Abstract
Introduction
Mobile robots are always autonomous and capable of navigating an uncontrolled environment without physical or electromechanical guidance devices. Catching object has always been a difficult task for mobile robots, 1 –3 especially for robot competition. This research aims to build an image model method, which can be used to analyze an effective and easy-to-build gripper for mobile robots to search for objects and catch them. The gripper is formed by an integrated easy-to-build structure, which includes just rock link and ground link. The Rocker–Finger gripper can be droved by controllable motor. The choices of arms or grippers decide whether to catch object, but this choice is usually based on the experience of competitors. Based on the experience, it needs a lot of time, but it is not always possible to choose the right arms or grippers. 4 –6 The purpose and significance of this research is to solve this problem of arms or grippers choice, and this research is able to identify the performance of the choice arms and grippers. There are three types of performance identification methods in the research field. First is the mathematical model, second is the image model, and last is the mock-up. In the field of identifying performance for arm or gripper, mathematical model is the most common one used by a researcher, followed by mock-up, and finally the image model. 7 –13 Mathematical models can quickly analyze the performance of arms or grippers, but it can be too different from real performance. The mock-up can analyze the real performance of the arms or the grippers, but it takes a lot of time and money. And the image model method is somewhere in between. In this research, the image model method was used to analyze the performance of the grippers.
For parameters of the optimization, there are size parameters of gripper and the geometrical dimensions of the objects. 9,14 –16 So first of all, this research analyzed the performance of the gripper by isocline image model analysis, followed by adjusting the geometry of grippers and objects, then analyzing the geometry of adjusted gripper and object again, and finally optimizing the performance of the grippers.
Materials and methods
Figure 1 shows the preparation of this research: first, select testing gripper; second, decide testing boundary; third, select testing object; forth, test and mark; fifth, identifying points or areas that are easy to catch; sixth, determine whether the boundary has been found; seventh, inward offset this boundary to find the optimal catching point or areas; and finally, adjust the gripper to the best, according to result.

Flow chart.
Select testing gripper
This research selects Rocker–Finger gripper to test, as shown in Figure 2, and then fix it on mobile robot to catch object, as shown in Figure 3. There are seven factors for this gripper. This gripper’s factors and object’s factors will affect each other, so there is a best ratio between them. The factors of Rocker–Finger gripper are

Rocker–Finger gripper.

Testing process.

The factors of Rocker–Finger gripper.
Decide testing boundary
The testing boundary can be determined by the researchers. The boundary of this research is shown in Figure 5. The range is 10,000 mm2 (100 × 100 mm2) and the sampling rate is 1 point/10 mm. The testing boundary’s origin position is 70 mm above the Rocker–Finger’s origin.

Boundary of scatter diagram.
Select testing objects
The testing object can be determined by the researchers. For researchers, they can choose cubes, cylinders, or any shape. In this research, the grasping objects are cubes, and their edge line (

The factors of grasping objects.
Testing and mark
After selecting gripper, objects, and testing boundary, the research can start for their test. The way is moving the gripper to the point where you want to catch object, and researchers start testing at this location. If this testing point of gripper can catch the object, it can be marked as

The marks for catch or no catch.
Identifying points or areas that are easy to catch
It is like a target. Sampling range is the range where we can shoot for this target, and catch range is the range where we can get point for this target. So the performance is the ratio of catch range to sampling range, as shown below
In order to find the best catch points or areas, the researchers can offset catch range. And then researchers can obtain level 1, level 2, level 3, and so on. If the level range is smaller, it means that the best catch points or areas have been found, as shown in Figure 8.

Inward offset.
Results
This research shows how to use the isocline method to analyze performance and adjust the Rocker–Finger gripper. This research presented below a set of control group and 14 experimental groups.
Control group
Factors
The control group factors, as shown in Figure 9, are as follows:

The factors of control group.
Performance
Control group’s performance is 31–56.5% for catching these grasping objects in the sampling range, as shown in Figure 10.

The performance of control group. (a) 20 mm; (b) 25 mm; (c) 30 mm; (d) 35 mm; and (e) 40 mm.
Different levels of comparison
For control group’s different levels of comparison, researchers compared three levels. After this comparison, researchers will be able to identify the size of the object that is suitable for control group. Control group’s three levels are presented in Table 1 and shown in Figure 11.
Levels comparison of control group.

Different levels of control group. (a) 20 mm; (b) 25 mm; (c) 30 mm; (d) 35 mm; and (e) 40 mm.
Small L 1
Factors
For small

Small
Performance
Small

Performance of small
Different levels of comparison
For small
Levels comparison of small

Different levels of small
Long L 1
Factors
For long

Long
Performance
Long

Long
Different levels of comparison
Levels comparison of long

Different levels of long
Small L 2
Factors
For small

Small
Performance
Small

Small
Different levels of comparison
For small
Levels comparison of small

Different levels of small
Long L 2
Factors
For long

Long
Performance
Long

Large
Different levels of comparison
For large
Levels comparison of large

Different levels of long
Small L 3
Factors
For small

Small
Performance
Small

Small
Different levels of comparison
For small
Levels comparison of small

Different levels of small
Long L 3
Factors
For long

Long
Performance
Long

Long
Different levels of comparison
For long
Levels comparison of long

Different levels of long
Small L 4
Factors
For small

Small
Performance
Small

Small
Different levels of comparison
For small
Levels comparison of small

Different levels of small
Long L 4
Factors
For long

Long
Performance
Long

Long
Different levels of comparison
For long
Levels comparison of long

Different levels of long
Small L 5
Factors
For small

Small
Performance
Small

Small
Different levels of comparison
For small
Levels comparison of small

Different levels of small
Long L 5
Factors
For long

Long
Performance
Long

Long
Different levels of comparison
For long
Levels comparison of long

Different levels of long
Small θ1
Factors
For small

Small
Performance
Small

Small
Different levels of comparison
For small
Levels comparison of small

Different levels of small
Large θ1
Factors
For large

Large
Performance
Large

Large
Different levels of comparison
For large
Levels comparison of large

Different levels of large
Small θ 2
Factors
For small

Small
Performance
Small

Small
Different levels of comparison
For small
Levels comparison of small

Different levels of small
Large θ2
Factors
For large

Large
Performance
Large

Large
Different levels of comparison
For large
Levels comparison of large

Different levels of large
Discussion and conclusions
In this research, the image model method was successfully used to analyze the performance of an effective and easy-to-build grippers in mobile robots to search for objects and catch them.
This method can identify the exact boundary of catch. Isocline of level 1 shows that long
This method has filtering characteristics. Isocline of level shows that isocline has a filtering characteristic that helps the user find the suitable factor. The closer the boundary area is to zero, the closer it is to the best catch ranges.
This method can find the best catch point or range. Isocline of level shows that the isocline can be filtered continuously to explore the best catch ranges until the boundary area is zero. This means that the method will surely find the best point to catch.
For this gripper, adjustment to increase
The gripper is formed by an integrated easy-to-build structure, which includes just Rocker–Finger and Fixed–Finger grippers. In warehouses, an innovative gripper technique can be installed for a mobile robotic to efficiently move and gather materials from floor to specified zones. The materials are like cube goods (e.g. box, stone, bricks, plastic, metal blocks, and wood blocks).
In order to reduce the time and money for building and manufacturing a gripper for a mobile robot to catch objects, this research implements gripper technique to reduce the error of catching the object, and competitors can win a mobile robot competition.
This research can be used for improving sweeping capability of road and street sweepers, which can more ideally remove debris from the gutter and roadsides that would otherwise go into storm drains, causing water pollution.
The next generation of an effective and easy-to-build structure gripper for mobile robots will be upgraded for not only better kinematics capabilities but also much better dynamics performances, which will be revealed in the future.

Performance comparison.
