A Ball-Jointed Tendon-Driven Continuum Robot with Multi-Directional Operability for Grasping Objects

doi:10.21203/rs.3.rs-3565502/v1

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A Ball-Jointed Tendon-Driven Continuum Robot with Multi-Directional Operability for Grasping Objects

https://doi.org/10.21203/rs.3.rs-3565502/v1

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Journal Publication

published 26 Mar, 2024

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A continuum robot, inspired by biological features, flexibly bends its body and conform to various shapes. The high compliance and low stiffness, however, causes low rigidity and ambiguity in control when it is applied to grasping and manipulating an object. In this study, we develop a ball-jointed tendon-driven continuum robot that can bend to arbitrary directions for manipulating and grasping an object. Discs are connected by ball joints, together with coil springs coupled with tendon threads, and form a backbone of the robotic body. The continuum robot is operated to bend to an arbitrary direction by pulling the tendons using three servomotors, and returns to the original straight shape by releasing the pulling force of the contracted coil springs. The robot is constructed by using 3D-printed parts. In the experiment, the manipulator's grasping performance was demonstrated by preparing five objects that have various shapes, sizes and softness. The robot successfully grasped all the objects by wrapping around them, adapting its shape to the object's shapes. Furthermore, the ability of the multi-directional operation was tested by bending the continuum body to specific directions, and then performing arc-following motion. The experiments verified the satisfactory operability of the continuum robot.

Continuum robot

Tendon driven robot

Grasping manipulation

Conventional robots with rigid links and joints are typically used in industry, and they can move quickly and accurately[1]. However, these rigid structures can be dangerous in human-interactive environments. Unlike these robots, continuum robots are usually made entirely of soft materials and are mainly inspired by biological features such as an elephant trunk and an octopus [2, 3], and they can bend (and sometimes stretch and twist) at any point along the body structure [4]. Thus, the high compliance of a continuum robot can improve the safety concerns. Also, since continuum robots can be actuated to conform to various shapes, robots are used for multiple tasks, such as rescuing in collapsed buildings [5] and minimally invasive surgery [6, 7].

Various actuating methods for continuum robots have been developed, including pneumatic actuation [8, 9] and actuation by shape memory effect [10]. One of the most common actuation methods is to use tendon structure, in which several tendons are routed along the flexible backbone of the robot, and the bending motion is achieved by pulling the tendons [11–13]. Compared to other actuations, tendon actuation is more compact in size and capable of large motion.

One of the advantages of continuum robots is the ability to grasp objects with the entire arm, called “whole arm grasping” [14]. The conventional manipulators which operate objects by its end effector can operate only relatively light objects. On the other hand, the whole arm grasping distributes the contact points between the robot and the object, thus it reduces the actuation power and improves the ability to manipulate heavy objects [15]. Furthermore, since there is no restriction by the end effector, objects of various sizes can be grasped [14].

However, when applying continuum robots with soft body to grasping, their high compliance and relatively low structural stiffness may cause a problem: soft materials have limited stiffness, so small interaction forces generate significant deformation of the robot itself [16].

To combine both soft and rigid components is one solution to this problem. Several robots driven by the tendon have been proposed [16, 17]. Although these robots successfully grasp objects having various shapes and sizes, the direction of motion is limited, and the free motion like actual living creatures has not been achieved.

By considering a flexible joint with high rigidity having no restrictions on the direction of motion, we introduce a ball joint that has been used in robots mimicking the tail of seahorses [16, 18]. In this study, by using balls for joints, we develop a tendon-driven continuum robot manipulator that can achieve flexible movement to bend arbitrary directions for grasping objects by wrapping around. The grasping performance and the operability of the robot are experimentally verified.

Robot design

The schematic structure and the operation of the tendon-driven continuum robot constructed in this study are illustrated in Fig. 1. In order to achieve flexible motion in all directions and to have the rigidity required to grasp different objects, we employ balls for the connection between the discs. Eight discs and seven balls are connected to each other, and an operon rubber string is threaded inside the balls to connect them. The discs are also connected to each other by compressed coil springs, and threads are penetrated inside the springs to work as tendons.

From the initial state (Fig. 1(a)), by pulling the threads toward the base using servo motors, the robot bends its body (Fig. 1(b)). Then, by releasing the pulling force, the restoring force of the contracted springs returns the manipulator to its initial state (Fig. 1(c)).

In consideration of the dimensions of the parts, the shape of the bent manipulator is illustrated by Fig. 2: if the maximum angle at which one joint can bend is $2\theta$, the diameter of the hole in the disc $\varphi$ can be expressed as

$$\begin{array}{c}\varphi =2{r}_{ball}\text{sin}\theta \#\left(1\right)\end{array}$$

where ${r}_{ball}$ is the radius of the ball.

Assuming that each point in the entire manipulator bends at an equal angle, the entire manipulator takes the form of an arc, as shown in Fig. 2(c). Then, the distance between balls $d$ can be expressed as

$$\begin{array}{c}d=2R\text{sin}\theta \#\left(2\right)\end{array}$$

where $R$ is the radius of the arc.

When$\varphi$=15mm,${r}_{ball}$=10mm, and $d=35$mm, the radius of the arc formed by the manipulator is calculated as $R=23.33$mm, which means that the radius of the disc should be about 20mm to be able to wrap around a small object.

Robot fabrication

The dimensions of the parts are determined to satisfy the above requirements, and the disc is designed as shown in Fig. 3. The large hole in the disc center shown in Fig. 3(a) is fabricated so that the rubber string is threaded inside the balls to connect the robotic body from the base to the tip. Three holes for tendons are settled at every 120 degrees so that the bending angles in arbitrary directions are controlled by pulling tendons from three directions.

A 3D printer (CR-10 Smart, CREALITY) is used to fabricate the discs using the PLA (Polylactic acid) material. The wooden-made balls with the diameter of 20mm are employed. The properties of the coil spring are shown in Table 1. The appearance of the completed manipulator is shown in Fig. 4. The total length and weight of the manipulator were 270 mm and 80 g, respectively.

Table 1

Properties of springs
Material	Height (mm)	Diameter ($\varphi$)	Spring constant (N/mm)
SUS304WPB	30	5	0.078

Next, the force required to wind the manipulator was measured in order to select motors to pull the tendons. Using a spring scale, the force required to wind the manipulator was determined to be approximately 0.52 kgf. We set the radius of the spindle, which is attached to the motor axis where the tendons are wrapped, is set at 5cm, so the required torque is $0.52\times 0.5=0.26$ [kg$\cdot$cm]. A 360° continuous rotation servo motor SG90-HV is employed, and the characteristics of this motor are shown in Table 2.

Table 2

Characteristics of the motor, SG90-HV
Weight (g)	Dimension (mm)	Stall torque (kg$\cdot$cm)
9	$23\times 12.5\times 22$	1.3(4.8V), 1.5(6V)

Referring to the dimensions of the motors, we design a stand to fix three motors, and fabricate it using the 3D printer. Each motor is controlled by Arduino UNO. The overall appearance of the robot is shown in Fig. 5.

Control program

The bending operations are executed by changing the length of tendons driven by the servo motors. The control program needs to calculate the amount of rotation of each motor according to the direction of bending. Assuming that the curvature of the manipulator is constant, the model of bent manipulator is defined as shown in Fig. 6.

We also assume that the backbone is constant with the length ${L}_{0}$, and the length of a tendon $L$ can be expressed as follows:

$$\begin{array}{c}{L}_{0}=\alpha {r}_{0}\#\left(3\right)\end{array}$$

$$\begin{array}{c}L=\alpha \left({r}_{0}+{\Delta }r\right)\#\left(4\right)\end{array}$$

where the radius of the arc is ${r}_{0}$, the center angle of the arc is $\alpha$, and the distance between the tendon and the backbone is ${\Delta }r$.

Therefore, the increase in the length of the tendon ${\Delta }L$ is then

$\begin{array}{c}\varDelta L=L-{L}_{0}\#\left(5\right)\end{array}$ $\begin{array}{c} =\alpha \varDelta r\#\left(6\right)\end{array}$

Next, by ignoring the diameter of the hole through which the tendon passes, a model of the positions of the tendons is defined as shown in Fig. 7. Three tendons in Fig. 7 are named Tendon 1, Tendon 2, and Tendon 3, respectively. We denote ${\Delta }r$ for each tendon as ${\Delta }{r}_{1}$, ${\Delta }{r}_{2}$, and ${\Delta }{r}_{3}$, which can be calculated by the following equation:

$$\begin{array}{c}\varDelta r=\left(\begin{array}{c}{\Delta }{r}_{1}\\ {\Delta }{r}_{2}\\ {\Delta }{r}_{3}\end{array}\right)=-d\left(\begin{array}{c}\text{cos}\theta \\ \text{cos}\left(\theta +\frac{2}{3}\pi \right)\\ \text{cos}\left(\theta +\frac{4}{3}\pi \right)\end{array}\right)\#\left(7\right)\end{array}$$

where $d$ is the distance between the backbone and a tendon, $\theta$ is the angle between the direction of motion and the direction of tendon 1.

From the equations (6) and (7), we obtain the relationship between the direction of bending and the amount of change in tendon length. Based on the calculations, the robot can bend to a specific direction by pulling the threads to the required lengths.

Grasping demonstration

To demonstrate the grasping performance of our manipulator, we prepared five objects shown in Table 3. Each object has a different shape and size.

The robot was fixed at the edge of a table as shown in Fig. 8. The manipulator grasped these objects by wrapping around them, held them for three seconds, and released them.

Table 3

Grasped objects
Object	Shape	Size (mm)	Weight (g)
Ball of yarn	Cylinder	${\upvarphi }$65	35
Reel	Cylinder	${\upvarphi }$33	190
Rubik's cube	Cube	$50\times 50\times 50$	67
Card case	Rectangular	$18\times 65\times 90$	100
Cushion	Rectangular	$300\times 220\times 80$	150

As shown in Fig. 9, all the objects were successfully grasped. The manipulator grasped the ball of yarn and the reel, which were shaped like a cylinder, by wrapping around their round bodies (Fig. 9(a) and (b)). When the manipulator grasped the Rubik’s cube by wrapping, it adjusted its shape to the object’s square shape (Fig. 9(c)). The card case was grasped by pinching it using two points of the manipulator (Fig. 9(d)). Lastly, the manipulator adjusted to the soft cushion’s flexible shape for firm grasping (Fig. 9(e)). It was confirmed that the objects having different shapes and sizes could be successfully grasped by wrapping around them.

Multi-directional operation

Next, the operability to bend to arbitrary directions was examined. We conducted experiments in which our manipulator was moved in various directions.

The manipulator was fixed as shown in Fig. 8, and was bent to the specified angles: $30^\circ$, $60^\circ$, $90^\circ$, $120^\circ$, and $180^\circ$. For each performance, the actual angle was measured three times.

The angle measurements were done as shown in Fig. 10. The measured angles and the average value at each angle are listed in Table 4.

Table 4

Measured angles and average
Target angle ($^\circ$)	Measured angles ($^\circ$)
Target angle ($^\circ$)	First	Second	Third	Average
30	19.4	19.5	19.4	19.4
60	64.3	64.8	69.0	66.0
90	105.6	118.5	110.6	111.6
120	125.5	119.5	123.9	123.0
180	187.6	184.2	182.7	184.8

In addition, we demonstrated to move the tip of the manipulator along an arc. First, the tip was moved about 80 mm in the radial direction from the initial position, and then the angle of the arc was changed by 20° to the direction of 180°.

The result of arc-following motion is displayed in Fig. 11. The red line in Fig. 11 represents the trajectory of the tip.

Although there was some misalignment, it was verified that the trajectory operated in accordance with the target trajectory.

Our manipulator succeeded in grasping objects up to 190g, which is about 2.4 times the weight of the manipulator itself. This capability is highly dependent on the torque of the used servo motor, so strong motors would make it possible to grasp heavier objects.

Since the manipulator has redundant structure and the robot model (Figs. 6 and 7) is simplified based on several assumptions, it is not suitable for precise control or positional control. Since the design concept of this robot was to combine grasping and omni-directional motion, the experimental results confirmed that these requirements were satisfied.

We designed and constructed a tendon-driven continuum robot manipulator with ball joints to achieve the articulation to arbitrary directions and also to grasp objects with different shapes and weights. The robot is bent by winding the tendons with connected servo motors, and returns to the straightened state by the restoring force of contracted springs settled between the discs. Using this robot, the experiments were conducted to confirm the grasping performance and the operability to arbitrary directions. As a result, the robot successfully grasped objects having different shapes and sizes, and also moved to arbitrary directions.

We will further develop the continuum robot to achieve complex movements that closely resemble those of actual living creatures and grasp various objects based on these movements. Further complex motions can be realized by making the robot composed of multiple sections. In addition, by introducing machine learning and developing a system that grasps objects in appropriate motion based on visual information, it will be possible to grasp a variety of objects in different environments.

Availability of data and materials

All data generated or analyzed during this study are included in this published article.

Funding

This work is partially supported by JSPS KAKENHI Grant-in-Aid for Scientific Research (B) 20H04214

Authors' contributions

All authors proposed the concept of the robot. RO designed and developed the robot. RO performed the experiments. All authors performed data analysis. All authors read and approved the final manuscript.

Acknowledgements

Not applicable.

Competing interests

The authors declare that they have no competing interests.

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No competing interests reported.

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Journal Publication

published 26 Mar, 2024

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Editorial decision: Revision requested
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You are reading this latest preprint version

A Ball-Jointed Tendon-Driven Continuum Robot with Multi-Directional Operability for Grasping Objects

Status:

Journal Publication

Version 1

Abstract

Figures

Introduction

Methods

Robot design

Robot fabrication

Control program

Experiment and Results

Grasping demonstration

Multi-directional operation

Discussion

Conclusions

Declarations

References

Additional Declarations

Status:

Journal Publication

Version 1

Object	Shape	Size (mm)	Weight (g)
Ball of yarn	Cylinder	\({\upvarphi }\)65	35
Reel	Cylinder	\({\upvarphi }\)33	190
Rubik's cube	Cube	\(50\times 50\times 50\)	67
Card case	Rectangular	\(18\times 65\times 90\)	100
Cushion	Rectangular	\(300\times 220\times 80\)	150

Target angle (\(^\circ\))	Measured angles (\(^\circ\))
Target angle (\(^\circ\))	First	Second	Third	Average
30	19.4	19.5	19.4	19.4
60	64.3	64.8	69.0	66.0
90	105.6	118.5	110.6	111.6
120	125.5	119.5	123.9	123.0
180	187.6	184.2	182.7	184.8