Dynamic Capture Using a Traplike Soft Gripper With Stiffness Anisotropy

Dynamic capture is a common skill that humans have practiced extensively but is a challenging task for robots in which sensing, planning, and actuation must be tightly coordinated to deal with targets of diverse shapes, sizes, and velocity. In particular, the impact force may cause serious damage to a rigid gripper and even its carrier, e.g., a robotic arm. Existing soft grippers suffer from low speed and force to actively respond to capturing dynamic targets. In this article, we propose a soft gripper capable of efficient capture of dynamic targets, taking inspiration from the biological structures of multitentacled animals or plants. The presented gripper uses a cluster of tentacles to achieve an omnidirectional envelope and high tolerance to dynamic target during the capturing process. In addition, a stiffness anisotropy property is implemented to the tentacle structure to form a “trap” making it easy for the targets to enter yet difficult to escape. We also present an analytical model for the tentacle structure to describe its deformation during the collision with a target. In experiments, we construct a robotic prototype and demonstrate its ability to capture dynamic targets.


I. INTRODUCTION
A WELL-TRAINED human is able to catch dynamic targets traveling in the air or water (e.g., a baseball or a fish) through real-time coordination between eyes and muscles that allows for highly skillful moves [1]. However, this task is particularly challenging for robotic systems because accurate sensing, planning, and responding should be completed in a very short period of time [2], [3]. This article proposes a new design of bio-inspired robotic gripper to reduce these challenges.
Previous works on dynamic capture employed a rigid gripper mounted on a robotic arm tip to grasp targets [4], [5]. This method has the advantages of good repeatability and high strength. However, it needs to identify the trajectory and posture of the dynamic targets rapidly, and requires accurate actuation of the rigid gripper [6]. Such a strategy will generate enormous impact forces, which may cause targets to bounce out of the gripper before being enveloped. In addition, the huge impact may damage the robot and target [7].
During the capture process using rigid grippers, it is important to implement active control on the robotic arm and gripper to provide synchronous movement and compliance between the gripper and target. Kim et al. [8] presented a synchronous motion planning method to capture irregular dynamic targets through a machine learning algorithm. This method was later improved by Salehian et al. [9], using a linear parameter varying strategy to control the robot to reach and follow the target, and therefore exhibiting some "compliance". Furthermore, impedance control methods were utilized to absorb the impact of the dynamic target, and maintain stability during the collision [10]. In recent works, the effects of impact forces were modeled as state-dependent uncertainties, and the robust locomotion of robotic systems under uncertainties has been achieved by using adaptive artificial time delay control and improved adaptive sliding mode control [11], [12].
The aforementioned methods are highly dependent on active control algorithms that require high-performance control hardware, e.g., high-speed sensors and actuators. In recent years, the fast development of compliant or even soft mechanisms provides a new way to achieve tolerant manipulation, making use of the redundant degrees of freedom (DOF) and reducing the demand for active control [13]. Moreover, the intrinsic compliance can increase adaptability and safety of the gripper. Wang and Lan [14] presented a statically balanced gripper to provide a constant grasping force to manipulate objects of various sizes through compliant mechanisms. Odhner et al. [15] presented a compliant underactuated fingers that are capable of both firm power grasps and low-stiffness fingertip grasps. Sinatra et al. [16] designed a soft gripper for ultragentle capture of marine organisms. Tawk et al. [17] presented a 3-D printed soft gripper equipped with three fingers and a suction cup, which is able to pick and place wide variety of objects. Besides compliance, strength is also an important factor when dealing with dynamic targets with high kinetic energy, and is a main limitation of existing compliant/soft robotic grippers. Although there have been many studies on tuning stiffness for soft actuators [18], [19], the output force and response time cannot generally meet the requirements for capturing dynamic targets [20].
The key point to capturing dynamic targets is how to combine strength with flexibility to achieve fast response and high adaptability while reducing the demand for active control that may be costly and time consuming. There are some impressive cases in nature, including animals and plants [21], [22]. Sea anemone stand still under the sea and use a cluster of tentacles to capture fish moving in various directions. Drosera use multitentacles to form an arc-shaped "trap" to envelop insects. They have very limited maneuvering ability, yet they are able to capture fast moving prey, with the help of a cluster of tentacles, as shown in Fig. 1(a) and (b). This tentacle cluster-based capture mechanism does not rely on the precise control of a single tentacle, but rather on cooperation between the tentacles to intercept dynamic targets in various directions, showing excellent tolerance. As long as the prey enters the tentacle cluster, it will be retarded and eventually enveloped by the tentacles. Meanwhile, we note that some plants in nature, e.g., Mimosa [23], can fold their leaves quickly in one direction while generating considerable stiffness in the reverse direction to maintain the folded structure [24], as shown in Fig. 1(c). If this anisotropic stiffness feature can be applied to a robotic gripper for capturing dynamic targets, it will be possible to achieve soft contact with the target in one direction while maintaining a strong grasp in the opposite direction. Although this anisotropic stiffness can be achieved via active control, we believe a passive mechanism will be more suitable for dynamic capture where fast and reliable responses are required.
Another key problem is the mathematical modeling for collisions, especially in the case where soft structures are involved. Previous soft robotic grippers were usually designed to grasp static or quasi-static targets, so their mathematical model mainly focused on static situations [25]. Yang et al. [26] presented a virtual work-based static model to describe the deformation and mechanics of continuum robots with a generic rod-driven structure. Kang et al. [27] presented a dynamic model for a hyperredundant tentacle robot using parallel mechanism theory and Newton's law. However, these models did not consider the collision process, so they cannot be used to analyze the soft capture of dynamic targets.
In this article, we present a novel soft gripper with multiple tentacles and anisotropic stiffness that can capture dynamic targets. The contributions of this work include the following aspects. First, the use of a bio-inspired tentacle cluster can achieve large tolerance to the position and incident angle of the dynamic target without accurate identification of its trajectory, posture, and shape. Second, the soft bodies of the tentacles help to dissipate and absorb the kinetic energy on impact. Finally, the implementation of anisotropic stiffness in the tentacles can passively block high-speed targets, making it easy for the targets to enter, but difficult to escape the gripper. Finally, a mathematic model to describe the collision dynamics of a tentacle is established and validated experimentally. The presented soft gripper provides a new solution for capturing dynamic targets.

A. Bio-Inspired Structure Design
When examining existing robotic grippers, error tolerance and grasping force are two major limitations to capture dynamic targets. Inspired by biological structures from animals and plants, we propose the concept of a tentacle cluster to achieve high adaptability to position and orientation errors with the implementation of stiffness anisotropy to passively enhance strength without losing compliance. The presented gripper is like a trap, making it easy for dynamic targets to enter but difficult for them to escape. The gripper consists of multiple flexible tentacles fixed to a rigid base, as shown in Fig. 2.
The tentacles are distributed on a circle, forming a "trap" for the dynamic targets coming from any direction. Each tentacle is composed of an elastic layer on its ventral side and discrete limiting blocks on its dorsal side, as shown in Fig. 2(a). This structure enables the tentacle to bend in only one direction, from the dorsal to ventral side, similar to the unidirectional movement of the Mimosas leaves. The limiting blocks are fabricated with resin (Somos Ledo 6060) material with an elastic modulus of 2600 MPa through 3-D printing. These blocks are glued to the elastic layer in series with the help of the concave and convex points. The elastic layer is fabricated with polyurethane rubber with an elastic modulus of 50 MPa [28], providing the "soft" feature to the gripper [29]. The deformation will occur at the gap between those limiting blocks, which is similar to the flexural hinge in a compliant mechanism [30]. In our case, the elastic layer is 200 mm in length, 24 mm in width, and 2 mm in thickness. The tentacle will bend inward when a dynamic target hits its dorsal side (i.e., outer side of the gripper), allowing the target to enter the gripper, because the tentacle has relatively low stiffness on this side. If the dynamic target keeps moving and hits the ventral side of another tentacle, the tentacle will hold its position and prevent the target from escaping because the bending stiffness on the ventral side is relatively large. Eventually, the target will lose its momentum in the collision process, and fall into the gripper.
Based on the design concept, a prototype of the robotic soft gripper was constructed, as shown in Fig. 2(b). The soft gripper includes nine modular flexible tentacles, which are individually attached to dc worm gear motors mounted on a base. The motors allow the tentacles to actively rotate about the base. This active rotating motion has two functions: first, making the tentacles able to bend inward when facing dynamic targets with low speed; second, allowing for active control of the tentacles to grasp targets.
The control system of the soft gripper is presented in Fig. 2(c). The control center sends the task commands (such as waiting for the target, releasing the target, etc.) to the control board through a Bluetooth module. The control board takes the task commands, as well as the sensor feedback, and then generates the motor commands for the tentacles. A Hall sensor is mounted on the dc worm gear motor and used to detect the vibration of the flexible tentacle when it is hit by a dynamic target. The limit switches provide the extreme positions for each motor to ensure a safe rotation range.

B. Modeling of the Tentacle
The flexible tentacle cluster will bend inward after being impacted by the dynamic target. The deflection angle of the tentacle is an essential factor to judge whether the target can travel through the tentacle and be captured, so it is necessary to develop a mathematical model for the collision-bending process, based on the information in Fig. 3(a). Because all tentacles have identical structure, in the model, we take a pair of tentacles to analyze the dynamic relationship between the initial velocity of the target and the deflection of the tentacles.
It is assumed that the center of mass of the tentacle is located in the middle of the elastic layer and the elastic layer will bend with constant curvature [31], as shown in Fig. 3(b). The variables contained in the model are summarized in Table I. A coordinate system Oxy is attached to the base of the left tentacle, where O is the origin, x and y indicate the horizontal and vertical directions, respectively. When the target collides with the dorsal side of the left tentacle, the angular momentum conservation formula for the left tentacle/target system is where m a is the mass of the dynamic target. m b is the mass of the tentacle. p is the distance between the collision point C and  the origin O. r s is the distance between the center of mass of the tentacle A and the origin O. v a0 is the initial velocity of the dynamic target. v a0' is the velocity component of v a0 , which is perpendicular to the direction of OC. v b0 is the initial velocity of the center of mass of the tentacle. v b0' is the velocity component of v b0 , which is perpendicular to the direction of OA.
The component velocities of the left tentacle and the dynamic target are obtained by applying Newton's hypothesis of kinematic restitution, which specifies the ratio of pre-and postimpact velocities as [32] So, the component velocities of the dynamic target and the center of mass of the left tentacle after a collision are where Here, r b is the total length of the tentacle. Then, the resultant velocities of the dynamic target and the center of mass of the tentacle are After collision, the left tentacle will bend inward. At this stage, as shown in Fig. 3(b), assuming the end deflection angle is θ, the kinetic energy of the tentacle is The potential energy of the tentacle is where E v I v is the flexural stiffness of the elastic layer on the ventral side of the tentacle. During the bending deformation, the left tentacle has internal damping that dissipates the impact energy. Assuming the damping coefficient is c, the generalized damping force is Substituting (7), (8), and (9) into Lagranges equation yields d dt The dynamic equation of the tentacle is then obtained as The position of the center of mass of the left tentacle can be obtained as When the target travels through the left tentacle and collides with the right one, the limiting blocks on the right tentacle are squeezed. Because the limiting blocks have high elastic modulus, the deflection of the right tentacle in the outward direction is small. In this collision process, the target will be decelerated rapidly and fall into the gripper, as shown in Fig. 3(b). Assuming that the target hits a cantilever beam (the right tentacle) and is stopped, the collision dynamics of the right tentacle/target system can be obtained as where v a" is the velocity component of the initial velocity v a of the target, x 1 is the displacement of target during the collision with the right tentacle, and x 2 is the displacement of the tentacle tip during the collision. The impact force acting on the tentacle is where k is the equivalent contact stiffness of the tentacle at the collision point D where E d I d is the flexural stiffness of the limiting blocks on the dorsal side of the tentacle, and l is the distance between the collision point D and the tentacle base B. As already mentioned, the deflection angle of the left tentacle is a key factor for the target to get into the gripper. The deflection angle θ of the left tentacle during the collision process can be obtained by solving (1) to (13) numerically. The parameters used for the collision simulation are listed in Table II, where the ball has a mass of 50g, radius of 10 mm, and an initial velocity of 1.5 m/s. It hits the tentacle horizontally with a height H = 120 mm from the base at time instant 0.02 s. Fig. 4 shows the maximum deflection angle (the vertex of the curve, denoted by a " " symbol) of the tentacle decreases from 174.5°t o 112.6°when the elastic modulus of the elastic layer gradually increases from E v = 30 MPa to E v = 90 MPa. According to the Euler-Bernoulli beam theory, the elastic modulus of the elastic layer ≥ 30 MPa is enough to ensure that the whole tentacle can maintain its initial position without buckling due to its self-weight in our case. However, the elastic modulus should not be too large in case the dynamic target cannot pass the tentacle and enter into the gripper after collision. For these reasons, we eventually selected a polyurethane rubber material with an elastic modulus of 50 MPa for the elastic layer of the tentacle. The deceleration effect of the right tentacle is also important for the gripper to stop the target. The deceleration process can be obtained by solving (14) to (16) numerically. Fig. 5 shows the time required to reduce the velocity component of the target v a" when the elastic modulus of the limiting blocks increases from E d = 0.5 GPa to E d = 3 GPa. A low-cost resin (E d = 2600 MPa), commonly used in 3-D printing machine, was selected to fabricate the limiting blocks in our prototype.
A successful capture means the target travels through the left tentacle and then is blocked by the right tentacle. We next investigated how the mass and initial velocity of the dynamic target would affect the success rate of the capture via simulation. Fig. 6 shows that only if the values of the mass and initial velocity of the dynamic target are within the region on the right side of the dotted line, can the target bend the tentacle enough to travel  through and be successfully captured by the soft gripper. A video is also attached to demonstrate this process. The color change from dark blue to red indicates the maximum deflection angle of the tentacle after collision increases from 60°to 240°. It is found that, in the region of success capture (the right side of the dotted line), the tentacle will bend with a maximum deflection angle greater than 120°. The aforementioned results are obtained by considering only the passive deflection of the tentacle after a collision. If active control of the tentacle is provided with the help of the dc motors, the requirements for the target mass or initial velocity can be further reduced.

III. RESULTS
In this section, a series of experiments carried out to assess the performance of the proposed soft gripper are reported. First, the stiffness anisotropy of a single tentacle is demonstrated. Then, a catapult constructed to adjust the launch angle and velocity of the target is described. Throughout the experiments, a high-speed camera was used to record the capturing process. From this, the velocity of the target and deflection angle of the tentacle could be obtained by mapping the image plane to the work plane. In addition, a series of grasping tests were carried out to show that the presented gripper is also able to actively capture static objects with different shapes and masses.

A. Implementation of the Stiffness Anisotropy
An experimental setup to measure the stiffness anisotropy of the tentacle is shown in Fig. 7. The tentacle was fixed to a frame at one end, such as a cantilever beam. The stiffness of the tentacle was characterized as k = F / ΔL, where F is the loading force in the vertical direction and ΔL is the deflection at the free end. Under an identical loading force F = 2 N, the negative deflection ΔL 1 was 3 mm while the positive deflection ΔL 2 was 96 mm. The force-deflection curves for both ventral and dorsal sides are shown in Fig. 7. The stiffness on the ventral side is 34 times greater than that on the dorsal side, which quantifies the anisotropic stiffness in the presented tentacle structure.

B. Deflection of a Single Tentacle Under Impact
To verify the dynamic model of the flexible tentacle presented in Fig. 4, a golf ball with a mass of 45g was used as a target. The velocity of the target was increased from 0.3 to 3 m/s in the tests, denoted by the "×" symbols in Fig. 6. The maximum deflection angle of the tentacle obtained from simulations and experiments is compared in Fig. 6. There is some gap between the simulated and experimental results due to the assumptions in the model of the tentacle (e.g., the location of the center of mass and the uniform curvature). In these tests, the bottom of the tentacle cannot actively rotate inward. The minimum velocity for the golf ball to travel through the tentacle was 1.5 m/s and the corresponding maximum deflection angle of the tentacle was 125°. These results also agree with the theoretical results in Fig. 8. Fig. 8. Simulations and experimental results on the dynamic collision for a single tentacle. The ball will successfully bend the tentacle enough so it will travel through the tentacle when its initial velocity ≥ 1.5 m/s and the corresponding maximum deflection angle is 125°.   . 9(a) shows that a failure test, denoted by the (•) symbol in Fig. 6, which is obtained by only using the passive deflection of the tentacle. A baseball (55g) bounced out of the tentacle because it did not have enough initial velocity. To deal with targets of relatively low velocity, the rotating control for the dc motors at the tentacle bases was utilized. Then, the tentacles could bend inward actively and the baseball successfully fell into the gripper, as shown in Fig. 9(b). Such an active rotating strategy can further extend the allowable range of the initial velocity for the targets. A video showing the reduced initial velocity is attached with this article for reference.

C. Capture of Targets With Different Incident Angles and Velocities
The next experiment aimed to verify the omnidirectional capture capability of the soft gripper for dynamic targets with different velocities. A coordinate system O 1x 1 y 1 was attached to the center of the base of the tentacle cluster, where O 1 is the origin, and x 1 and y 1 indicate the horizontal and vertical direction, respectively. A cubic box (100g and 100 mm) was launched into the soft gripper in a low horizontal direction (the vertical distance from the coordinate origin O 1 was 130 mm) with velocity v 1 = 1.5 m/s, a high horizontal direction (the vertical distance from the coordinate origin O 1 was 180 mm) with velocity v 2 = 2 m/s, a diagonally downward direction (incident angle 45°) with velocity v 3 = 1.5 m/s, and a vertical direction with velocity v 4 = 1.5 m/s, as shown in Fig. 10(a) (1)- (4). As expected, the box falls into the "trap" in all tests. A video showing these capturing operations is attached with this article for reference.
The soft gripper thus allows for a wide range of incident angle and velocity to capture the dynamic target, which means there is no need for accurate control for the position and orientation of the gripper. To quantify how the incident angle and velocity of the target affect the capture success rate, we executed the following experiment for a target ball with ten incident angles (ranging from 0°to 90°with increments of 10°) and four initial velocities (1, 2, 3, and 4 m/s,). For each combination of incident angle and initial velocity, the test was repeated for 20 times. The number of successful captures is recorded, and the success rate is presented in Fig. 10(b).
The experimental results show that the capture success rate was 90% or higher when the incident angle was from 0°to 50°a nd the velocity over 2 m/s. However, the capture success rate of the soft gripper dramatically decreased as the incident angle increased from 50°to 90°[see Fig. 10(b)]. The main reason was that the maximum deflection angle of the tentacles was not sufficient for the target to successfully run into the interior of the soft gripper. In summary, the results demonstrate the optimal conditions for the soft gripper to capture dynamic targets, which is 0°to 50°for the incident angle, and more than 2 m/s for the target velocity.

D. Coordination With a Robotic Arm
The performance of the proposed soft gripper was evaluated on a 7-DOF robotic arm, KUKA LBR IIWA. As depicted in Fig. 11(a), the target was thrown by a catapult, allowing its flight trajectory to be calculated. In this experiment, the interception position on the trajectory is specified artificially. In practical applications, the trajectory and interception position can be obtained by autonomous devices, but there is no need for accurate calculation and control of them with the help of the presented gripper. The KUKA arm only needs to approximately move the gripper to the interception position, facing to the dynamic target, as shown in Fig. 11(b) (1)(2)(3)(4)(5)(6)(7)(8). A video is also attached to demonstrate the capture process.
The positioning tolerance of the soft gripper is evaluated as the area where the gripper can be placed to capture the target. As shown in Fig. 11(a) and (b), a Cartesian coordinate system O'x'y'z' was attached to the desired interception point O' on the flight trajectory of the target. The z' axis was tangent to the flight trajectory. The throw tests for a cube (10 mm in side length) were repeated 169 times with the same initial velocity (2 m/s) and launch angle (45°). The KUKA arm placed the gripper onto the x'-O'-y' plane, with a constant incident angle of 20°t o the z'-axis. However, the position of the gripper in these tests was distributed within a circle about the interception point O' (i.e., the origin of the coordinates), as shown in Fig. 11(c). The red crosses "×" indicate a successful capture, whereas the blue circles "•" represent failures. It can be seen that the successful capture points are basically distributed within a circle of 150 mm in radius. We divided the circle to three concentric parts with interval distance of 50 mm. The success rate for each part is shown in Fig. 11(d). The higher capture success rate is achieved when the gripper is closer to the desired interception position. Even if the gripper deviated from the desired interception position by 100-150 mm, the success rate is still 66%. This demonstrates the presented gripper has a high tolerance to the positioning error, which can reduce the complexity of active control.

E. Grasping of Static Target
As mentioned before, the gripper is able to actively rotate its tentacles. So, it can grasp targets moving at very low speed as well as static ones. In another experiment, the adaptability of the soft gripper was confirmed by grasping various static targets with different shapes, sizes, and weights. As shown in Fig. 12, the gripper opened its tentacles and moved above the targets. Then, the gripper closed the tentacles to envelop and grasp the targets, such as a ball or another robot. We also show that the soft gripper is able to grasp some special structure on a target much larger than the gripper itself (e.g., grasp the thrust nozzle on a satellite). Release operations are achieved by reopening the tentacles. A video showing the grasping operations is attached with this article for reference.

IV. CONCLUSION
This article presents a novel bio-inspired soft robotic gripper capture mechanism using a tentacle cluster configuration featuring anisotropic stiffness structure for each tentacle.
Due to the unique mechanical design, the presented gripper does not require precise prediction of the target trajectory, nor precise position and orientation control of itself. It is able to capture targets with a large tolerance to their shapes, sizes, incident directions (0°to 50°), velocities (over 2 m/s), and positions (achieving 90% success rate even if the actual interception position deviates from the desired one by 100 mm). The use of rotating base motors to each tentacle further improves the capability of capturing low speed as well as static targets.
An analytical model for the tentacle structure is established to describe its bending deformation during the collision. The simulated results generally match the experimental results, which verifies the efficacy of the dynamic model of the tentacles.
The proposed methods pave a new way to design and analyze soft robots for use in collection or removal of dynamic targets in unconstructed environments. Future work will expand the single tentacle analytical model into a multitentacle model and implement the gripper/arm system on a moving vehicle to increase the maneuverability of the system. Shangkui Yang received the B.S. degree in