. The commonly designed body of legged robots
are three, four, five or six dimensions. A proper type
synthesis model should consider all of the above output
Not only the type synthesis for legged robots is
important, the control the robots is equally crucial.
The control architecture of robots mainly includes
four models: sense–plan–act (SPA) architecture, the
layered architecture, the subsumption architecture and
the hybrid architecture [
In 1960, Stanford University developed “Shakey”, the
first robot to deploy a SPA architecture [
on the initial and the target status, The SPA architecture
plans series of sequences of actions . The method
is mostly used in the field of machine manufacture to
accomplish repetitive and monotonous tasks, such as
arm operation and workpiece handling. However, the
SPA architecture provides poor maneuverability and
flexibility when facing complicated tasks, commands in
In 1983, Saridis, a famous scholar in the field of
intelligent control, proposed a three-layer model, namely,
executive level, coordination level and organizational
]. This model is regarded as the most
representative framework among the layered architectures.
It usually consists of one or more main controllers and
many nodes, both of which have processing capacity.
This architectural pattern was later applied to NASREM
structures proposed by NASA and the U.S. National
Bureau of Standards [
]. Layered architecture has a wide
range of applications depending on different tasks,
environments and the robots’ capability [
In 1986, Brooks proposed a behavior based
architecture “subsumption architecture” from the standpoint of
studying the structure of a mobile robot control system
]. It is based on behavioral control by
decomposing complex tasks into a series of relatively simple and
specific sub-behaviors. The subsumption architecture
was later widely used, including the intelligent control
of spacecraft in the United States, mountainous terrain
specialized climbing robot and other projects [
The subsumption architecture is less flexible for multiple
tasks in unstructured and unknown environments.
In 1998, Gat proposed one of the most representative
hybrid architectures [
]. Usually hybrid architecture for
decision-making system has two states, one is the
planning oriented; the other is behavior oriented [
the top layer of hybrid architecture utilizes the
programcontrolled architecture for decision-making to achieve
better performance and efficiency. The bottom layer
utilizes subsumption architecture to achieve improvement
in surrounding adaptability, robustness and real-time
The control of legged robots is complicated and
challenging because they are multi-input multi-output with
multiple end-effectors systems. Furthermore, there is
no direct mapping between the task that is given to the
robots and the output behavior of the robots. In order
to achieve intelligent, full autonomous control or sole
human control are not suitable for current stage of
legged robots. Therefore, the best control architecture is
human-robot interaction with self-regulated autonomy
Many human-robot interaction (HRI) models
utilize force sensors, touch sensors, voice commands and
visual information [
]. Recently, the development
of machine learning, particularly deep learning and
big data analysis, promotes general artificial
intelligence in robotics [
]. Several research results were
published on Nature and Science, which are related
to autonomous control [
]. However, for the
legged robots, the mapping between input and output are
highly complicated. Currently, few control models are
applicable to them. In order to achieve HRISRA, the
control framework needs to consider the high level
tasks, commands and perception that are given from
the human or observed from the environment. In
addition, the framework should take the low level robot
behaviors such as end effector topology, motion
characteristics and trajectory into consideration. Therefore,
there is high demand for a control architecture which
can achieve HRISRA for legged robots.
The control system of legged robots consists of three
layers as shown in Figure 1. The lower layer is
execution layer, which is usually based on Linux for real time
control purpose [
]. The middle layer is
communication layer, which could be based on Robot Operating
System (ROS) [
]. The top layer is a “brain-like” robot
operating system (BROS) which serves as a high level
control system to deal with tasks, instructions and
sensor fusion processing. Currently there is no mature
top layer control. The establishment of BROS system
will play a key role for legged robot HRISRA
control. The goal of BROS system is to reveal the
association between “Task - Command - Perception” and end
effector’s “Topology - Motion –Trajectory” for legged
The construction of BROS confronts the challenges
of various tasks, commands and environments that
change over time. In addition, several conflicts should
be resolved: human command versus autonomous
Figure 1 The “Brain-like” robot operating system
control, human command versus environment
information, human command versus the given task, human
command versus robot ability.
The development of legged robot control framework
has come a long way. The event that brought world
attention is DRAPRA Robotics Competition [
Particularly, after the Fukushima nuclear accident in Japan,
the U.S. Defense Department held the DRAPA
Robotics Competition for emergency rescue by conducting
the following tasks: driving car, get off the car, open and
close the door, screw the valve, break the wall, plug the
power, clear obstacles, climb up and down the stairs
]. It is noteworthy that all the participating teams
are using HRI control [
Teams competing in the DARPA Finals exhibited one
or more of the following HRI characteristics [
The robot had more autonomy when performing
simpler manipulation and mobility tasks; (2) The operators
had more interaction performing complex
manipulation and mobility tasks; (3) More models are placed
manually to assist robots in performing complicated
manipulation tasks; (4) Operators were well trained
with ample practice and more than one operator split
responsibilities in task executions.
After the competition, a comprehensive analysis
review published in International Journal of
Robotics Research (IJRR) summarized the experience and
lessons learned in the DRAPA competition [
paper concludes that the state of autonomous control
in robotics was far from sufficient to support
effective teleoperation when completing complex tasks.
One of the most critical issues encountered in HRI is
to achieve the right balance between human
supervision and robot autonomy. Effective interaction should
balance robot autonomy with the skills and capabilities
that humans are superior at. These skills include
decision making, perceptual capabilities, strategic thinking,
and overall task awareness [
]. Therefore, HRI control
framework allows the robot focus on low-level tasks
such as terrain transversal, while maintaining the
highlevel control from human.
Designing the control framework for legged robots, still
faces many issues: (1) How to balance between human
supervision and robot autonomy? (2) How to decompose
complex tasks into a sequence of subtasks by forming a
subtask chain? (3) How to mathematically express the
robot behaviors including the topology, the
end-effector motion and trajectory characteristics by forming a
sequence of behavior chains? (4) How to establish the
relationship between subtask chains and behavior chains?
The research of answering these basic questions helps the
advancement of the field. Therefore, it is worthwhile to
find the proper models to the issues mentioned above.
3 Type Synthesis of Legged Robots Based on GF
The type criteria, as the design objectives of the type
synthesis, should be precise in describing the motion
characteristics of end-effectors and providing complete
]. In order for type synthesis to be
utilized in the designing of legged robots, the type criteria
should be non-algebraic and dimensionless, independent
of coordinate systems and endowed with physical
meanings. Therefore, the type criteria could be a set of several
elements, which represent the characteristics of
endeffectors with succession .
One of the mathematical tool that can describe the
end-effectors characteristics of legged robot is the
generalized function (GF) sets [
24, 32, 34, 70
fundamental elements of the end-effectors characteristics space
include three-dimensional translations (Ta, Tb, Tc) and
three-dimensional rotations (Rα, Rβ, Rγ). The three
translation axes a, b, c are non-coplanar simultaneously and
two of them are not collinear. The three rotation axes α,
β, γ always intersect at a common point, not coplanar
simultaneously and two of them are not collinear. Rγ is
the last rotation axis relative to the middle rotation axis
Rβ, which is relative to the base rotation axis Rα.
The fundamental elements in GF sets express the types,
quantities, succession, and completeness of elements.
The six-dimensional universal set is represented by GF
(Ta, Tb, Tc, Rα, Rβ, Rγ). The elements represent the
existence of end-effectors characteristics. They are
non-algebraic, dimensionless, and independent of the choice of
coordinate systems. Therefore, the GF sets are more
suitable for the type synthesis of legged robots.
The GF sets are classified into three categories and
twenty-five types in total [
]. The first category of GF
sets is to represent mechanisms of end-effectors that
contain complete rotation (Rα, Rβ, Rγ) in all configurations.
The second category is to represent the end-effectors that
have none complete rotation characteristics in all
configurations. The third category is for the end-effectors
containing two or three dimensional rotation characteristics
and only one of which is complete among any
configuration. Among these 25 types of GF sets, 9 types of them are
suitable for designing legged robots as shown in Table 1.
The first column shows the degree of freedom (DoF) of a
given end effector. The second column shows the
characteristics of the end-effector with GF sets notion. The last
column provides images to demonstrate the motion of
Our research group developed several hexapod
robots based on different type synthesis categories
shown in Table 1. The first robot shown in Figure 2 is
an isotropic hexapod robot driven by 18 actuators.
Each leg of the robot is a 3-DoF parallel mechanism
and the actuation can be controlled both by position
and force. The characteristics of body movement is
GFI Ta, Tb, Tc, Rα, Rβ , Rγ . All the legs are
distributed evenly around the body. In a single leg, the ankle
is connected to the body via 3 limbs: 1 UP and 2 UPS.
Another spherical joint is added between the foot and
the ankle for the adaption of the uneven ground. The
robot body can move with 6 DoF similar to Stewart
The 18 actuators with 6-DoF parallel hexapod robot
derives different types of robots by varying the length of
the legs, the size of the body, the manipulators mounted
on the body and the sensors mounted on the legged
robots. Several robots were developed and shown in
Figure 3, including dexterous operating robot, heavy load
shipping robot, heavy load precision operating robot,
heavy load operating robot, fire rescue robot and heavy
load dexterous operating robot.
Besides the isotropic hexapod robot, other hexapod
robots with less actuators are also developed shown in
Figure 4. These robots can also achieve tasks with heavy
loading capacity. The reduction of actuator has the
following advantages: (1) Reducing the cost: the main
expenses of the robot come from the actuation system,
hence less input means less cost. (2) Reducing the weight
and the size of the robot. (3) Improving the reliability of
the robot: the less of the actuators, the lower probability
of malfunction. (4) Improving the battery life; (5) More
flexibility in designing the structure of legs and the body
to adapt to different tasks and environments; (6) Simpler
One of robots with reduced actuators is a 5 DoF
hexapod robot driven by five actuators as shown in Figure 4.
The six legs form two groups. Each group consists of
three non-adjacent legs and is driven by two actuators.
Among the two actuators, one is utilized to adjust the
height of the legs, and the other is to power the legs to
move forward. The robot is suitable for crossing ditch
and climbing stairs by adjusting the length and height
of the legs. The topological gait of this robot is 3-3, that
is, the robot can only lift the legs group by group. The
fifth actuator mounted on the waist is responsible for the
turning. Therefore, its body comes with 3 DoF, 2
translational and 1 rotational. The characteristics of body
movement is GFII16(Rα, Ta, Tb, 0, 0, 0).
The 13 DoF hexapod is driven by 13 actuators shown in
Figure 4. Each leg is driven by 2 actuators, one is utilized
to move forward and the other is to adjust the height of
the leg. Similar to the 5 DoF robot, the 13th actuator is
mounted on the body by providing the robot with
turning ability. Hence, the robot body can move with 4 DoF, 2
translational and 2 rotational. The characteristics of body
movement is GFII2I5 Rα, Ta, Tb, Rβ , 0, 0 .
The 14 DoF hexapod robot derives from the 13 DoF
robot. The shell is mounted on the body of the 13 DoF
robot. The head, which is a part of the shell, comes with 1
actuator. The head can be adjusted to grab objects,
serving as an operational arm. The robot body can move with
5 DoF, 2 translational and 3 rotational. The
characteristics of body movement is GFIII Rα, Ta, Tb, Rβ , Rγ , 0 .
Meanwhile, a 3 DoF hexapod robot is still under
development. The structure is similar to the 5 DoF robot, but
each leg group is driven by 1 actuator, which controls
the robot to move forward. Hence there is no height
adjustment of the legs. As a result, the robot is not
suitable for crossing the ditches or climbing stairs. The
robot body can move with 2 DoF, 1 translational and 1
rotational. The characteristics of body movement is
F19(Rα, Ta, 0, 0, 0, 0).
Based on the body movement characteristics shown
in Table 1, the GF sets can be utilized to classify and
describe the body movements of existing vehicles. Since
the two DoF of a typical car are coupled (1 translational
and 1 rotational), the car has 1.5 DoF and its body
movement is characterized as GII
F19(Rα, Ta, 0, 0, 0, 0). For
AGV cars, two-wheeled vehicles, tanks which utilize
the Mecanum wheel, their rotation and translation are
decoupled. Therefore, their body has 2 DoFs and the
movement is characterized as GFII19(Rα, Ta, 0, 0, 0, 0).
4 Control Framework of Legged Robots
Currently, few control frameworks are designed for
legged robots. In order to achieve intelligent control, the
framework should include the data driven layer which
consists of high level tasks, perception of the
environment and human given commands. Furthermore,
the control framework should contain robot behavior
layer by modeling the robot’s end effector topologies,
the motion characteristics and trajectories. Finally, the
mapping between data driven layer
“task-commandperception” and robot behavior layer “topology-motion
characteristics-trajectory” should be studied in the
To illustrate the legged robots control framework in
details, Figure 5 shows the data driven layer, the robot
behavior layer and the actuators execution layer. Each
layer consists several building blocks. One of the
challenging tasks is to find the mapping between two layers.
For instance, matrix A encodes task-behavior logical
mapping and matrix B expresses the
behavior-actuator mapping. The rest of this section will focus on the
three key components in data driven layer and three key
components in robot behavior layer and the mapping
4.1 Three Components in Data Driven Layer
4.1.1 Task Component
In unstructured environment, the legged robots needs to
accomplish various tasks. Figure 6 illustrates the division
of tasks space, including external and internal tasks. The
mobility and manipulation tasks are part of the external
tasks; static stability, dynamic stability and safety belong
to the internal tasks.
There is a continuing need for research to
mathematically model different tasks, such as expressing the
external tasks as a sequence of subtasks or task chains. For
internal task, overturning resistance, shock resistance,
disturbance resistance and anti-collision should be
considered and mathematical formulation are required.
4.1.2 Human Command Component
Human-robot interaction commands could be expressed
by speech, gesture, force feedback and body language,
etc. The goal of interactive expression has to be simple
enough for the robots to understand and to be integrated
to their actions. For example, Table 2 shows a list of single
action commands. When given a legged robot as shown
in Figure 2 with 18 actuators, human commands can be
expressed in a sequence of actions shown in Table 2. For
instance, the command can be in the form of “walk
forward for 5 m, turn left for 30°, go up for 5 m. In Table 2,
the actions include forward, backward, up, down, left
and right. If the robot has high DoF, it could also achieve
more complex single actions such as forward left,
backward right, etc.
4.1.3 Perception Component
The advancement on various sensors progressed the
development of legged robots. The perception
information collected from the sensors should be interpreted by
the robot. An even more challenging task is to integrate
different sensor information and learn the suitable model
when there is disagreement.
The perception information is diverse and complex.
There are two type of perceptions, external and
internal. For external perception, the close range vision
sensors help the robot for gait planning while the long
range sensor can assist in creating 3-D grid map. The
force perception can assist walking in unstructured
terrain. In addition, the force sensors are crucial in creating
a safety workspace for legged robots when interacting
with human. The internal perception mainly describes
the kinematics and dynamics parameters of the robots.
Those sensors include gyroscopes, accelerometers, motor
encoder and motor current, measuring the robot
position, velocity, acceleration. The mathematical description
of these information serves as constraint condition for
4.2 Three Components in Robot Behavior Layer
The behavior of legged robot is reflected by its leg
movement, body motion and hand (manipulator) action.
Unlike wheeled robot, the varieties in the combination
of those motion types pose a challenging task. Hence
the key to design useful control framework for six
legged robot is providing mathematical tools to describe the
motion and movement of the legs, body and
manipulator. In addition, the description should be simple enough
to be implemented. The following three aspects will be
explained: end effectors topology, motion characteristics
4.2.1 End Effector Topology
Topology is the top layer of legged robot behavior
control and directly associates with the tasks. The design
of topology is crucial in dealing with different payloads
under unstructured environments. Currently, how
different topologies can be connected based on sensor inputs
and environments needs further study.
For instance, a hexapod robot has seven types of
topologies. Table 3 shows different types of topologies by
including [0, 1, 2,…, 6] legs lifted simultaneous. MT0−6
defines the topology when no leg is lifted. This topology
is particularly useful for adjusting the overall posture of
the body during operation. It can also be utilized when
transiting from one topology to another, such as from
MT3−3to MT2−4. MT1−5 defines one leg is lifted and the
other five are on the ground. It is suitable for tough
environments and heavy loading conditions. The
characteristic of the motion generated by topology MT1−5 is slow and
stable. MT2−4 is the topology when two legs are lifted and
the other four are on the ground. It is useful in crossing
ditches, climbing stairs and slopes, etc. Compared with
MT1−5, MT2−4 is faster but less stable. MT3−3 represents
three nonadjacent legs are lifted simultaneously and is
the most popular topology for hexapod robots. It is the
fastest configuration for walking. MT4−2, MT5−1 and MT6−0
can be executed as running and jumping configurations.
When one or two legs are on the ground, the hexapod
robot will lose its stability and have a high tendency of
falling. Hence the control of these three topologies are
4.2.2 End‑effector Motion Characteristics
The middle component of the robot behavior layer
encodes the motion characteristics of the end-effectors.
This component is particularly important for guiding the
low level trajectory planning process. For instance, with
18 motors as shown in Figure 2, the legs, the body and
the manipulators of an isotropic six-legged robot have six
DoFs. If the task given to the robot is to walk through a
narrow passage, the robot needs to rotate its body (just
like how a human would rotate our body by facing
sideways to pass a narrow passage). Hence planning
endeffector motion characteristics can facilitate trajectory
Generally, the low-level planning has been established
to describe the end-effector’s kinematic mobility,
including the workspace, velocity, acceleration, payload,
stiffness, etc., all of which are in algebraic form with units.
These parameters are related to coordinate systems
and cannot handle the diverse range of topology
performances of the body of the legged robot. In order to
describe the motion of the body and end-effectors over
time, the GF sets can be utilized.
4.2.3 End Effector Trajectory
End effector trajectory can be classified as manipulator,
body and foot trajectories. All of them can be expressed
by fifth-degree or seven-degree polynomials, according
to the parameters shown in Table 4. If the position,
velocity and acceleration in the start point and end point are
known, fifth-degree polynomial can be utilized to express
trajectory. Besides the above 6 parameters, if jerk is also
considered, seven-degree polynomial is more suitable.
The trajectories can also be designed with simpler
function such as triangular, rectangular, trapezoidal and
elliptical trajectories. The choice of the trajectory depends
on different terrains and tasks. Table 4 shows how foot
tip trajectory relates to terrain and speed adaption when
given various tasks and environments. The second
column shows the expression for a given trajectory.
4.3 Logical Relationship between Data-driven Layer and Robot Behavior Layer
The modeling and learning of the logical relationship
between two layers is a challenging issue in legged
robot control. As illustrated in Figure 5, the connection
matrix A indicates the logical mapping between
datadriven layer and robot behavior layer. The matrix B
indicates the logical mapping between robot-behavior
layer and execution layer. The learning of the elements
in A and B depends on the mathematical representation
of each layer and the training process.
The task, human command and robot perception
form a complicated high dimensional space on the data
driven layer. The mathematical models that can
discretize each component are described in previous
sections. If enough data is collected, a knowledge database
is needed for further learning. Constructing a sequence
of tasks, human commands and perceptions chain can
facilitate the process of finding the mapping of
consecutive layers. Given a temporal window, in the robot
behavior layer, a sequence of end-effector topologies,
motion characteristics and trajectories are formed. The
goal is to find the logical mapping for the chains formed
in the two layers.
The elements in the logical mapping can be expressed
as adjacency matrix, directed graph or a classification
model. All of the mappings require a large dataset to
train on. This is crucial in building an intelligent control
system for legged robot. Therefore, much work should
be put into data collection and construction that allows
the robot to explore, build and train itself on. Similar to
], the utilization of large data,
computational power and self-learning capability are the keys to
build such a knowledge database for legged robots.
5 Experiments on Hexapod Robots
Hexapod robot possesses the capability to finish various
complicated tasks in unstructured environments. Based
on our mechanical and control design, several hexapod
robots are developed. The following examples
demonstrate their capabilities in execution of complicated tasks.
5.1 Climbing Stairs
One of the advantages of the legged robot is its
flexibility in climbing stairs. During stair climbing
process, a hexapod robot may utilize different topologies,
depending on the slope, height, payload and other
factors. During the starting phase and ending phase, the
robot sometimes need to use different topologies when
encountering steep stairs. As shown in Figure 7, before
the robot starts climbing, it walks on the flat ground by
utilizing MT3−3 for speed. When it starts to climb the
stairs, it utilizes different topologies in different stages.
MT0−6 is used to adjust the posture of body without
lifting legs, MT1−5, MT2−4 and MT3−3 are utilized for
climbing based on the center of mass, stability requirement,
location of all the legs, etc. This example illustrates the
significance of creating topology chain when dealing
with human commands.
5.2 Conducting a Sequence of Tasks
Often, the legged robot needs to accomplish a sequence
of tasks given by human. In this experiment, the robot
utilizes autonomous control to conducted four
different tasks: obstacle avoidance, barrier crossing,
climbing upstairs and downstairs in succession. In order to
finish this sequence of tasks, the robot utilized the
perception information acquired from camera, gyroscopes,
accelerometers and force sensor which are mounted on
itself. Figure 8 presents the screenshots from a
singletake video. Such experiment exhibits the efficiency of
autonomous control based on the framework.
5.3 Other Complicated Tasks
Besides the tasks mentioned above, the hexapod robots
developed in our research group possess the
potential capabilities to conduct other tasks. Mounted with
various hands (manipulators) on the body, the
hexapod robots are capable of finishing complicated tasks,
including plugging the pipe, climbing steps with heavy
burden, opening a door, screwing the valve, grasping
the pipe and cutting the pipe, etc., as shown in Figure 9.
These results demonstrate the ability to conduct
various complicated tasks in unstructured environment.
It is still far from sufficient to establish the intelligent
control system of legged robots. Therefore,
continued research is needed to improve of the design and
the control of legged robots. The followings are main
points in this paper.
(1) The distinctive type synthesis models of legged
robots mechanical design are reviewed. Based on nine
Figure 9 Other complicated tasks accomplished by hexapod robot
in unstructured environments (Additional files 3, 4, 5, 6, 7 and 8)
types of GF sets, various hexapod robots are designed
(2) The control framework of legged robots is
discussed, including three layers, namely data driven
layer, robot behavior layer and execution layer. Each
layer contains several components and are discussed in
detail. To fully understand the association of the data
driven layer and robot behavior layer is a key role in
achieving intelligent control of the robots.
(3) Experiments on hexapod robots are implemented
to execute different tasks. These results indicate the
capabilities of the robots developed in our research
The investigation on the basic issues of type
synthesis and control design for legged robots would promote
the community to focus on the challenging issues and
accelerate the advancement of the theoretical and
practical aspects of legged robots.
Additional file 1. Climbing stairs.
Additional file 2. Hexapod robot with a single take.
Additional file 3. Climbing steps with heavy burden.
Additional file 4. Opening the door.
Additional file 5. Plugging the pipe.
Additional file 6. Grasping the pipe.
Additional file 7. Cutting the pipe.
Additional file 8. Screwing the valve.
LF was in charge of the whole experiment and data analysis; LF and FG wrote
the manuscript. Both authors read and approved the final manuscript.
Ling Fang, born in 1987, is currently a post-doctoral fellow at State Key
Laboratory of Mechanical System and Vibration, Shanghai Jiao Tong University, Shanghai
200240, China. Feng Gao, born in 1956, is currently a distinguished chair
professor at State Key Laboratory of Mechanical System and Vibration, Shanghai
Jiao Tong University, China.
The authors declare no competing financial interests.
Supported by National Natural Science Foundation of China (Grant No.
Springer Nature remains neutral with regard to jurisdictional claims in
published maps and institutional affiliations.
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