An Extendable and Deflectable Modular Robot Inspired by Worm for Narrow Space Exploration

Abstract

Inspired by earthworm peristalsis, a novel modular robot suitable for narrow spaces is proposed, capable of elongation, contraction, deflection and crawling. Unlike motor-driven robots, the earthworm-inspired robot achieves extension and deflection in each module through “on–off” control of the SMA springs, utilizing the cooperation of mechanical skeletons and gears to avoid posture redundancy. The return to the initial posture and the maintenance of the posture are achieved through tension and torsion springs. To study the extension and deflection characteristics, we established a model through kinematic and force analysis to estimate the relationship between the length change and tensile characteristics of the SMA on both sides and the robot’s extension length and deflection angle. Through model verification and experiments, the robot’s extension, deflection and movement characteristics in narrow spaces and varying curvature narrow spaces were comprehensively studied. The results show that the earthworm-inspired robot, as predicted by the model, possesses accurate extension and deflection performance, and can perform inspection tasks in complex and narrow space environments. Additionally, compared to motor-driven robots, the robot designed in this study does not require insulation in low-temperature environments, and the cold conditions can improve its movement efficiency. This new configuration design and the extension and deflection characteristics provide valuable insights for the development of new modular robots and robot drive designs for extremely cold environments.

1. Introduction

The bionic robot shows great application potential in unstructured environments because of its inherent adaptability [1]. Compared with a traditional electromagnetic motor, a flexible actuator is more suitable for the bionic robot [2]. Flexible materials have a very broad application prospect as a new type of actuator [3]. Meanwhile, because the flexible actuator can safely interact with the restricted environment, this advantage makes it a better choice than a rigid actuator in specific application fields [4]. A novel structure based on biological characteristics and a flexible actuator is beneficial to many applications, including space systems, underwater robots and small equipment [5]. Research shows that flexible driven robots can imitate animals, such as snakes, worms, earthworms and inchworms, to form various configurations [6,7,8,9]. Owing to these different configurations, the robot can adapt to some inaccessible terrain and play a very important role in complex environmental motions [10,11].

For a long time, biology has been the source of inspiration for engineers to make high-performance robots [12,13]. In general, engineers use rigid materials to make robots. However, due to the lack of flexibility, it is difficult for robots with rigid structures to adjust their dynamic postures, which causes great differences in their motion performance [14]. Flexible-driven robot technology is a sub-field of robotics, which involves the design, control and manufacturing of robots made of compliant materials, rather than pure rigid links [15]. Compared to traditional rigid-driven robots, flexible-driven robots are more suitable for biomimetic motion. Different from the complex transmission systems of rigid-driven robots, flexible-driven structures are relatively simple, lightweight and energy-efficient. Moreover, during human–robot interaction, they can absorb energy from collisions through deformation or variable stiffness, or draw inspiration from animal organs for motion control, which can enhance safety [16,17]. The spine plays an important role in supporting the motion of quadruped reptiles. Geckos and lizards improve their athletic ability by periodically swinging their trunks laterally [18,19,20]. However, due to the limitations of a spine structure, it is difficult for robots to expand and contract. Hence, they are not suitable for narrow and space-limited environments. Mollusks have no skeleton structure and can move and change their shapes, and thus they can move in limited space and complex environments. Earthworm-like robots [21] can solve problems in scenes with environmental constraints, such as underground rescue [22,23], pipeline inspection [24] and gastrointestinal examination [25]. Although advanced control algorithms and strategies can improve the control precision [26], it remains challenging to achieve the same level of accuracy in controlling soft-bodied robots as with rigid robots. In addition, its structural stability is weak, which makes it difficult to bear external loads [27,28]. Therefore, by combining rigid materials with flexible materials, not only can characteristics of continuous change be realized, but certain stiffness and stability during the motion can be ensured [29,30]. For example, Niu et al. [31] designed a biomimetic earthworm robot by combining smart electroactive polymer (EAP) materials with efficient telescopic structures. They utilized ionic polymer–metal composite (IPMC) to directly provide the driving force for the telescopic lifting structure, which can enable the robot to mimic the movement mechanism of earthworms. To support a foldable flexible structure, Fang et al. [32] employed a four-bar linkage driven directly by a servo motor. This structure possesses both axial and radial deformation capabilities, which can allow for more precise control of the flexible structure by following the motion of rigid elements. Luo et al. [33] achieved a controlled three-dimensional deformable structure by mixing different design types of linkage mechanisms. They smoothly extended and retracted the structure by controlling servos, which can enable programmable bidirectional deformation for each modular segment. The traditional actuators are usually driven by the motor, fluid, pneumatic or rope [34]. This ensures the accuracy of the robot while increasing overall weight and energy consumption. In contrast, based on the lightweight characteristics of flexible actuators, shape memory alloy (SMA) is widely used in the field of biomimetics because of its simple driving mode, noiseless operation and high energy density [35,36,37].

The robot’s bending capability, coupled with its periodic lateral swinging motion, significantly enhances its mobility. Furthermore, the extension function allows for straight-line locomotion when bending is restricted, thereby improving its accessibility and enabling efficient performance in search and rescue operations within confined spaces [38]. This study proposes a modular robot with extension and deflection capabilities. Each module can both bend and adjust its dynamic posture through extension. By combining multiple modules, it can mimic various forms of motion observed in worms, inchworms and snakes, such as peristaltic motion, slithering and erecting. It can be the spine for biomimetic crawling animal robots, such as lizards, geckos and crocodiles, which can effectively increase stride and movement speed by coordinating with limb movements. Sequentially assembling different modules rotated axially by 90 degrees enables motion within a certain spatial range, which can fulfill some simple spatial task requirements. Furthermore, the use of the extension function allows for linear movement in narrow environments and navigation through complex pipelines. This paper focuses on applying modular robots in narrow environments. The sections are arranged as follows. Firstly, based on the study of the morphology and kinematics of organisms including worms and snakes, the paper presents the design of the unit module structure of the robot. The static and dynamic parameters of SMA springs are experimentally measured. The relationship between the driving force, deformation and temperature of SMA springs is preliminarily studied. The kinematic and mechanical model of the unit module is also established. By combining kinematic simulations, the relationship between the variation of memory alloy, extension distance and bending angle is analyzed in detail to validate the accuracy of the model. Finally, the performance and environmental adaptability of the module robot is verified through motion experiments and on-site experiments that simulate actual scenarios.

2. Robot Design and Method

Although traditional worm-like robots [27] can bend and elongate their bodies simultaneously, the lack of a spine in worms can result in insufficient stiffness. Although traditional snake-like robots [39,40] can bend their bodies, the fixed spinal structure of snakes makes it difficult to control length changes during operation, which can lead to a gap in exploring straight-line motion as a robot solution for navigating narrow spaces. This study designed a novel modular robot. Figure 1a,b show the modular robot and its unit module. Each module can independently achieve both bending and extension. Through designing link joints combined with tension springs, torsion springs and synchronous gears, the travel distance can be expanded and the overall structural reset capability can be enhanced to ensure that the robot returns to its initial posture. Both sides are driven by two memory alloy springs. By controlling the memory alloy spring in different charging and discharging modes, the module can expand and contract or deflect. The flexible driving robot with multiple modules can move in a narrow space and bend in any direction. To ensure the unique spatial position of the unit module and avoid redundant driving, each link is fixed with a gear to ensure the synchronization of the rotation fit of the two links. The extension and contraction capabilities of this mechanism are utilized to mimic the motion of earthworms. Compared to traditional earthworm-inspired robots, this design features a structure that incorporates eight link joints, coupled with tension springs and torsion springs. This design retains the flexible contraction and bending capabilities of earthworms. Hence, it exhibits superior environmental adaptability.

Figure 1c is a schematic diagram of bionic motion. It moves by changing the width and length by imitating earthworm motion. The short and thick part provides moving friction for the long and thin parts. When the shape changes in sequence from head to tail, the earthworm can move forward. Additionally, this motion mode allows the robot to perform climbing movements within pipes that meet certain diameter conditions. Its effective payload capacity is influenced by the frictional force provided by the pipe, which is directly related to the pipe’s diameter and the contact area with the pipe walls. As shown in Figure 1d–f, it is able to be the spine of various organisms, such as lizards, geckos, crocodiles and other reptiles with its excellent scalability. By combining multiple modules, it can replicate the crawling motion of worms and the slithering motion of snakes, which expands its application scope.The sequential assembling of modules at 90-degree angles enables it to achieve motion within a certain spatial range, thereby fulfilling some simple spatial task requirements. Furthermore, due to the inherent properties of SMA springs, the robots discussed in this paper are better suited for extreme low-temperature environments without the need for additional insulation measures, and they can also increase the robot’s mobility speed. This design enhances the adaptability of the robot in complex environments. This paper focuses on the study of the peristaltic motion of modular robots in confined environments.

3. Materials and Methods

3.1. Overview of Shape Memory Alloy Spring

Shape memory alloy (SMA) is a new material. Because of its special properties, SMA is often employed as the driver of flexible driving robots. It uses its expansion and contraction action when the temperature changes to drive the robot to move. The SMA spring can increase the expansion and contraction of the actuator while ensuring a certain output force. This feature is suitable for scenes with high driving stroke and low output force requirements.

Shape memory alloys (SMAs) offer unique advantages as actuators for modular robots. Their exceptional flexibility and adaptability make them well suited for robotic applications in confined or interactive environments. Compared to traditional motor-driven actuators, SMAs are compact and lightweight, significantly reducing the size and weight of the drive system, making them particularly ideal for miniature modular robots. Additionally, traditional motors often experience performance degradation in extremely low-temperature environments and require insulation to maintain functionality. In contrast, SMA actuators typically operate stably under extreme cold conditions without the need for insulation. Given these properties, we have chosen SMA as the actuator for our modular robot.

To control the SMA spring better, it is necessary to study the electrical, thermal and mechanical characteristics of the SMA spring. The SMA spring purchased from Gao’an Memory Alloy Materials Co., Ltd. (Yichun, China), was studied experimentally. The spring diameter was 4.2 mm. The wire diameter was 0.6 mm. The phase-transition temperature was 55 °C.

3.2. Experimental Devices and Procedures

To accurately understand the thermomechanical properties of the SMA, select the most suitable types of springs and torsion springs and determine the range of motion of the mechanism, it is crucial to avoid the potential impact of variations in SMA material performance on the performance of the mechanism. The experimental test platform is constructed as shown in Figure 2a. The experimental device includes a programmable power supply, an LVDT displacement transducer, a miniature tension and pressure transducer, a T-shaped ultra-fine thermocouple and a data-acquisition card. The shape memory spring provides a constant current through the power supply for Joule thermal activation. The T-type ultra-fine thermocouple fixed in the middle section of the spring can measure the temperature of the spring during the phase-change process. The LVDT displacement transducer measures its displacement during heating. In the driving process, the other end of the SMA spring is connected with the tension transducer to measure the tension change of the spring during the phase change. The data-acquisition card is applied to obtain the output signal of the transducer and to collect the electrical-thermal-mechanical characteristic data of the sample spring. Two experimental platforms with different variables were built, as shown in Figure 2b,c. Firstly, the SMA spring was heated with different initial lengths in experimental mode 1 to verify the influence of initial tensile length on tensile force and temperature. Then, an initial tensile length was selected to conduct experiments on the influence of different currents on the tensile force and temperature of the memory alloy spring. Finally, the experimental study on the changes of tension, temperature and displacement with time under different currents was carried out by using experimental mode 2 for SMA springs with the selected initial tensile length. Equivalent reset springs were utilized to experimentally study the resetting capability, which can validate the rationality of the selection of springs and torsion springs in the unit modules.

3.3. Electrical-Thermal-Mechanical Characteristics

Because the tensile force produced by the phase transformation of the SMA spring was different under different initial tensile lengths, six SMA springs with an initial length of 6.6 mm were selected for the experiment. The acrylic plate with a fixed baffle was fixed with screws at different hole positions. The distance between each hole position was 5 mm. The initial tensile lengths of 10 mm, 15 mm, 20 mm, 25 mm, 30 mm and 35 mm were studied, respectively. As shown in Figure 3a, the spring tension increased with the increase in temperature. In a certain range (stretching ratio of 3.0), it increased with the increase in initial stretching length. When the stretching length exceeded the range, it decreased with the increase in the initial stretching length. The maximum temperature of the spring decreased with the increase in the initial tensile length. Therefore, it can be concluded that the initial length of the spring influences the maximum temperature and maximum tension of the spring. The initial length of the SMA spring integrated into the robot should be within an appropriate range. Excessive tension will not increase the mechanical properties of the spring. By analyzing the experimental curves of electrical-thermal characteristics of SMA springs with different initial lengths, 20 mm was selected as the fixed initial tensile length. The current was selected to be 0.8 A–2.6 A. The test was conducted per 0.2 A. Before the experiment, the temperature of the shape memory spring was 28.56 °C (taking the ambient temperature). In Figure 3b, the curves of temperature and tension of the memory alloy with time under the influence of Joule heat are shown. The maximum tension of the spring increased with the increase in current, while the increased amplitude of the maximum tension decreased with the increase in current. The temperature increased with the increase in current. The amplitude of temperature change was almost proportional to the current change. Therefore, it can be concluded that the current affects the maximum temperature and maximum tension of the spring at a fixed initial length. The current applied to the SMA spring integrated into the robot should be in a proper range. Excessive current will not significantly increase the mechanical properties of the spring while increasing the energy consumption of the robot. Electrical-thermal-mechanical experimental results of the SMA spring are shown in Figure 3c,d. The maximum tension of the spring increased with the increase in current, whereas the increased amplitude of the maximum tension decreased with the increase in current. The tensile length increased with the increase in current. The speed change of the spring increased with the increase in current, while the recovery speed of the spring was almost the same under the power-off cooling state. The temperature increased with the increase in current. The amplitude of temperature change was almost proportional to the current change. It can be concluded that, for a fixed initial length, the current influences the SMA spring’s maximum temperature, maximum force and maximum elongation. The temperature of the SMA spring is intrinsically linked to its phase-transition behavior. As the temperature rises, the phase-transition process is accelerated, thereby enhancing the spring’s force and deformation capabilities. With increasing current, the heating rate of the spring also increases, resulting in a faster deformation rate. While this is beneficial for applications requiring rapid response, it also leads to higher energy consumption. Therefore, in practical applications, it is essential to optimize the current based on specific task requirements to strike a balance between deformation speed and energy consumption.

Shape memory alloys (SMAs) undergo reversible phase transitions between the martensitic and austenitic states in response to temperature changes. During the transformation from martensite to austenite, the material exhibits a phase with relatively stable stress, characterized by a gradual change in stress and the ability to produce large, recoverable strains without a significant increase in external stress. This property enables SMA springs to generate substantial force while achieving significant deformation, making them highly efficient actuators. However, as observed from the stress–strain curve of SMA, the material is highly sensitive to temperature variations. Deviations from the optimal temperature range can hinder phase transition, reducing actuator force output and introducing thermal hysteresis, which may delay the response time. Additionally, humidity can accelerate corrosion and aging effects, including shifts in the phase-transition temperature and reductions in recoverable strain, further limiting long-term performance. Despite these challenges, SMAs remain one of the best actuator choices for modular robots where space, weight and reliability are critical. By precisely controlling temperature, humidity and material aging, the impact of these factors can be effectively mitigated, ensuring stable performance in complex applications.

4. Kinematics and Mechanics Characteristics

The unit module was simplified into a link mechanism. A plane geometric frame model was established, as shown in Figure 4a. The model is used to determine the mathematical relationship between the contraction variable of the SMA spring and the expansion, contraction and deflection angle of the unit module. Each link in the module was marked as $O_i{A}_i$, $A_i{B}_i$, $C_i{D}_i$ and $D_i{O}_i$, where the length of $O_i{A}_i$ and $O_i{D}_i$ is $l_1$; that of $A_i{B}_i$ and $C_i{D}_i$ is $l_2$; and that of $B_i{C}_i$ and $O_i{O}_j$ is $l_3$. $A_0{A}_3$ and $D_0{D}_3$ represent the initial lengths of the SMA springs on both sides. $\alpha$ represents the $O_i{D}_i$ rotation angle, $\beta$ represents the $O_i{A}_i$ rotation angle, $\theta$ represents the deflection angle of the deflection unit and $\phi$ represents the deflection angle of a single module, where the clockwise direction is positive.

$$\left\{\begin{array}{c}\alpha =\beta \\ \Delta m=\Delta n\end{array}\right.$$

(1)

Figure 4a shows that the module performs expansion, contraction and deflection motions, while the initial position of the module is indicated by dotted lines. When the SMA springs contract and deform, the lengths of the SMA springs on both sides are changed to $m^{\prime }$ and $n^{\prime }$, with the shape variables of $\Delta m$ and $\Delta n$.

SMA spring lengths are related by the following equation:

$$\left\{\begin{array}{c}m=n=\sqrt{2}·l_1+l_2\\ m^{\prime }=2·l_{1}sin\left({\displaystyle \frac{\pi }{4}}-\alpha \right)+l_3\\ n^{\prime }=2·l_{1}sin\left({\displaystyle \frac{\pi }{4}}-\beta \right)+l_3\end{array}\right.$$

(2)

Then, the variation amounts $\Delta m$ and $\Delta n$ of the SMA and the deflection angle $\theta$ of the deflection unit are calculated. The deflection angle $\phi$ of a single module, the variation amount $\Delta H$ of the diameter of a single module and the variation amount $\Delta L$ of the expansion and contraction amount of a single module are as follows:

$$\left\{\begin{array}{c}\Delta m=m-m^{\prime }=\sqrt{2}{l}_1-2l_{1}sin\left({\displaystyle \frac{\pi }{4}}-\alpha \right)\\ \Delta n=n-n^{\prime }=\sqrt{2}{l}_1-2l_{1}sin\left({\displaystyle \frac{\pi }{4}}-\beta \right)\\ \theta ={\displaystyle \frac{\alpha +\beta }{2}}\\ \phi =2\theta =\alpha +\beta \\ \Delta H=2l_{1}sin\left({\displaystyle \frac{\pi }{4}}+\alpha \right)-\sqrt{2}{l}_1\\ \Delta L=2\left[(l_1+l_2)sin{\displaystyle \frac{\pi }{4}}-\sqrt{l_2^2-{\left(l_{1}sin\left({\displaystyle \frac{\pi }{4}}+\alpha \right)-{\displaystyle \frac{l_3}{2}}\right)}^2}+l_{1}sin\left({\displaystyle \frac{\pi }{4}}-\alpha \right)\right]\end{array}\right.$$

(3)

To verify the mathematical model, Adams simulation software was used to construct a corresponding physical model. Figure 4c,d indicate the relationship between theoretical calculation and Adams simulation data. These figures show that the theoretical calculation and simulation results are highly consistent. The model can accurately describe the relationship between the variation amounts $\Delta m$ and $\Delta n$ of the memory alloy, the deflection angle $\phi$ of a single module and the expansion and contraction amount $\Delta L$. Under extension and contraction conditions, there is an approximate relationship where $\Delta L$ is approximately twice $\Delta m$.

Figure 4b shows the moment equilibrium equations of the module performing expansion, contraction and deflection motions:

$$\left\{\begin{array}{c}{F}_{S1}·sin\left({\displaystyle \frac{\pi }{4}}-\alpha \right)=F_{L1}·sin\left({\displaystyle \frac{\pi }{4}}+{\displaystyle \frac{\alpha }{2}}-{\displaystyle \frac{\beta }{2}}\right)+{\displaystyle \frac{1}{2}}·F_{N1}\\ F_{S2}·sin\left({\displaystyle \frac{\pi }{4}}-\beta \right)=F_{L2}·sin\left({\displaystyle \frac{\pi }{4}}+{\displaystyle \frac{\alpha }{2}}-{\displaystyle \frac{\beta }{2}}\right)+{\displaystyle \frac{1}{2}}·F_{N2}\end{array}\right.$$

(4)

The forces are balanced in the Y direction at point O:

$$\left\{\begin{array}{c}{F_{S1\mathrm{y}}}^{\prime }+{F_{L1y}}^{\prime }={F_{S2\mathrm{y}}}^{\prime }+{F_{L2y}}^{\prime }\\ sin\left({\displaystyle \frac{\pi }{4}}+\alpha \right)·\left[F_{S1}·sin\left({\displaystyle \frac{\pi }{4}}+\alpha \right)+F_{L1}·sin\left({\displaystyle \frac{\pi }{4}}+{\displaystyle \frac{\alpha }{2}}-{\displaystyle \frac{\beta }{2}}\right)\right]\\ =sin\left({\displaystyle \frac{\pi }{4}}+\beta \right)·\left[F_{S2}·sin\left({\displaystyle \frac{\pi }{4}}-\beta \right)+F_{L2}·sin\left({\displaystyle \frac{\pi }{4}}-{\displaystyle \frac{\alpha }{2}}+{\displaystyle \frac{\beta }{2}}\right)\right]\end{array}\right.$$

(5)

When deflected to the left, the length of the tension spring and the angle of the torsion spring are related to $F_S$ and $F_L$, respectively, we obtain:

$$\left\{\begin{array}{c}{F}_{S1}=sin\left({\displaystyle \frac{\pi }{4}}-\alpha \right)\left[\left[2·K_1·sin\left({\displaystyle \frac{\pi }{4}}-{\displaystyle \frac{\alpha }{2}}+{\displaystyle \frac{\beta }{2}}\right)·l-\sqrt{2}·K_1·l\right]·sin\left({\displaystyle \frac{\pi }{4}}+{\displaystyle \frac{\alpha }{2}}-{\displaystyle \frac{\beta }{2}}\right)+K_2·\beta \right]\\ F_{S2}=sin\left({\displaystyle \frac{\pi }{4}}-\beta \right)\left[\left[2·K_1·sin\left({\displaystyle \frac{\pi }{4}}-{\displaystyle \frac{\alpha }{2}}+{\displaystyle \frac{\beta }{2}}\right)·l-\sqrt{2}·K_1·l\right]·sin\left({\displaystyle \frac{\pi }{4}}+{\displaystyle \frac{\alpha }{2}}-{\displaystyle \frac{\beta }{2}}\right)\right]\end{array}\right.$$

(6)

When only compression is applied without deflection, the relationships between the length of the extension spring, the angle of the torsion spring and the forces $F_S$ and $F_L$ are as follows:

$$\left\{\begin{array}{c}{F}_{S1}=\left[\left[2·K_1·sin\left({\displaystyle \frac{\pi }{4}}-{\displaystyle \frac{\alpha }{2}}+{\displaystyle \frac{\beta }{2}}\right)·l-\sqrt{2}·K_1·l\right]·sin\left({\displaystyle \frac{\pi }{4}}+{\displaystyle \frac{\alpha }{2}}-{\displaystyle \frac{\beta }{2}}\right)+K_2·\beta \right]sin\left({\displaystyle \frac{\pi }{4}}-\alpha \right)\\ F_{S2}=\left[\left[2·K_1·sin\left({\displaystyle \frac{\pi }{4}}-{\displaystyle \frac{\alpha }{2}}+{\displaystyle \frac{\beta }{2}}\right)·l-\sqrt{2}·K_1·l\right]·sin\left({\displaystyle \frac{\pi }{4}}+{\displaystyle \frac{\alpha }{2}}-{\displaystyle \frac{\beta }{2}}\right)\right]sin\left({\displaystyle \frac{\pi }{4}}-\beta \right)\end{array}\right.$$

(7)

This indicates that this mechanism amplifies the expansion and contraction range of the shape memory alloy. It provides a theoretical basis for the research. It can help better study and predict the motion state and parameters of unit modules under various parameters and conditions.

5. Experimental Verification

Based on the mechanical properties of SMA, the module driven by SMA was designed and manufactured. The parts of the unit modules were printed in 3D with nylon material. Each unit module had a mass of 0.05 kg. Four groups of modules were assembled to form a robot with scalability. Four motion modes (including expansion and contraction, deflection, plane linear motion and vertical climbing in pipe) were tested with different programming configurations. For each motion mode, PLC provided periodic sequence signal control for relays. By controlling current parameters and power-on time, different robot motion speeds, paces and modes could be realized to perform different tasks.

5.1. Motion Experiment

To evaluate the robotic motion performance, we conducted a series of experimental studies by constructing a dedicated testing platform. The experiments included testing for elongation, deflection, planar linear motion, vertical climbing within pipes and simulating complex, curved pipeline inspections. As shown in Figure 5, the robotic motion performance test platform was established for these assessments. A programmable DC power supply was used to power the robot, while a PLC was employed for programming and control. High-speed cameras were utilized to record and analyze the experimental data.

5.2. Expansion, Contraction and Deflection Experiments

To test the actual expansion, contraction and deflection ability of the robot, the expansion and contraction experiment and the deflection experiment were conducted after the robot bottom was fixed. The relationship curves of the displacement, deflection angle and time of the robot were obtained. As shown in Figure 6a, the curve is the relationship curve of the displacement of the top of the robot with time. The initial length of the robot is about 300 mm, the length after contraction is about 220 mm and the expansion and contraction rate is about 26.67%. The inclination of each module fluctuated along the y-axis, and the fluctuation range is −0.25° to 0.77°. This is because there may be a difference in the initial tensile size of SMA memory alloy springs on both sides. As shown in Figure 6b, the curve shows the relationship between the deflection angle of the top of the robot and time. As can be seen, the initial angle of the robot is 0°. With the change of time, the deflection angle became larger and larger and finally reached 93°.

5.3. Experiment of Climbing Motion in a Pipe

To test the vertical climbing ability of the robot, the robot was placed in an acrylic pipe perpendicular to the plane. A climbing motion experiment in the vertical pipe was carried out. For the results of robot motion, Supplementary Video S2 can be taken as a reference. The average duration of a single cycle is 120 s, with an average energy consumption of 317.98 w·s per cycle. Over the course of five cycles, the robot climbs a total of 11.55 cm, resulting in a movement energy consumption of 13.77 w·s/mm. In the test, the robot completed seven complete gait cycles on the crawling plane. Through using the multibody dynamics software ADAMS 2019, dynamic modeling of the robot and pipeline was conducted. The motion of the bio-inspired robot in actual working pipeline environments was simulated, with the linkages on both sides of each unit module set to make contact and experience friction with the pipe wall. The extension and contraction capabilities of the robot were used to adjust its width, and then frictional forces were generated by the contact between the linkages and the pipe wall. Through sequential control of each unit module, the simulation of the robot’s climbing motion inside the pipe was achieved. Figure 7a is a screenshot of the vertical climbing motion. Figure 7b shows a comparison diagram of a vertical climbing motion trajectory and a theoretica calculation. Figure 7c displays the theoretical and experimental error curves for the position of each unit module. The results are as follows: The expansion and contraction of each cycle were basically the same, which was highly consistent with the theoretical model. Module 4 had errors and would increase slowly with the periodic motion of the robot. This was because the heat in the pipe was not easy to dissipate. The time interval between the power failure of the SMA spring and the next power-on was not enough for complete cooling. It caused a decrease in its variable. Thus, the above error was generated. According to the fluctuation trajectory, the climbing amount of joints between each cycle was 16.5 mm, 17.1 mm, 16.3 mm and 17.0 mm, respectively. The theoretical values were −0.6 mm, −0.7 mm, 0.3 mm and −1.1 mm separately in different periods. In addition, these errors will not increase obviously with the increase in the robot motion cycle. This may be related to the initial stretching state of the robot. The module trajectory indicates that the robot moved forward about 115 mm in seven expansion and contraction cycles, with an error of 0.3% compared to the model calculation of 111 mm. The average position error of each module was within 6%, and this result is consistent with the model calculation expectation.

5.4. Experiment of Climbing Motion in a Winding Pipe

To verify the practical application of the robot in the detection of winding and complex pipelines, a winding pipeline-detection experiment was carried out in a PVC steel hose with a diameter of 45 mm. For the results of the robot motion, the Supplementary Video S3 should be referred to. Figure 8 shows a screenshot of the robot’s motion. Driven by the controller, the robot moved slowly along the pipeline. Because of the different curvatures of PVC steel hose, when the robot was located in a curved pipe, it adapted to the shape of the pipe through active and passive deformation. The deformation was caused by the reaction force from the pipe wall to both ends. The speed of the robot was different with different curvatures. This was because the inner diameter of the S-shaped pipe made by hand bending deviated. This caused different maximum expansion and contraction distances of the robot, and thus the speed was reduced. With the robot going deep into the pipeline, the robot successfully carried out a simulated winding pipeline-detection experiment in the pipeline. Although it moved in the pipeline at a relatively low speed, the robot could overcome the curved pipeline with different curvatures and long distances. This result shows that it can be deployed in other complex pipelines. With the assembly of more unit modules, the flexibility of the robot could be increased.

5.5. Experiment of Expansion and Contraction in Extreme Cold Environments

Modular robots are commonly used for exploration in unstructured environments, which may also face extreme temperatures. Traditional actuators in such extreme cold environments require thermal protection designs or the use of electrical heating pads to maintain normal operating temperatures. In contrast, actuators made from shape memory alloys (SMAs) do not require insulation. Additionally, low temperatures can enhance the efficiency of SMAs, making them better suited for extreme cold conditions. We use a single-module robot, where compression is controlled through SMA heating. The efficiency of compression can be ensured by increasing the electrical current. Thus, this study tests the recovery rate of the robot after compression at different environmental temperatures. As shown in Figure 9a, a unit module testing platform was set up using a high–low temperature chamber for efficiency tests. Figure 9b demonstrates that, with decreasing environmental temperatures, the recovery time of the robot unit module significantly decreases. Without convection, recovery time decreases by an average of 15.74% for every 10 °C drop in temperature; with convection, it decreases by an average of 15.93% per 10 °C drop in convective temperature. Additionally, convective temperatures reduce recovery time faster than environmental temperatures.

6. Conclusions

In this article, we demonstrate the design, modeling and validation of a worm-inspired modular robot with telescoping and deflection characteristics, specifically designed for narrow spaces. The modular robot consists of linkages, tension springs, torsion springs, gears and shape memory alloy (SMA) springs for telescoping and deflection. Each module can independently achieve bending and extension. By integrating the design of tension springs, torsion springs and gears, the overall structural stability and resetting capability are enhanced, avoiding structural redundancy. The robot is driven by two SMA springs on both sides, and by controlling different charging and discharging modes of the SMA springs, telescoping or deflection is achieved. We studied the contraction and deflection characteristics of the robot’s unit modules and developed a mathematical model to estimate the relationship between telescoping length, deflection angle and SMA actuation. Through model validation and experiments, we found that due to the difficulty of dissipating heat in narrow pipelines, the interval between disconnecting the SMA spring’s power supply and the next powering is insufficient for complete cooling, resulting in partial errors. According to the oscillation trajectory, the joint climbing amount between each cycle and the theoretical error is 4.03%, and these errors do not significantly increase with the robot’s motion cycles. This may be related to the robot’s initial stretching state. The results demonstrate that the robot can operate stably and flexibly in confined space environments and extremely low temperatures. Although the modular robot has broad prospects, there are still several aspects that need further optimization. Currently, due to limitations in structural size and actuator force output, the robot is only capable of adapting to a limited range with a diameter of 45 mm. Moreover, its payload capacity is directly dependent on its overall dimensions. To further optimize the robot’s motion characteristics, structural improvements are expected to enhance both its load-bearing capacity and spatial adaptability. By adding more unit modules, a more flexible robot can be formed to explore more complex environments. The robot is powered by a cable, which may lead to significant drag force, preventing the robot from penetrating deeper into pipelines. In the future, high-energy-density batteries will be considered to make the robot cable-free. To ensure the robot’s safe operation in unpredictable or hazardous conditions, future development will prioritize the integration of advanced protective measures, including the addition of high-temperature-resistant, insulating flexible skins on the robot’s exterior and the incorporation of heat-exchange systems within its internal structure. Additionally, the robot’s motion control system will be optimized to enable autonomous operation in cable-free or hazardous environments, further enhancing its stability and reliability in complex, dynamic scenarios. Furthermore, given the potential scalability of this module, further applied research should be conducted in broader biomimetic fields and scenarios to continue our exploration.