A Hyper-redundant Elephant’s Trunk Robot with an Open Structure: Design, Kinematics, Control and Prototype

As for the complex operational tasks in the unstructured environment with narrow workspace and numerous obstacles, the traditional robots cannot accomplish these mentioned complex operational tasks and meet the dexterity demands. The hyper-redundant bionic robots can complete complex tasks in the unstructured environments by simulating the motion characteristics of the elephant’s trunk and octopus tentacles. Compared with traditional robots, the hyper-redundant bionic robots can accomplish complex tasks because of their flexible structure. A hyper-redundant elephant’s trunk robot (HRETR) with an open structure is developed in this paper. The content includes mechanical structure design, kinematic analysis, virtual prototype simulation, control system design, and prototype building. This design is inspired by the flexible motion of an elephant’s trunk, which is expansible and is composed of six unit modules, namely, 3UPS-PS parallel in series. First, the mechanical design of the HRETR is completed according to the motion characteristics of an elephant’s trunk and based on the principle of mechanical bionic design. After that, the backbone mode method is used to establish the kinematic model of the robot. The simulation software SolidWorks and ADAMS are combined to analyze the kinematic characteristics when the trajectory of the end moving platform of the robot is assigned. With the help of ANSYS, the static stiffness of each component and the whole robot is analyzed. On this basis, the materials of the weak parts of the mechanical structure and the hardware are selected reasonably. Next, the extensible structures of software and hardware control system are constructed according to the modular and hierarchical design criteria. Finally, the prototype is built and its performance is tested. The proposed research provides a method for the design and development for the hyper-redundant bionic robot.


Introduction
With the introduction of the concept of Industry 4.0, robots have become more and more essential in intelligent manufacturing [1]. Despite the wide application of robots in the industry [2][3][4][5], medical sector [6][7][8][9][10], aerospace field [11,12], and other fields, consumers' needs are becoming increasingly dynamic and complex [13]. This challenge can be resolved with better motion flexibility, stiffness and load capacity of robots. While traditional robots cannot meet the flexible demands of users, bionic robots can simulate the motion characteristics of elephant's trunk and octopus tentacles efficiently. Compared with traditional robots, the hyper-redundant bionic robots can accomplish complex tasks in unstructured environments with narrow workspace and numerous obstacles because of their flexible structure [14]. These contemporary robots have attracted the attention of industry experts and researchers [15][16][17][18][19].
Having the capability to complete complex tasks in unstructured environments by simulating the motion characteristics of the elephant's trunk and octopus tentacles, bionic robots can be divided into two categories: (1) Continuous robots are a kind of machines that are driven by flexible and extensible materials such as elastic links and biological muscles [20]. Jones et al. [21] developed a continuous robot driven by both pneumatic and tendon by observing the motion principle of tentacles and elephant' trunks. The flexible motion control of the robot was achieved based on the new kinematic modeling method. In order to improve the flexibility and adaptability of the robot in an unknown environment, Wang et al. [22] proposed a cable-driven continuous robot. They established its kinematic model and controlled it by a visual servo system. Eventually, Lyapunov theory was used to prove the stability of the control system. Continuous robots can bend continuously like invertebrates and avoid obstacles flexibly. However, the structure construction and the precise position control of such robots are difficult to achieve practically. What's more, the load capacity of continuous robots is relatively low because of structural limitations. (2) The hyper-redundant robots are a type of robots, which are in series with single-degree-of-freedom driving joints or in series with 2-4-degree-of-freedom parallel mechanism unit modules [23]. Transeth et al. [24,25] studied the obstacle-crossing gait of snakes and developed a snakelike robot Aiko with high flexibility and adaptability. This robot can survey many unknown and complex terrains and can carry out rescue missions in the rubble. Gallardo et al. [26] developed an open-structured hyper-redundant robot with a 3-DOF parallel mechanism as a unit module. Screw theory was employed to analyze the kinematics of this robot. Finally, a 30-DOF robot was used as an example to show that this robot has good motion performance. Taherifaret [27] proposed a hyper-redundant elephant's trunk robot driven by a hydraulic system. The robot realizes the motion of the end moving platform through the control of the hydraulic valve, which has the advantages of high stiffness and strong load capacity. Generally, the flexibility of hyper-redundant robots is not as efficient as that of continuous robots. However, because of rigid rods and motors, hyper-redundant robots have better stiffness and load capacity, and they are easier to achieve accurate position control when accomplishing complex operational tasks in the unstructured environment with narrow workspace and numerous obstacles. Especially in the ocean environment, the buoyancy of seawater counteracts gravity effect of the robot to a certain extent, the dynamic performance of these kinds of robots can be better, so the hyper-redundant robots have broad application prospects in the ocean monitoring, deep-sea exploration and other fields. The motivation of the paper is to present the development of the HRETR with an open structure including mechanical structure design, kinematic analysis, virtual prototype simulation, control system design, and prototype building.
In this paper, a HRETR with an open structure, which is composed of six 3UPS-PS parallel mechanism unit modules in series, is built based on the principle of mechanical bionics and based on the special structure characteristics and motion mechanism of an elephant's trunk muscle group. The main content in this paper includes the overall conception, mechanism design, kinematic model, virtual prototype, control system, physical prototype construction, and performance testing. The rest of this paper is arranged as follows. In Section 2, the mechanical structure design and the overall configuration layout are introduced. In Section 3, the kinematic modeling method of the robot is elaborated. In Section 4, virtual prototype technology is used to carry out the dynamic and static stiffness analysis of the robot. In Section 5, the design of software and hardware of the control system is presented. In Section 6, the construction and performance test of the prototype are introduced, and the performance of the prototype is summarized. Finally, the conclusion is drawn in Section 7.

Mechanical Structure Design
The hyper-redundant elephant's trunk robot is based on the analysis of the external shape and the motion mechanism of an elephant's trunk. The hyper-redundant robot is applied to imitate the motion characteristics of an elephant's trunk. Therefore, the structural design of the HRETR mainly includes two sections: the overall configuration layout and the structural design of the unit module. Both determine the number of modules according to the connection mode of each unit module and functional requirements.

Mechanical Structure Design of the Unit Module
Elephants can grasp things flexibly with their trunk, which can achieve various irregular bending forms. A small segment of an elephant's trunk is taken as the research object. The cartilage and muscle tissues are distributed around the two expiratory holes. The trunk can move axially and bend radially by contracting the cartilage and muscle. The larger plane of the small segment will represent the reference plane. With the smaller one regarded as the moving plane and the center normal vector of the reference plane regarded as the z-axis, the coordinate system is established. The motion plane can move along the z-axis and rotate around three coordinate axes within a certain range. The motion schematic diagram is shown in Figure 1.
According to the physiological and motion characteristics of an elephant's trunk, a 3UPS-PS parallel mechanism (see Figure 2) is designed to complete the three-dimensional rotation and one-dimensional movement of the small segment of an elephant's trunk. Taking 3UPS-PS parallel mechanism as a unit module has the advantages of high stiffness and high load-weight ratio [28][29][30]. The mechanism consists of a moving platform, a base platform, and four motion limbs. The central limb is PS limb and three external limbs are UPS limb. Here, the U, P, and S denote universal, prismatic, and spherical joints, respectively, and the underline denotes the driving joint. The moving platform of the parallel mechanism can perform three-dimensional rotation and one-dimensional movement within a certain range by changing the length of the four driving limbs, which corresponds to the four motion forms of an elephant's trunk. Drive mode adopts the servo-electric cylinder.

Integral Configuration Design of the HRETR
The overall configuration of the HRETR comprises several 3UPS-PS parallel mechanism modules in series based on the research and analysis of the structural characteristics, motion mechanism of an elephant's trunk, and the principle of miniaturization and lightweight. A 7-point coplanar design criterion (the rotating centers of spherical joints of the former unit module are coplanar with the rotating center of the universal joint of the latter unit module) is adopted for the convenience of kinematics and dynamics modeling. The connecting mode of the unit modules is in the form of staggered 60 degrees between the head and the tail to avoid mutual interference ( Figure 3) in order to realize a 360-degree rotation of the moving platform of the HRETR. Besides, six   3UPS-PS parallel mechanism modules are connected in series according to engineering practice experience and considering the constraint of the rotation angle of the spherical joint (±35°). The size of the HRETR decreases accordingly.

Spatial Backbone Curve
The basic idea of the backbone modal method is based on differential geometry theory [12]. The mode equation of the curve is constructed by mode sub-function and mode parameters.
The expression of the spatial curve is shown in Eq. (1). The integral form of the whole center line of the HRETR is described by the backbone modal method.
where s ∈ [0, 1] , L denotes the arc length of the curve, κ(s) represents the tangential vector of the spatial curve at s, α(s) denotes the angle between the y-axis and the projection of the vector κ(s) projecting on the x k O k y k plane, and β(s) denotes the angle between the κ(s) and the x k O k y k plane. According to Figure 4, Eq. (1) can be expanded as: Based on the mode function, α(s) and β(s) can be parameterized as follows: where a i denotes the mode synergetic parameter, n 1 refers to the number of the modal function related to α(s) , n 2 represents the total number of the modal function, b ia and b iβ denote the auxiliary control parameters of the orientation angle, f i (s) is the modal sub-function, and g i (s) is the auxiliary orientation control function of the orientation angle of the backbone curve. Generally, functions g i (s) and f i (s) can usually be initialized as g 1 (s)=1 − sin(πs/2), and g 1 (s)= sin(πs/2). The configuration of the backbone is restricted by at least 3 linearly independent modal functions because the endpoint of the spatial curve is with three-dimensional geometric constraints. The initial modal function can be defined as: After parameterization, p(s) is mainly related to a i , b ia , and b iβ , and the configurations of the backbone curve can be obtained by the searching parameters a i , b 2a , and b 2β . The iteration approach can be used to search the appropriate control parameters, as given in Eq. (5): where T denotes the position and orientation control parameters of the spatial backbone curve at s, a 1m , a 2m , a 3m , a 4m , b 2αm , and b 2βm denote the value of a 1 , a 2 , a 3 , a 4 , b 2α , and b 2β iterating m times respectively, is a positive constant that controls the convergence of the iterative equation, v m (s) = p(s) T α(s) β(s) T refers to the vector of the position and orientation angle at s, v D is the target configuration. J c is not a square matrix, J + c is a pseudo-inverse matrix of J c .

Spatial Backbone Fitting
The spatial backbone curve equation is constructed based on the searched parameters. Searched by dichotomy are the fitting points of the center of the moving platform on the backbone curve of each parallel mechanism module of the HRETR. The variable p k denotes the vector from the center of the moving platform of kth parallel mechanism module to the (k−1)th parallel mechanism module. Because the base parallel mechanism module is mounted vertically on the fixed frame, the fitting point of the moving platform position cannot be on the spatial backbone curve, p 1 = 0 0 −l 1 T . The length of the ith limb of the kth parallel module need to meet the following requirement: where l b,ki and l r,ki denote the length of the sleeve and the push rod of the ith limb, respectively. Also, L c represents the length of the middle limb which can be writing as follows: where H = h 1 h 2 · · · h n T is the parameters for controlling the length of the middle limbs. In each iteration, the parameter h i (i ∈ (1, n) ) is randomly selected between 0 and 1. When the lengths of other limbs obtained by the inverse displacement of the fitted parallel mechanism module do not satisfy the constraint conditions, the parameter H can be adjusted to search again. The variable 0 R O k , which is defined by the Euler angle, denotes the rotation matrix of the moving platform of the kth parallel mechanism module.
Assuming n k = n k,x n k,y n k,z T denotes the unit normal vector of the moving platform of the kth parallel mechanism module in the base coordinate system O 0 − x 0 y 0 z 0 . As n k is equal to the third column of 0 R O k , it can be obtained as: Equation (10) is not relevant to φ zk , hence, the target orientation of each parallel module can be pre-set based on a suitable weight.
In sum, the transformation matrix k−1 k T of the position and orientation of the moving platform, which is relative to the base platform in the kth parallel mechanism module, can be described as: (7) l b,ki ≤ q ki ≤ l r,ki + l b,ki , (i = 0, 1, 2, 3; k = 1, 2, · · · , n),

Inverse Kinematics of the Parallel Mechanism Module
The coordinate systems O k−1 − x k−1 y k−1 z k−1 and O k − x k y k z k are established at the geometric center of the base platform and the moving platform of the kth parallel mechanism module, respectively. The position vector equation of the ith limb of the kth parallel mechanism module is where i = 1, 2, 3, k = 1, 2, 3, · · · , n, a ki denotes the vector from the origin of the coordinate system O k−1 − x k−1 y k−1 z k−1 to the center of the universal joint, b ki represents the vector from the origin of the coordinate system O k − x k y k z k to the center of the spherical joint.

Velocity and Acceleration Analysis of the HRETR
The specific kinematic solution of the HRETR is as follows: 1) It involves providing the position and orientation x, y, z, φ x , φ y , and φ z of the distal moving platform of the HRETR.
2) The inverse displacement algorithm of the HRETR based on the spatial backbone curve modal method is used to obtain the position and orientation of the moving platform relative to the base platform of each parallel mechanism module before interpolating the trajectory in the joint space. 3) It involves taking the time derivative of the trajectory, linear velocity v k , angular velocity ω k , linear acceleration v k , and angular acceleration ω k of the moving platform of the kth unit module. 4) The kinematics of the HRETR is transformed into that of the unit module. The velocity and acceleration of each limb of the unit module are obtained by the inverse kinematics of the unit module.
where J k is the velocity of the Jacobian matrix, ω ki and a ki are the angular velocity of the limb in the basic coordinate system of the unit module and the coordinates of the hinge points of the moving platform, respectively.
The kinematic analysis method of the HRETR is designed according to the content shown in Figure 5.

Virtual Prototype Simulation
In the process of prototype development, the virtual prototype simulation technology of robots can be used in the whole life cycle of product development or system design, which includes feasibility demonstration, technical performance index determination, system design, equipment operation, and maintenance among others.

Static Stiffness Analysis of the HRETR
In order to ensure that the designed components can meet the stiffness requirements, ANASYS is used to analyze the static stiffness of the HRETR. The results are shown in Figure 14.
The static stiffness of the HRETR is analyzed on some typical configurations by using software ANSYS. The  (Table 2), it meets the mechanical requirements.

Control System Design
The control system is divided into hardware design and software design. The design of the software and hardware follows the principle of hierarchical and modular design. Based on the established overall framework, the control system is divided into different modules according to its functions. This design principle facilitates subsequent maintenance and upgrading.

Integral Structure Design of Software of the Control System
The aim of the control system of the HRETR mainly aims is to simulate a movement like an elephant's trunk. In the process of the motion, the control system needs to have a reliable kinematic calculation and trajectory planning interpolation algorithm, and it also needs to monitor the state of the real-time motion via a friendly control interface. At the same time, the design of the control system software of the HRETR needs to consider the extensibility of structure of the robot in order to meet different working requirements. This software system adopts the modular design method. From the human-computer interaction interface to the hardware driver, the system is divided into four-fold: application layer, function layer, execution layer, and driver layer. The overall control architecture is shown in Figure 15.

Control Interface
The control interface is between the user and the robot control system. Most of the content of the robot is displayed on the control interface, thus providing the user with a concise and intuitive operation environment. Figure 16 shows the main interface of the control interface, which is composed of several modules. The main interface is used to display the current three-dimensional position and the orientation information of the robot, to query the current status of each mechanism parallel module, to record and display the user's operation and the running status of the system in real time, and to save the information in the log file. At the same time, it also includes the control system's function buttons, which control the motion planning, return home, parameter setting, starting, suspending, and exiting. The motion planning interface is shown in Figure 17. It can set up the motion planning parameters of the HRETR, including point motion, motion interpolation, and obstacle avoidance planning. The state monitoring and setting interface of the mechanism module is shown in Figure 18. It can monitor the status of each axis of the mechanism module, including the actual position, the planning position, the actual velocity, the planning velocity, and the planning acceleration.

Hardware Design of the Control System
The HRETR adopts the extensible hardware system platform of IPC + multi-motion control card. The hardware structure of the system is shown in Figure 19. In order to meet the interchangeability of the hardware system structure, the system hardware is divided into the industrial computer, the motion module, the servo drive module, the controller, the servo system module, and other main modules. These modules have relatively independent functions, and users can replace them based on their needs. The virtual prototype technology is used to simulate the motion of the prototype. The estimated parameters of important performance indexes such as rated torque and rated velocity of the servo motor are obtained in conjunction with the dynamic analysis in the virtual environment. The type of selected hardware of the control system is shown in Table 3.

Prototype Building
The prototype construction is the last stage in the development of the HRETR. It involves the problems of processing technology and engineering technology. In the construction process, the steps of installation, debugging, and operation need to be arranged properly and carried out orderly to minimize hazards and ensure personal safety. In order to improve the assembly efficiency, the virtual prototype is simulated in SolidWorks to provide support for the assembly of the physical prototype. Also, the software must be installed efficiently and sequentially. The steps of building the physical prototype are shown in Figure 20.
It is necessary to test the performance of the prototype when the prototype is built. Before testing, it is necessary to import the control data obtained from the kinematic   Table 4 shows the motion performance of the HRETR.

Conclusions
In this paper, a prototype of a HRETR with expansibility is designed based on the principle of mechanical bionics while considering the special structure and movement mechanism of an elephant's trunk muscle group. A summary can be drawn as follows: (1) Based on the principle of bionic design, a HRETR with an open structure which is composed of six modules of 3UPS-PS parallel mechanism in series is designed. Using the spatial backbone modal method, the kinematic model of this robot is established. The dynamic and the static stiffness of the robot are analyzed with virtual prototype technology, which provides the basis for the refinement of the structure, the selection of the prototype material and the electric cylinder.
(2) According to the structural characteristics of the HRETR, an extensible software and hardware control system is constructed according to the modular and hierarchical design criteria, a construction method that fully maximizes the potential extensibility of the HRETR.    (3) The performance of the prototype is tested and it is shown that the HRETR can realize the functions of bending like an elephant's trunk. This finding verifies the rationality and feasibility of the mechanical structure design and control method of the robot.