This paper presents a novel bio-inspired modular robotic arm that is purely evolved and developed from a mechanical stem cell. Inspired by stem cell whilst different from the other robot “cell” or “molecule”, a fundamental mechanical stem cell is proposed leading to the development of mechanical cells, bones and a Sarrus-linkage-based muscle. Using the proposed bones and muscles, a bio-inspired modular-based five-degrees-of-freedom robotic arm is developed. Then, kinematics of the robotic arm is investigated which is associated with an optimization-method-based numerical iterative algorithm leading to the inverse kinematic solutions through solving the non-linear transcendental equations. Subsequently, numerical example of the proposed robotic arm is provided with simulations illustrating the workspace and inverse kinematics of the arm. Further, a prototype of the robotic arm is developed which is integrated with low-level control systems, and initial motion and manipulation tests are implemented. The results indicate that this novel robotic arm functions appropriately and has the virtues of lower cost, larger workspace, and a simpler structure with more compact size.
In the field of robotics, researchers and engineers have a dream of
developing robotic arms with agile characteristics like the human arm to
perform dynamic tasks under complicated and unconstructed environment.
However, more than sixty years passed since the first robotic manipulator
being patented by George G. Devol in 1954 (see
In order to achieve desired flexibility, manipulability and
reconfigurability, one of the efforts is devoted to the development of novel, high
performance module-based robotic arms. These include, to mention but a few,
the one degree of freedom T-type and I-type modules proposed by
In addition, bio-inspired robotic arms have also been designed and developed.
One of the earliest bio-inspired robot is a new robotic system coined DRRS
(Dynamically Reconfigurable Robotic System) proposed by
In this paper, we propose a stem-cell-inspired mechanical robotic arm. Different from the robotic arms discussed above that each of their mechanical cells or molecules is not separated but a completed robotic module being integrated with control and software system, the mechanical stem cell proposed in this paper, inspired by the character of stem cell, at a more basic and fundamental level, is a type of pure mechanical unit. This unit can be used to build different robotic modules in according to the practical applications.
Using the unit, a bio-inspired mechanical muscle based on Sarrus linkage is
proposed, leading to the development of a 5-DOF bio-inspired robotic arm. This
novel design helps augment workspace and overcome some shortcomings of
conventional serial robotic arms. According to the available literature,
although Sarrus linkage
In this paper, a robotic arm evolved from a fundamental mechanical stem cell is for the first proposed, and its associated kinematics, simulation, prototype and initial test results are presented.
Stem cells have the remarkable potential to be developed into different cell
types during their life cycles, and under certain physiological or
experimental conditions, they can be induced to become tissue- or
organ-specific cells with special functions. Inspired by the evolution of
stem cell, this paper proposes the concept of mechanical stem cells that are
immature and have the potentiality to evolve into various robotic modules,
such as bone, joint and muscle etc. A typical example of such a concept is
illustrated in Fig.
Bio-inspired mechanical cell.
The FNMN and FFMM mechanical cells can further evolve themselves into
mechanical bones forming structure modules that can be used as links or rigid
bodies for constructing bio-inspired robotic arms. For example, the FNMN and
FFMM mechanical cells can interact and grow into different mechanical bones
such as the cubic bone, cuboid bone and polyhedral bone that are indicated in Fig.
Bio-inspired mechanical bones.
The cubic bone is a stable structure consisting of six FFMM cells, and by
adding four more FFMM cells to a cubic bone, a cuboid bone can be generated
as shown in Fig.
A bio-inspired mechanical bone developed through the mechanical cells have three advantages. First, its structure is simple, modular and apt-to-be fabricated. Second, its structure is reconfigurable and flexible. Third, the inner hollow space of these mechanical bones can be used to accommodate sub modules of robot, which is very useful for some special applications such as space technology.
Sarrus linkage
Based on the Sarrus linkage, we can artificially nurture the FNMN and FFMM
mechanical cells into a bio-inspired mechanical muscle that is composited of
six mechanical cells connected by six revolute joints as indicated in
Fig.
Bio-inspired Sarrus-linkage-based mechanical muscle.
To meet the requirement of practical engineering applications, a robuster
Sarrus-linkage-based mechanical muscle is symmetrically developed by
integrating four additional FNMN cells into the standard Sarrus structure
associated with six extra joints, as illustrated in Fig.
Further, given the structure parameters of the Sarrus structure as
illustrated in Fig.
Based on the mechanical bones and muscle developed from the mechanical stem
cells in the previous section, different type of robotic arms can be evolved
and grown satisfying specific purpose and environment, and one bio-inspired
modular-based 5-DOF robotic arm is developed in this paper as illustrated in
Fig.
For this robotic arm, through the shoulder revolute joint, it can realize an
circular 360
As described above, the dexterous motion generated by the proposed robotic arm provides augmented workspace. Regarding its application, the shoulder can be fixed on the base or combined with the other robots, we can also directly connect the upper Sarrus arm to the base or the other robots with the shoulder revolute joint. By accurate controlling the motion of each joint, the robotic arm can execute specific mission satisfying various customer requirements.
A bio-inspired modular 5-DOF robotic arm.
As aforementioned, the bio-inspired 5-DOF robotic arm developed in this paper
is evolved from the mechanical stem cell consisting of bone cells and
Sarrus-linkage-based muscles. Kinematics of such a robotic arm is different
from the conventional ones and is investigated in this section. In order to
describe the position and orientation of the proposed robotic arm, a global
coordinate system
Considering the motion sequence of the robotic arm, it involves both
translational and rotational transformation. Herein, the homogeneous
transformation matrix for translation is denoted as Trans(
As discussed above, the bio-inspired robotic arm is built by the FFMM and
FNMN mechanical cells evolved from the mechanical stem cell, thus all the
unit modules used to construct the robotic arm have the same structure
parameters and we assume that lengths of the side and thickness of a unit
module are respectively
Referring to Fig.
Coordinate system
Geometry and coordinate systems of the robotic arm.
Similarly, according to Fig.
Further, by defining the displacement vector of the origin of frame
From Fig.
Finally, multiplying all the four transformation matrices in Eqs. (
Furthermore, combining Eq. (
Inverse kinematics provides background for position control of a robotic arm.
Given the Cartesian coordinate of the end-effector in the transformation
matrix
Dividing matrix
Assuming that elements of the matrix in Eq. (
However, as aforementioned, due to the hybrid structure of the proposed
bio-inspired robotic arm, there is no analytical solution for the set of
non-linear transcendental equations, there exist only numerical solutions or
approximate solutions. Further, unless in the case of special circumstances,
there is no general direct method to get the numerical solution structure of
non-linear equations, including the existence of solution and multiple
solutions. At present, there are two approaches for obtaining the numerical
solution, i.e. the indirect method based on fixed point theorem, and the
optimization method based on variational principle, both of these methods are
based on iterative numerical solution adopting the strategy of the “time for
accuracy” termed in
Given elements to matrix
In order to convert the equation solving problem into an equivalent optimization
problem, Eq. (
Thus, the problem of solving non-linear transcendental equations is
transformed into the problem of solving the energy function complying with a
given constraint. That is, given a sufficiently small positive number
The numerical solutions of non-linear transcendental equations can be
implemented in three steps as presented in the existence of solutions: checking whether the equations have solutions; solution isolation: dividing the solution interval into smaller sub-intervals,
for each sub-interval, there may exist a solution or not, and if so, we can
refer to any point in the sub-intervals as an approximation solution; solution precise: efforts to improve the accuracy of the approximation
solution, make it satisfy a certain accuracy requirement.
Considering the approach of solving non-linear equations based on global
optimization method, a numerical iterative algorithm is proposed with its
procedures shown in Fig.
Firstly, define the maximum number of iteration
Secondly, allocate values of the five variables
Flow chart for numerical solution of the proposed inverse kinematics.
Thirdly, continue allocating the five variables
Repeat the above steps until the value of energy function is less than the
threshold error or the iteration times reached the maximum number, the final
output of the five variables
Obviously, this algorithm can reliably obtain a set of solutions satisfying the equations through a series of continuous divide and iteration. To seek a more accurate solution, more divided intervals and iteration times are required, which naturally increases the operation time. It can be found that the above algorithm can satisfy the general application requirements without involving any kind of complex algorithm such as genetic algorithm or neural networks. In this paper, the results obtained indicate that this algorithm is sufficient to compute the inverse kinematics and provide results for position and orientation control, the results are indicated by numerical simulation and physical prototype validation.
Workspace of the bio-inspired robotic arm.
Based on the transformation matrix of the wrist bone centroid
Figure
The workspace of the robotic arm in Fig.
In addition, Fig.
Geometric configurations of the bio-inspired robotic arm.
Based on the changes of the lengths of the three equivalent links
Workspace augmentation function of the two Sarrus-linkage-based muscles.
Figure
Similarly, as shown in Fig.
Hence, with the two Sarrus-linkage-based muscles integrated in this novel bio-inspired robotic arm, it can break through the limitation of conventional robotic structure and enlarge its workspace, which makes the robotic arm particularly suitable for performing large-scale motion in a compact space, not only as a general industrial robotic arm, but also as a device carried by mobile robot to perform investigation, detection, rescue, transportation and other tasks.
Further, in order to validate the feasibility and accuracy of the proposed
algorithm for inverse kinematic analysis, one numerical example is provided
in this section. The validation method and process is: first, give an initial
value for the five variables
Here, we assume that the mechanical stem cell has structure parameters
Firstly, substituting the variables in Eq. (
Then, by equating matrices Eqs. (
Subsequently, substituting the above matrix into the algorithm developed in
Matlab™ program, and setting subdivision number as
Finally, by substituting the results in Eq. (
Comparing the results in Eq. (
Based on the forward and inverse kinematic analysis of the bio-inspired
robotic arm, the mechanical cells were designed and fabricated, and a
prototype of the proposed 5-DOF robotic arm was constructed, assembled and
integrated with low-lever control system as illustrated in Fig.
Errors of the inverse kinematic solutions.
Prototype of the proposed bio-inspired robotic arm.
To validate the forward and inverse kinematic models of the robotic arm, a
virtual obstacles is designed to construct obstacle avoidance motion test of
the robotic arm. As shown in Fig.
Obstacle avoidance motion test of the robotic arm.
It can be seen that if the shoulder joint rotates directly, the whole arm
will swing toward the obstacle, which may lead to an interference between the
arm and the obstacle. Therefore, in order to avoid potential collision with the
obstacle, a simple but efficient motion control strategy is used based on the
property of the Sarrus-linkage-based muscles. Figure
Initial tests indicate that the proposed robotic arm can not only perform the functions desired in the design but also overcome obstacles through the shrinking motion of the upper arm and forearm Sarrus-linkage-based muscles, which greatly simplifies control strategy and reduces the financial cost for establishing complex control system.
In this paper, a novel bio-inspired robotic arm was for the first time proposed and presented. This robotic arm was designed and developed based on a single type of mechanical stem cells.
Inspired by the function and characteristics of the stem cell but different from the other robot “cell” or “molecule”, the mechanical stem cell presented in this paper is simple but capable of evolving into different functional cells, bones and muscles. Using the bones and a mechanical muscle developed based on the Sarruse linkage, a 5-DOF bio-inspired robotic arm was designed and its associated kinematics was investigated. In order to solve the inverse kinematics of the proposed robotic arm, an optimization-method-based numerical iterative algorithm was proposed and verified with a numerical example and computer simulations. Further, a physical prototype of the proposed 5-DOF robotic arm was developed and initial tests were carried out to validate the correctness of forward kinematics and the applicability of inverse kinematics solving algorithm.
Overall, the paper has indicated that the stem-cell inspired pure mechanical stem cell has parallels in biology and provides a flexible modular way to build mechanical bones and muscles for robotic arm development. Advantages of the proposed bio-inspired robotic arm can be summarized in three aspects: first, its structure is simple, modular and apt to be fabricated; second, its structure is reconfigurable and flexible; and third, the inner hollow space of these robot bones can be used to settle sub modules of robot, which is very useful for some special application such as space technology.
Designed and developed the robotic arm: Zirong Luo. Kinematics Analysis: Zirong Luo, Jianzhong Shang, Guowu Wei and Lei Ren. Simulation ad prototype: Zirong Luo, Jianzhong Shang. Wrote the paper: Zirong Luo, Jianzhong Shang, Guowu Wei and Lei Ren.
The author wishes to thank Ernest Appleton, Bo Liao, Yunkai Yang and Jun Zhang for their valuable contributions in developing the prototype. Edited by: K. Mianowski Reviewed by: L. Bruzzone and one anonymous referee