Design of a Flexible Capture Mechanism Inspired by Sea Anemone for Non-cooperative Targets

Robotic grippers have been used in industry as end-effectors but are usually limited to operations in pre-defined workspace. However, few devices can capture irregularly shaped dynamic targets in space, underwater and other unstructured environments. In this paper, a novel continuum arm group mechanism inspired by the morphology and motions of sea anemones is proposed. It is able to dissipate and absorb the kinetic energy of a fast moving target in omni-direction and utilize multiple arms to wrap and lock the target without accurate positioning control. Wire-driven actuation systems are implemented in the individual continuum arms, achieving both bending motion and stiffness regulation. Through finite element method, the influence of different configurations of the continuum arm group on the capture performance is analyzed. A robotic prototype is constructed and tested, showing the presented arm group mechanism has high adaptability to capture targets with different sizes, shapes, and incident angles.


Introduction
Traditional grippers with rigid links and joints, usually adopt two-finger or three-finger configurations to pick and hold objects, taking the advantages of high precision and stiffness. They are suitable for operations in pre-defined workspace. For instance, Drigalski et al. [1] developed a versatile two-finger gripper that can grab ultra-thin objects such as textiles and clothing. Samavati et al. [2] presented a three-finger robotic gripper to grasp cylindrical objects via "force-closure" and "form-closure". Nie et al. [3] combined two simple grippers, including an inner one for precise alignment and an outer one for stable holding, for the use of assembly. Bolboe and Staretu [4] developed a gripper with two symmetrical fingers that can grasp objects within a certain size range by placing sensors on the articulated modules. Humanoid robotic hand is an improvement for traditional gripper with high degrees of freedom (DOF), and can therefore provide more delicate operations through the coordination of multiple fingers. Butterfass et al. [5] developed the DLR-Hand II with four fingers, which can achieve precise grasp and fine manipulation. Odhner et al. [6] presented the iHY hand capable of in-hand repositioning tasks. Dai et al. [7] presented a metamorphic hand that has augmented orientation and workspace. Note that, existing robotic grippers and hands were mostly designed to deal with objects that remain still or move in a given direction and relatively low speed, e.g., the parts on an industrial assembly line.
With the developments of robotic technologies, human beings are expanding their exploration field to unknown environments, such as space and underwater, where the operation objects become non-cooperative, like satellites, space debris, marine life and wreckages. Compared with those pre-identified targets in industrial scenarios, non-cooperative ones have unknown shapes and undefined moving trajectory. In addition, they are impossible to communicate with in most cases.
Many efforts have been paid on exploring the capture technologies for non-cooperative targets. Yoshida and Nakanishi [8] presented a satellite capture device that can insert an impedance controlled probe into the thruster nozzle of the satellite. Meng et al. [9] presented a method to fully identify the inertial parameters of a non-cooperative object on orbit. Li et al. [10] found that accurate measurement of position and orientation for non-cooperative targets is of great importance and has a direct impact on the success rate of capture. Rekleitis et al. [11] proposed to use two 7-DOF manipulators for the on-orbit capture and service, and successfully performed ground tests. To access the ocean depths, Khatib et al. [12] developed the Ocean One, a bimanual force-controlled humanoid robot that affords intuitive haptic interaction in underwater environments. The above devices basically have rigid structures and adopt "point-to-point" operating mode which requires accurate calculation of the trajectory and orientation of the non-cooperative target. In the meantime, the capture devices need to take real-time adjustment of its own position and orientation to contact the fast moving targets as gentle as possible, preventing from collision and damage. These requirements are very challenging and so far there is no successful case of capturing noncooperative target in space [13].
On the contrast, it is noticed that flexible capture devices made of semi-soft or fully soft materials can provide redundant passive DOF to fit the non-cooperative targets while reducing the contact impact. Walker [14,15] designed a series of continuum arms inspired by elephant trunks, which are capable of wrapping an object with the body structure. The presented continuum arms usually consist of several modules connected in series. Each module contains 3 to 6 pneumatic muscles arranged in parallel to achieve stretching and bending motion. It is found that the continuum robot can reduce the velocity of a non-cooperative target through structural compliance and surface friction [16]. Zhai et al. [17,18] proposed a flexible flynet mechanism that can be catapulted to the target and envelope it. Whitesides et al. [19,20] designed a variety of soft actuators and used them to achieve grasping of fragile objects such as eggs. Galloway et al. [21] presented a design of an underwater gripper that utilizes soft materials to delicately sample fragile species on the reef. Kang et al. [22][23][24] designed a series of compliant continuum arms, driven by pneumatic muscle and rod, for grasping tasks in complex environments. Dong et al. [25,26] designed a series of continuum robots which can perform in-situ maintenance in an aeroengine, reducing the impact and damage. However, the above-mentioned flexible capture mechanisms still have the following limitations: insufficient adaptability to the shape and size of the target, high requirements for position/orientation accuracy, and difficulties in capturing dynamic targets.
It has been found that the sea anemone is an amazing predator in the nature. It is soft and boneless, with a large number of cylindrical or vermicular tentacles as shown in Figure 1 [27]. Although the movement and load capacity of its single tentacle is not outstanding, multiple tentacles can be activated simultaneously to hook and wrap a prey coming from any direction, showing high flexibility and large tolerance.
In this paper, a flexible capture mechanism inspired by sea anemone is proposed, which can significantly improve the robustness of the capture operation for noncooperative targets while reducing the control difficulty. This paper is organized as follows: Section 2 describes the structural design of the capture mechanism; Section 3 analyzes the influence of the arm group configuration, as well as the velocity and size of the target body, on the capture success rate via a finite element model. Section 4 shows the experimental results, and the last section presents our conclusions.

Design of the Capture Mechanism
In order to deal with non-cooperative targets that are irregularly shaped and moving fast in omni-direction, the following requirements for the capture mechanism should be satisfied.
1) The mechanism should have high tolerance to the position and orientation errors during capture operation. In other words, it does not have to precisely adjust its arms to point to the target. 2) The mechanism should have appropriate compliance that can absorb the kinetic energy of the target, and therefore reduce the collision impact, as well as the damage to either the target or the capture mechanism itself. 3) The mechanism should have high adaptability to the shape and size of the target.
As mentioned in Section 1, a natural paradigm demonstrating high tolerance, compliance and adaptability in predating operation is the sea anemone. Inspired by this, we presented a capture mechanism using a number of flexible continuum arms to form an arm group to intercept and capture non-cooperative targets. The robotic prototype is composed of nine under-actuated continuum arms and a drive box, as shown in Figure 2. Parameters of the capture mechanism can be seen in Table 1. Figure 3 shows the construction of a single continuum arm, consisting of a silicone sleeve, a central skeleton, and two driving wires 1 and 2 for bending and stiffness control, respectively.

Continuum Arm
The silicone sleeve covers the central skeleton, providing the arm a soft surface to contact with a target. The central skeleton is composed of multiple segments (14 segments in our case) connected in serial by the spherical joints. The segments are made of photosensitive resin via 3D printing. As shown in Figure 3(b), each segment has a central guide hole for the routing of driving wire 2, as well as a side guide hole which offsets from the center guide hole by 4.5 mm for the routing of driving wire 1.
Both driving wires 1 and 2 are attached to the tip of the arm and go through the whole arm length to the base.
By applying a pulling force to driving wire 1, the offset arrangement will generate a moment to the arm tip, making the arm bend to the direction of side holes. In our prototype, the direction of the side holes are arranged toward the center of the base platform of the drive box, so all arms will bend to the center of the base platform when pulling driving wire 1. As the segments are connected by spherical joints, the arm is also allowed to passively and locally bend to other directions when touching the object. By applying a pulling force to driving wire 2,  The overall height of the capture mechanism H (mm) 300 The overall length of the capture mechanism L (mm) 140 The overall width of the capture mechanism K (mm) 120 Height of drive box h (mm) 140 Length of the continuum arm l (mm) 160 The diameter of the continuum arm φ (mm) 20 The thickness of the silicone sleeve m (mm) 2.5 Length of driving wire 1 λ 1 (mm) 190 Length of driving wire 2 λ 2 (mm) 240 Diameter of driving wire 1 Φ 1 (mm) 0.4 Diameter of driving wire 2 Φ 2 (mm) 0.48 The distance of adjacent segments δ (mm) 9 The offset distance of side guide hole s (mm) 4.5 Maximum rotating angle of the spherical joint α (°) 25 the tension will increase the contacting force between individual segments and therefore limit the relative rotating motion between them, achieving the stiffness augment of the arm. Both driving wire 1 and driving wire 2 are made of NiTi alloy wire with high compliance. In addition, a spring is placed between two adjacent segments to improve the resilient force of the arm to its neutral position.
To sense the contact between the arm and an object, a microswitch is installed at the bottom of the arm. As shown in Figure 2(a). Once there is vibration on the arm, the microswitch will be activated to generate a low level signal. The base positions of the nine arms can be adjusted on the base platform of the drive box through the sliding tracks to achieve different arm configurations.
The use of arm group allows for flexible deformation to grasp target coming from a wide range of direction and position. Even if failures occur to a single continuum arm, the rest arms can still complete the task. This mechanism provides significant tolerance, compliance and adaptability required by the capture operation for non-cooperative targets.

Drive Box
As shown in Figure 2, the prototype includes nine continuum arms, so there are nine driving wires 1 and 2 whose bottom ends go into the drive box and fixed to two sliding plates 1 and 2, respectively. The movement of sliding plate 1 will simultaneously apply tension to all driving wires 1 and initiate a bending motion to all arms to grasp an object. Similarly, the movement of sliding plate 2 will simultaneously apply tension to all driving wires 2 and stiffen all arms. The sliding plates 1 and 2 are connected to and driven by two linear stepper motors 1 and 2, respectively. The maximum stroke of the linear stepper motor 1 is 25 mm, resulting a maximum bending angle of the individual continuum arms by 125°. Parameters of the stepper motors are given in Table 2.

Control System
As explained in Section 2.1, the presented prototype uses an arm group instead of a single arm to achieve high tolerance and adaptability in capture task. All arms are actuated by two stepper motors to perform bending motion and stiffness regulation, respectively. The control structure is shown in Figure 4. The computer sends the desired length of driving wires 1 and 2 to a microprocessor, Arduino (Mega2560). The Arduino processor then generates corresponding electrical pulses to the motor drivers and control the linear displacement of the stepper motors, Figure 4(a). If the microswitches detect vibration on any of the arms, the stepper motor 1 will be activated to pull the driving wires 1, making all arms bend toward the center of the arm group to grasp the target. The stepper motor 2 will be activated to pull the driving wires 2 and stiffen the arms once stepper motor 1 reaches its maximum stroke, Figure 4(b).

Finite Element Model
This section establishes a finite element model (FEM) for the arm group mechanism to investigate the influence of group configuration, target size and velocity on the success rate of capture operation. The following assumptions are used in the model.
A single continuum arm can be simplified to an elastic rod whose bottom end fixed to the drive box while the tip end considered as a free end.  Step (mm) 0.003048 0.015875 Step angle (°) The material properties of the arm body are uniform, ignoring the internal structure of the arm. The finite element model is established in the ABAQUS/CAE integrated environment. As mentioned above, the continuum arm is considered to be made of single material, and the equivalent elastic modulus is determined by the experiments. A DS2-50N material Tester is used to impose a transverse load on the free end of the arm to obtain the equivalent elastic modulus [28], according to where ω is the deflection of the arm, representing the displacement of the arm along the direction of the transverse load, θ is the angle between the tangent line of the flexure and the vertical position of the arm. A and B are the integration constants whose values are determined by the boundary conditions. In the case of a cantilever beam, we assume A = B = 0. M is the bending moment generated by the transverse load applied to the arm, which can be computed as the product of the transverse load and the length of the arm. E is the equivalent elastic modulus of the arm. I is the moment of inertia of the cross section of the arm and can be computed as I = π D 4 64 , in which D is the diameter of the cross section. Through Eqs. (1) and (2), the elastic modulus of the arm can be estimated as E 1 = 3.5 × 10 2 MPa.
The continuum arm has a flexible body and its cross section is circular, so we can estimate the Poisson's ratio of the continuum arm according to the method of lateral compression test [29]. The obtained Poisson's ratio is The element type of the continuum arm is set as C3D8R in the finite element model. The size of the element is set as 3 mm, and the number of the elements is 10440. Also, friction is considered due to the surface contact between the continuum arms and the target. In our case, the materials used for the silicone sleeve and the target body are ELASTOSIL ® 4601 and Somos Imagine 8000 photosensitive resin, respectively. Thus, the static friction factor is obtained as f µ = 0.3 by performing sliding movement experiments between these two materials.
The material of the target ball is nylon whose modulus of elasticity is E 2 = 8.3 × 10 3 MPa and Poisson's ratio is µ 2 = 0.28 [30].
The output force of the linear stepper motor 2 can reach 330 N which is considered to be evenly applied to nine driving wires 2. Therefore, the tension of each driving wire 2 is set to 36 N in the finite element model.
When t = 0 s, a target ball with different diameters, d = 30, 40, 50, 60 and 70 mm, were launched to the center of the arm group with different initial speeds, v =1, 2, 3, 4 and 5 m/s, as shown in Figure 5(a). If the ball can be  We start the tests with a simple configuration that all arms are arranged in a circle, as shown in Figure 6. The Here, we define a concept of average distribution radius, R a = n i R i n to describe the density of the arm group, where R i (i=1, 2,…, 9) is the distance between the arm center to the group center. A large value of R a means average distribution radius in Figure 6(a) is R a = 90 mm while that in Figure 6(b) is R a = 60 mm . The diameter and velocity of the target ball resulting in successful captures are denoted by squares on a diameter-velocity plane. In Figure 6(a), the successful captures are mostly located from d = 50-70 mm, around the clearance of the arms C = 61.6 mm . In Figure 6(b), the range of d is between 30 mm and 60 mm, which is also near the clearance C = 41.0 mm . These indicate that the success rate can be increased by making the clearance of the arms close to the diameter of the target ball. The velocity range in Figure 6(a) between 1 m/s and 4 m/s is lower than that in Figure 6(b) between 3 m/s and 5 m/s. This is because the arms in Figure 6(a) has lower distribution density so it cannot provide sufficient resistance to stop the target ball with high velocity. In addition, the continuum arms can be divided into two sets and arranged on two concentric circles with different radius, R 1 and R 2 , as shown in Figure 7. Here, we set R 1 = 30 mm and R 2 = 60 mm . We define the incident angle θ of the target ball as the sharp angle between its velocity direction and the x axis. Three incident angles are then tested for this configuration. In Figure 7(a), if the incident angle is 0°, the target ball will firstly hit the leftmost arm. In Figure 7(b), the incident angle is 40°, and the target ball will contact with three continuum arms at the beginning of collision. When the incident angle is 90°, the target body can contact with 5 arms at the beginning of collision, Figure 7(c). As a result, there are 7, 10 and 13 successful capture points in Figure 7(a), (b) and (c), respectively. This is because the incident angle in Figure 7(c) can make more arms to contact with the target when the collision occurs.
Based on the arm group configuration shown in Figure 7(c), we reduce the average distribution radius of the arms from 50 mm to 40 mm to carry out the simulation. The results are plotted in Figure 8.  Figure 6.
From the above analysis, we can summarize the following three conclusions: 1) The success rate of the capture can be improved by setting an appropriate average distribution radius, making the clearance of the arms close to the diameter of the target ball.
2) The incident angle of the target ball has an impact on the capture performance. The incident angle which makes more arms to contact with the target ball can help to absorb the kinetic energy and improve the success rate.
3) The density of the arm group also affects the capture performance. Increasing the density of the arm group can improve the capture ability of the target body with high velocity, and vice versa.
According to the simulated results, we implement the configuration shown in Figure 8 to our prototype to achieve high success rate because the dynamic target used in the following experiments are around 42 mm in diameter and 4 m/s in velocity.

Capture of Static Objects
The grasping ability of the continuum arm group was verified firstly by grasping static objects with different sizes, shapes and stiffness. As shown in Figure 9, the capture mechanism was installed on the tip end of a KUKA robotic manipulator. Firstly, the KUKA robotic manipulator moves the capture mechanism with multiple arms to envelope the target body. Then, the linear stepper motor 1 is activated, which can simultaneously apply tension to all driving wires 1 and initiate a bending motion to all arms to grasp the object. Finally, the linear stepper motor 2 is activated, simultaneously applying tension to all driving wires 2 to stiffen the arms. Seven different irregular objects including tape, tennis ball, keys, pen, wrench, screwdriver, and scissors were tested. These objects can be successfully grasped, showing that the flexible capture mechanism inspired by sea anemone has strong adaptability to targets with various shapes and sizes.

Dynamic Capture
Three different shapes of targets, including a golf ball, an equilateral tetrahedron and a cylinder, were selected for the dynamic capture experiment. In addition, different incident angles of the target and postures of the arm group were utilized to demonstrate the capture adaptability, as shown in Table 3.
The dynamic capture experiment of a 42 mm diameter golf ball is shown in Figure 10. A spring initiated catapulting device is fabricated to launch the target. By compressing and releasing the spring in the catapulting device, the initial velocity of the target can reach 4 m/s. In Figure 10(a), The golf ball is launched to the center of the arm group at time t 0 . In this time instant, the microswitch has not yet been triggered so its output stays at a high level. Motors 1 and 2 are disabled by the high level signal, as shown in Figure 10(d). When the dynamic target hits the arm group at time t 1 = 0.04 s , Figure 10(b), the microswitch at the arm bottom detects the vibration of the arm and changes its output from high to low, Figure 10(d). Subsequently, the motor driver 1 sends pulse signal to the stepper motor 1 and activates the arm group to envelop the target. In Figure 10(c), the stepper motor 1 reaches its maximum stroke and stops at time t 2 = 0.2 s , and the motor 2 begins to work, forcing the arm group to lock the target. The arm group completely locks the target body at time t 3 = 0.31 s.
The tests were repeated 50 times, among which the golf ball was successfully captured for 45 times. The capture success rate is 90%.
We also use a 3D printed equilateral tetrahedron with side length of 40 mm to test the dynamic capture capability of irregular shape. In this test, we put the arm group upside-down as shown in Figure 11. It is found that the dynamic target can also be successfully captured, which  proves that the presented arm group mechanism has strong adaptability and robustness.
The tests were also carried out 50 times, in which 41 tests achieved successful capture. So the capture success rate is 82% in this case.
A cylinder with a diameter of 35 mm and a height of 50 mm was used as the dynamic target body as well. The launch angle of the catapulting device is changed from horizontal to 45° upward, as shown in Figure 12. In this case, 39 out of 50 tests achieved successful capture. The capture success rate is 78%.

Effects of Variable Stiffness
The tendon-driven variable stiffness mechanism makes the continuum arms achieve the combination of flexibility and load capacity. This part presents the feasibility of stiffness changes by pulling the driving wires. In our scenario, firstly, we control the linear stepper motor 1 to pull the driving wires 1 by 15 mm to envelop the target ball and apply an upward pulling force to the target, Figure 13. We use a dynamometer to record the maximum pulling force that the arm group can fight against to hold the target. The value of the maximum pulling force is defined as the locking force of the arm group, and is tested for 5 times as shown in Figure 14.
Then, the linear stepping motor 2 is activated to pull the driving wires 2 by 10 mm and therefore increases the arm stiffness. The corresponding locking force recorded by the dynamometer are also given in Figure 14.
It can be seen that, the average locking force is 7.32 N in the case of grasping with low stiffness, and will reach