# Extremely modular Arm-Z manipulator

Ela Zawidzka, Yuki Chikahiro, Ichiro Ario

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Ela Zawidzka, Yuki Chikahiro, Ichiro Ario. Extremely modular Arm-Z manipulator. Japan Society of Civil Engineers 2023 Annual Meeting, Japan Society of Civil Engineers, Sep 2023, Hiroshima, Japan. hal-04970495

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Submitted on 4 Mar 2025

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[I-13] Extremely modular Arm-Z manipulator
Extremely modular Arm-Z manipulator

Zawidzka Ela²、*近広 雄希¹、有尾 一郎³ (1. 信州大学、2. ポーランド科学アカデミー、3. 広島大学大学院)

Ela Zawidzka², *Yuki Chikahiro¹, Ichiro Ario³ (1. Shinshu Univ., 2. IPPT PAN, 3. Hiroshima Univ.)

キーワード：Hiper-redundant manipulator、Robustness、Snakebot、Bionic trunk、Extremely modular
Hiper-redundant manipulator, Robustness, Snakebot, Bionic trunk, Extremely modular

Various snake-like robots have been built; most of the designs were intended for crawling on ground, some of them for swimming, and even fewer for both swimming and crawling on the ground. The main disadvantage of such robots is the difficulty of control due to their high non-linearity.

Biological snakes are extremely well adapted for different environments. This is mostly the result of the high redundancy of the snake mechanisms. In many instances of irregular environments the bio-inspired robots outperform conventional wheeled, legged or tracked robots. Snakeresembling robots are researched already for a few decades. In late 90's, a trunk-like locomotors and manipulators have been introduced in. Various snake-like robots have been built; most of the designs were intended for crawling on ground, some of them for swimming, and even fewer for both swimming and crawling on the ground. The main disadvantage of such robots is the difficulty of control due to their high non-linearity.
# Extremely modular Arm-Z manipulator

IPPT PAN,
Shinsyu Univ.
Hiroshima Univ.

Poland
Member
Member

○ Ela Zawidzka,
Yuki Chikahiro,
Ichiro Ario

## 1. Introduction

Biological snakes are extremely well adapted for different environments. This is mostly the result of the high redundancy of the snake mechanisms. In many instances of irregular environments the bio-inspired robots outperform conventional wheeled, legged or tracked robots. Snake-resembling robots are researched already for a few decades. This type of locomotion has been studied already in the 1940s ²), and a half century later, its rigorous mathematical model has been developed. In late 90's, a trunk-like locomotors and manipulators have been introduced in ³). Various snake-like robots have been built ⁴); most of the designs were intended for crawling on ground ¹), some of them for swimming ⁵), and even fewer for both swimming and crawling on the ground ⁹). The main disadvantage of such robots is the difficulty of control due to their high non-linearity

## 2. Discrete planar Arm-Z

A concept of an extremely modular planar manipulator composed of a single type of module was presented in ¹⁰). In order to make it as simple conceptually as possible, the relative states have been discretized to only two possible positions: $-\frac{\pi}{6}$ (left, encoded as 0) and $\frac{\pi}{6}$ (right, encoded as 1), but it still is considered as a hyper-redundant-manipulator (HRM ⁷). This manipulator is a chain of 24 congruent modules linked together by pivot joints. Arm-Z manipulators have as many degrees of freedom (DOFs) as the number of units less of one.

<figure><img src="image_2.png" /><figcaption>**Fig. 1** Left: CAD drawing of two modules linked together and exploded view showing the connection. Right: top and bottom of the 3D-printed prototype.</figcaption></figure>

Fig. 1.1 illustrates the way of connecting the modules together. The modules for the mock-up prototype has been 3D printed with PLA filament, as shown in Fig. 1.2. The experimental environment was defined by geometry of given space and location of points to be inspected as well as the placement of the base of manipulator. At first, the manipulator must crawl inside the inspection space. Next, the tip of manipulator must visit five given points (A-E). Finally, it must crawl out of the inspection space. Each configuration was encoded in binary list of 0s and 1s starting from the base and ending at the tip. Fig. 2.1 shows the experimental setup with the mock-up manipulator in the initial configuration (before entering the test area A-E) with its binary representation.

<figure><img src="image_3.png" /><figcaption>**Fig. 2** Left: Experiment with 5 inspection (yellow) points. The tip of the manipulator (T) is shown in red. Right: The envelope of all configurations during experiment including generated intermediate transitions is shown in red. Fixed unit (F) is indicated by the white dot.</figcaption></figure>

The experiment was performed by setting manually the mock-up prototype with fixed base module in 7 main configurations (initial, A, B, C, D, E, final = initial). By using binary encoding of manipulator states, the transition from one configuration to another is straightforward. Simple subtraction of respective encodings identifies the differences. This method was applied to all key configurations and produced quasi-continuous operation of the manipulator. The rotation rate was the same for each module. Fig. 2.1 shows the corresponding envelope.

Keywords Hiper-redundant manipulator, Robustness, Snakebot, Bionic trunk, Extremely modular

Contact Info. 1-4-1 Kagamiyama, Higashi-hiroshima, 739-8527, Graduate School of Eng., Hiroshima Univ., TEL 082-424-7792
### 3. Arm-Z (3D) manipulator

In principle, six degrees of freedom (DOFs) are enough to complete any motion in three-dimensional space. A conventional industrial manipulator has low number of DOFs - usually just six. On the other hand, human arm is the biological prototype of a kinematically redundant manipulator with 7 DOFs: 3 at the shoulder, 1 at the elbow and 3 at the wrist. Alike biological snakes or bionic trunks, in various environments the characteristic type of motion gives this type of manipulators certain advantage over conventional robotic manipulators. They can operate in geometrically complicated environments which are not accessible by other approaches. Depending on the required task, various working heads can be installed on such manipulators, e.g. for: welding, cleaning, monitoring, etc.

The redundancy in DOFs allows Arm-Z to perform complicated spatial movements, but also may improve the robustness and fault tolerance of the system. Fig. 3.1 shows an early mock-up of a 12-unit Arm-Z. Fig. 3.2 shows the preliminary 4-unit Arm-Z prototype.

<figure><img src="image_4.png" /><figcaption>Fig. 3 Left: 3D-printed mock-up of a dodecagonal 12 module Arm-Z. Middle: An early prototype of a 4-unit Arm-Z. Right: Isometric cutaway showing the drive for rotation which is carried by the gear system.</figcaption></figure>

The actual (3D) Arm-Z manipulator is also comprised of linearly joined congruent modules. The first module in the sequence is fastened to a solid base. In the preliminary prototype, for simplicity, the drive was applied directly to the first module and transferred to subsequent units by internal gears as shown in Fig. 3.3. Each module was equipped with a set of cylindrical and bevel gears with straight teeth with involute profile.

Inverse kinematic problem of typical industrial manipulator can be solved easily ⁶). Thus, its control is straightforward. However, HRMs are highly non-linear systems, therefore their control is by no means straightforward, and requires application of artificial intelligence ⁸).

### 4. Control methods of Arm-Z

Particle Swarm Optimization (PSO) has been successfully implemented for certain Arm-Z tasks in ¹¹). This heuristic method is suitable for this highly non-linear optimization problem as it allows to search a large and irregular space of potential solutions. Experiment has been set as follows: there is a given environment (a box with

a hole in its side); the initial state of a 12-module Arm-Z is given ($S_s$); the goal is to transition Arm-Z so the tip of the manipulator enters without collisions and at minimal wobbling through the hole in the box. PSO found the good result (see Fig.4) already in a few minutes and improved it during approximately 3.5h.

<figure><img src="image_5.png" /><figcaption>Fig. 4 Transition for Arm-Z found by Particle Swarm Optimization.</figcaption></figure>

### 5. Conclusion

Arm-Z presents new approach to robotic manipulators. Its construction is extremely simple but control- difficult.

### Acknowledgments

This is a part of the project titled *Arm-Z: an extremely modular hyperredundant low-cost manipulator - development of control methods and efficiency analysis* funded by OPUS 17 research grant No. 2019/33/B/ST8/02791 supported by the National Science Centre, Poland.

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