Seafloor Landing Dynamics of a Novel Underwater Robot Using ALE Algorithm

Abstract

Seafloor landing research is crucial for underwater robots tasked with long-term fixed-point observation missions, particularly those requiring prolonged operations on the seabed. Developing safe and stable landing technology is essential for the success of these missions. This paper introduces a novel underwater robot by establishing its dynamic model and using the arbitrary Lagrangian–Eulerian (ALE) method to conduct a comprehensive study of its deep-sea landing process. Prior to detailed parameter analysis, the ALE algorithm’s effectiveness and accuracy were validated through experimental data and simulation results from previous studies. This study examines the penetration depth and force conditions during the landing process by varying factors such as seabed soil properties, landing velocity, and the robot’s mass. Findings indicate that seabed soil properties significantly influence penetration depth and pressure, with variations in soil density and strength affecting the robot’s landing behavior. In contrast, the robot’s mass has a relatively minor effect, suggesting that the choice of structural materials has limited impact on penetration depth and pressure during landing. Additionally, landing velocity was found to significantly affect penetration depth and pressure; higher velocities result in greater penetration depths and pressures. This highlights the importance of controlling landing velocity to minimize impact forces and protect the robot. The results of this study provide theoretical support and data for developing deep-sea landing technology for novel underwater robots and inform the selection of structural materials, ensuring the successful execution of long-term fixed-point observation missions in deep-sea environments.

1. Introduction

1.1. Background

The deep sea holds abundant resources and many unknowns [1,2], but the extreme environment poses significant challenges for marine exploration. In recent years, the application of underwater robots in deep-sea exploration has rapidly advanced. These robots are capable of adapting to harsh underwater environments and performing long-duration tasks, thereby expanding the possibilities for deep-sea research. Simultaneously, long-term in situ observation of deep-sea areas has become a key focus in marine science research. To facilitate these observations, the residency technique for underwater robots has been developed and applied to enable long-term fixed-point monitoring. This technique ensures that robots remain stable at target locations while continuously collecting data, thus providing reliable support for marine scientific studies and overcoming the spatial and temporal limitations of traditional observation methods. As a result, more comprehensive and continuous deep-sea data are obtained, enhancing the scope of deep-sea research and promoting interdisciplinary cooperation in marine science. Consequently, deep-sea residency is crucial for human exploration and utilization of the oceans, offering new perspectives on deep-sea environments and ecosystems. However, before establishing residency in the desired area, underwater robots must first conduct a safe landing, a process that involves impact and penetration between the seabed and the robots. This landing process can potentially damage the robots or alter their positioning. Therefore, the present study investigates the dynamic process of a novel underwater robot landing on various soil types at different impact velocities.

1.2. Previous Works

In recent years, scholars have extensively studied the impact and penetration of objects into soil. Some researchers [3], combining Det Norske Veritas (DNV [4]) standards and Newton’s second law, have investigated penetration depth, proposed theoretical calculation methods, and established motion prediction models of deep-sea landers in sediments. They have simulated landing processes on various seabed substrates and analyzed the effects of different parameters on stress and strain during the landing of key components of deep-sea landers. Additionally, many researchers have performed detailed studies on object penetration through both experiments and simulations.

In experimental studies on penetration dynamics, William, Earle, and Harvey [5] experimentally investigated the penetration dynamics of non-rotating conical projectiles in sandy soil. They proposed a new penetration theory and established new penetration equations. True [6] conducted model tests to study the penetration behavior of different penetrators in various media. By analyzing test data, relationships between penetration velocity, acceleration, and embedment depth were derived, and the mechanical mechanisms and influencing factors of penetration behavior were explored. It is important to note that these studies are primarily based on model tests, and actual conditions are more complex. Boguslavskii et al. [7] studied the penetration phenomena of low-speed projectiles in soil through experiments and theoretical models. They found a non-monotonic relationship between projectile deceleration and penetration depth and evaluated the soil’s static properties using dynamic characteristics. Uehara et al. [8] experimentally investigated the characteristics of impact craters formed by spheres in dry granular media. They discovered that the penetration depth of an object is related to its total energy. The crater diameter is proportional to the fourth root of the impact energy, while the crater depth is proportional to the cube root of the impact height. This study indicates that crater depth and diameter are controlled by different physical mechanisms and that crater depth is also influenced by the density of the impacting object and the properties of the sand. Ciamarra et al. [9] used experiments and molecular dynamics simulations to study the impact process of projectiles in granular media. They found that the average deceleration of projectiles is proportional to the impact velocity and independent of penetration depth, while the penetration depth is related to the impact velocity. Brandao et al. [10] discovered through experiments that increasing the internal ballast of anchors can reduce tilting during the installation process, using lead as ballast to lower the center of gravity of the pile and reduce tilting. Richardson et al. [11] used centrifuge model tests to study the setting effects of dynamic anchors in clay. Results showed that the short-term bearing capacity of dynamic anchors is related to impact velocity and that consolidation is slow. Hossain, Kim, and Gaudin [12] studied the installation and extraction behavior of torpedo anchors in kaolinite and calcareous silt, summarizing the effects of anchor drop height and soil strength on embedment depth. Lee et al. [13] assessed the perforation effects of differently shaped bases in clayey sand sediments. O’Loughlin et al. [14] utilized experimental data to explore the penetration effects of dynamically installed anchors in normally consolidated kaolinite.

In numerical simulation studies on penetration dynamics, Tsimring and Volfson [15] used a two-dimensional soft particle molecular dynamics simulation method to study the penetration process of large projectiles in dry granular media. By systematically changing the physical parameters of the projectiles (density, size, and impact energy), they investigated the energy dissipation mechanisms and scaling relationships of low-speed impacts in granular media and discovered a constant deceleration effect during the penetration phase. Raie and Tassoulas [16] introduced a computational model for predicting the embedment depth of torpedo anchors. This model uses computational fluid dynamics (CFD) algorithms to assess the resistance on the anchor body and simulates soil as a viscous fluid. The advantage of the CFD method is that it not only provides estimates of embedment depth but also predicts the pressure and shear distribution at the soil–anchor contact surface and within the soil. Carter et al. [17,18] used the arbitrary Lagrangian–Eulerian (ALE) numerical simulation method to study the penetration process of conical rods in clay. Their study considered material nonlinearity, soil deformation, dynamic loads, and strain rates. Simulation results indicated that the penetration effect primarily depends on the initial kinetic energy, length-to-diameter ratio, and soil strength. Kim et al. [19,20] used the coupled Eulerian–Lagrangian (CEL) method for three-dimensional large-deformation finite-element calculations to study the dynamic penetration of torpedo anchors in clayey and calcareous silt soils. They also investigated the dynamic installation and extraction behavior of dynamically penetrating anchors under different soil conditions. Experimental results showed that the penetration depth of anchors increases with drop height and terminal velocity and decreases with increasing soil strength. The authors also studied the effects of anchor geometry, impact velocity, and soil strength on dynamic installation. In the same year, Kim et al. [21] found that the embedment depth of dynamically penetrating torpedo anchors is related to impact velocity, anchor shaft length, diameter, and other geometric parameters. Building on O’Loughlin’s [14] work, they proposed a simple total energy method that considers factors such as anchor mass, impact velocity, surface area, projected area, and the gradient of the undrained shear strength of the soil.

Despite progress in research on the penetration of objects into soil, most studies have focused on torpedo anchors, and the dynamic process of underwater robots landing on the seabed remains in its early stages. In the early 21st century, the U.S. Navy pioneered the concept of seabed landing for underwater robots and developed the NPS autonomous underwater vehicle (AUV) II [22,23], as shown in Figure 1a. This AUV controls landing posture through thruster thrust and ballast tank flooding speed but lacks a dedicated landing and residence device, posing a risk of damage upon landing. Subsequently, some research institutions and scientific teams have made progress in developing underwater robots with seabed landing capabilities. As shown in Figure 1b, the Ocean Explorer II AUV [24] developed by the University of Atlanta in the United States has a descent speed control function, achieving precise descent speed control through a buoyancy adjustment system that inflates and deflates seawater. As shown in Figure 1c, Germany’s “FLUFO” [25] deep-sea benthic observation station adopts a three-support frame structure with supporting legs and footpads. To reduce sediment adhesion, the upper part of the circular footpad structure is designed with rounded corners. As shown in Figure 1d, the “ALBEX” [26] multifunctional benthic in situ observation deep-sea lander developed by the Netherlands Marine Research Institute can monitor seabed sediment oxygen consumption and also uses a three-support frame structure. The experimental instruments it carries are installed in the lower middle part, and the support leg structure at the bottom is disk-shaped. The disk-shaped footpads are reinforced with plates between the footpads and the support leg structure, effectively increasing the strength of the footpads and support legs. The above underwater robots mainly achieve seabed residence through buoyancy adjustment systems and support frames. This paper focuses on the support legs and footpads of underwater robots, using simulation to explore the seabed landing process of underwater robots in depth. The aim is to provide more accurate theoretical basis and technical support for the design and application of underwater robots, promoting the development of underwater robot optimization design technology.

1.3. Research Focus

With increasing attention on marine resource development and the rapid advancement of underwater robot technology, these robots are now widely used for tasks such as deep-sea exploration, seabed environmental monitoring, and shipwreck searches. To ensure the stability of underwater robots on the seabed during such tasks, it is crucial to study their collision processes with the seabed. However, the existing literature predominantly focuses on the factors affecting the penetration depth of anchor-like objects into soil, and the research scope is relatively narrow. Additionally, there is a lack of studies specifically examining the penetration dynamics of underwater robots in submarine soil. Most existing research is limited to macroscopic analysis and seldom includes detailed observation and recording of field variables, such as pressure changes and soil deformation. Despite these limitations, previous studies have provided a solid theoretical foundation for understanding the process of object penetration into soil, and the penetration formulas are continually being refined.

This study aims to address the gap in the literature by focusing on a novel underwater robot with a specially designed landing structure. The robot is equipped with four rigid support legs and footpads at the bottom to ensure a safer and more stable landing on the seabed. The study systematically analyzes the penetration depth and pressure experienced by the underwater robot by varying seabed soil properties, initial penetration speed, and robot mass, with a particular focus on the relationship between impact force and material selection following the robot’s collision with the seabed. The aim is to provide new insights for the structural design and application of underwater landing mechanisms, identify the key factors affecting penetration depth and underwater pressure, and optimize the design and material selection of underwater robots to enhance their safety and reliability, thereby advancing underwater robot technology.

1.4. Organization of the Paper

This paper investigates the penetration process of underwater robots colliding with the seabed in the context of deep-sea exploration, offering theoretical foundations and technical support for their design, material selection, and safety performance enhancement. The first section reviews the current state of deep-sea resource development and underwater robotics technology, summarizing relevant research to establish the groundwork for this study. Section 2 details the numerical computation methods and the validation of software algorithms. Section 3 introduces the new underwater robot model and the mesh modeling process. In Section 4, simulation analysis is used to examine the impact of various variables on penetration depth and maximum forces experienced by the underwater robot, revealing the mechanical principles underlying the collision process. Based on the simulation results, a more rational approach to material selection is proposed. Finally, Section 5 summarizes the study and discusses future research directions, providing new insights for the advancement of underwater robot technology.

2. Numerical Methods and Verification

2.1. Numerical Methods

LS-DYNA 2022R1 [27] is a well-known general-purpose explicit dynamics commercial software widely used for simulating and solving complex real-world problems. It employs several algorithms, including the Lagrangian, Eulerian, and arbitrary Lagrangian–Eulerian (ALE) methods. The Lagrangian algorithm attaches the mesh to the material, making it effective for simulating solid deformation, though it can suffer from mesh distortion in cases of significant deformation. The Eulerian algorithm, in contrast, fixes the mesh points in space, making it suitable for simulating fluids but less effective at tracking material movement. The ALE algorithm combines the advantages of both the Lagrangian and Eulerian methods. It maintains the Lagrangian approach’s capability to track material boundaries at structural interfaces, while incorporating the Eulerian method’s advantage of allowing internal mesh elements to exist independently of the material. Unlike the Eulerian mesh, the ALE mesh can adjust its position during the simulation based on defined parameters, thus preventing severe mesh distortion. This flexibility makes the ALE algorithm suitable for a wide range of problems, including solids, fluids, and large deformations. It offers high accuracy by enabling the selection of appropriate mesh movement methods for specific problems and provides good stability by effectively avoiding issues of mesh distortion and material penetration.

This study employs the ALE algorithm for simulation, leveraging its capabilities to describe material movement and deformation in nonlinear dynamic problems. The ALE method is particularly effective for handling impact issues, making it well-suited for simulating and analyzing the seabed penetration process of underwater robots in this study.

2.2. Numerical Verification

To validate the reasonableness and accuracy of the numerical methods used in this study, we first compared the simulation results with field test data from a full-scale torpedo anchor (0.762 m × 12 m × 40.77 t) as reported by Medeiros et al. [28]. The simulation setup involved dropping the torpedo anchor vertically at a speed of 22 m/s onto a seabed composed of cohesive soil. The soil model was represented as a finite cuboid with dimensions 7 m × 7 m × 70 m. Non-reflecting boundary conditions were applied to the model’s boundaries to simulate an infinitely extended seabed. Full constraints were imposed at the bottom of the soil, and a gravity field was introduced throughout the model to better approximate real marine conditions. Soil properties are detailed in

Table 1. Properties of the torpedo anchor model in Ref. [28].

Density (kg/m3)	Elastic Coefficient (Pa)	Poisson’s Ratio
7850	2.10 × 1011	0.29

, and the torpedo anchor model and mesh used for algorithm validation are illustrated in Figure 2.

This study evaluated three mesh sizes: 0.093 D_A (where D_A is the diameter of the torpedo anchor, D_A = 0.762 m), 0.039 D_A, and 0.026 D_A. Figure 3 shows the penetration curves for each mesh size, illustrating the simulation results for different levels of grid refinement. The penetration depths obtained for the three grid sizes were 23.3 m, 26.4 m, and 27.4 m, respectively. The results for the finer grid sizes of 0.039 D_A and 0.026 D_A were closer to the field data (29.0 m) reported in Ref. [28], with relative errors of 8.97% and 5.52%, respectively. This indicates that the numerical method used in this study effectively simulates the penetration dynamics of the anchor and provides accurate measurements of penetration depth. Furthermore, the verification demonstrates that decreasing the mesh size in the finite-element discretization significantly improves simulation accuracy. This suggests that finer mesh divisions better capture the complex dynamic behavior of anchors during penetration.

3. The New Underwater Robot and Mesh Independence Verification

3.1. Robot Model and Characteristic Parameters

The simulation model investigated in this study is a newly proposed underwater robot developed by our research group, with a simplified representation shown in Figure 4a. The unmanned underwater vehicle (UUV) hull is centrally located in the model and serves as the core component of the robot. It performs several critical functions, including attitude control, precise navigation, sensor data acquisition and processing, mission planning, and autonomous decision-making. The hull is equipped with eight external panel wings arranged in overlapping pairs that can be mechanically unfolded and folded.

The robot is designed with underwater landing capabilities, featuring four rigid support legs and footpads on its bottom. These components are symmetrically distributed around the cabin’s center, with the support legs positioned at a 45° angle relative to the footpads and wing panels. The support legs are telescopic and adjustable, allowing the robot to achieve an optimal landing posture across varying depths and underwater terrain conditions. The footpads effectively absorb and disperse impact forces when the robot contacts the seabed, minimizing direct collision forces and protecting the hull’s structural integrity. Additionally, the larger contact area and enhanced friction provided by the footpads improve the robot’s stability on the seabed, ensuring accurate and reliable sensor data. Without footpads, the robot might face excessive collision forces upon direct contact with the seabed, which could lead to structural damage or instability. Therefore, the design of the footpads is critical for enhancing the robot’s overall performance and extending its service life. This design approach for the support legs and footpads is inspired by the Apollo 11 lunar module of the United States [29,30].

Figure 4b illustrates the main working scenario of the newly designed robot, which consists of two processes: gliding from a to h and landing starting from h. At position h, the robot begins to descend vertically, simultaneously deploying its legs and releasing its footpads, ultimately landing on the seabed.

3.2. Finite-Element Modeling of the Underwater Robot the Seabed Domain

This section details the three-dimensional finite-element modeling of the underwater robot and seabed soil domain, with a schematic diagram provided in Figure 5. The dimensions of the soil domain are set to 35d × 35d × 15d (where d is the diameter of the hull, d = 200 mm) to ensure that the domain is sufficiently large to prevent boundary effects during dynamic analysis. The mesh of the soil domain is illustrated in Figure 5b; during the entire modeling process, the mesh is encrypted in the area around the new underwater robot to more accurately determine its penetration trajectory. The new underwater robot is simplified as a rigid body and is assumed to remain vertical without tilt during the penetration process. The new underwater robot is modeled from the soil surface, and its landing velocity v is given. This simplified approach reduces computational demands while preserving key physical characteristics, thereby satisfying the requirements for simulation analysis.

Based on the working environment of the novel underwater robot, the constitutive laws and material parameters of the soil are determined under undrained conditions. Therefore, the soil is modeled as an elastoplastic material following the Tresca yield criterion. The Tresca yield criterion effectively describes the plastic deformation behavior of soil under stress and shows good applicability in simulations of the interaction between the underwater robot and seabed soil. To realistically simulate the marine seabed environment, non-reflective boundary conditions are applied around the soil domain, and the bottom surface is fully constrained, meaning the soil at the bottom is completely fixed, preventing any movement or rotation.

3.3. Mesh Independence Tests

To accurately capture the interaction between the new underwater robot and the soil and to ensure the reliability of the simulation results, it is essential to finely mesh the soil domain. This paper performs a mesh independence study to identify the optimal mesh density that balances accurate simulation of the robot–soil interaction with computational efficiency.

This study assessed five mesh densities with minimum cell sizes of 0.8d, 0.5d, 0.4d, 0.35d, and 0.3d (see

Table 2. Mesh independence tests.

Mesh	Number of Elements	hmin/d
mesh 1	18,375	0.8
mesh 2	147,000	0.5
mesh 3	294,272	0.4
mesh 4	430,000	0.35
mesh 5	684,450	0.3

). The simulation setup involved the underwater robot’s footpad initially contacting the soil surface at an impact velocity of 3 m/s, with the robot falling vertically onto sandy soil. Time penetration curves for each mesh density are shown in Figure 6. The results indicate that the final penetration depths for meshes with cell sizes of 0.35d and 0.3d are nearly identical, suggesting that a cell size of 0.35d is optimal. Consequently, a cell size of 0.35d was selected for subsequent parameter analysis. Additionally, as illustrated in Figure 6b, the robot’s velocity stabilized at zero after 0.4 s, confirming that the robot had fully stopped. This finding further validates the accuracy of the simulation and provides a solid foundation for further analysis.

4. Results and Discussion

The novel underwater robot achieves an initial penetration velocity after moving through the water, followed by contact and penetration into the seabed. During this process, the resistance encountered by the underwater robot is highly complex, ultimately causing it to decelerate gradually until its velocity reaches zero due to soil resistance. The penetration depth of the underwater robot is closely related to factors such as its initial penetration velocity, the properties of the seabed soil, and its weight. To more accurately predict the penetration depth and force conditions, these factors need thorough investigation. This study assumes that the descent posture of the underwater robot is controllable, so only the penetration process in the typical vertical direction is considered.

4.1. Force Analysis

During the penetration of the novel underwater robot into seabed soil, the forces involved are complex, including hydrodynamics and soil resistance. To facilitate research, this paper simplifies the analysis by focusing on the primary forces: effective buoyant weight, end-bearing resistance, side friction resistance, and soil drag force. The detailed force analysis during the penetration process is illustrated in Figure 7. By analyzing these primary forces, a theoretical basis can be provided for subsequent simulation and experimental studies.

Based on the force acting on the novel underwater robot in the soil, the dynamic equation of its motion in the seabed soil can be established using Newton’s second law.

$$\left(\begin{array}{c}M+m_a\end{array}\right){\displaystyle \frac{dv}{dt}}=G^{\prime }-F_b-F_f-F_d$$

(1)

where m_a represents the added mass of the novel underwater robot, calculated as m_a = 2m_s; m_s denotes the mass of seabed soil occupied by the volume of underwater robots; G′ signifies the effective buoyancy of the robot. F_b represents the bearing resistance force. F_f denotes the lateral friction force. F_d signifies the inertial drag force of the soil. The sizes of F_b and F_f are closely related to the density and water content of the soil.

$$F_d={\displaystyle \frac{1}{2}}{C}_d{\rho }_s{A}_{tip}{v}^2$$

(2)

where C_d represents the drag coefficient of the seabed soil. ρ_s denotes the density of the seabed soil. A_tip signifies the total projected area of the robot’s pads. v represents the robot’s landing velocity.

Through the above force analysis, it can be seen that the penetration depth of the new underwater robot into the seabed soil is related to factors such as the properties of the seabed soil (density, shear modulus, and bulk modulus), the robot’s own weight, the landing speed during penetration, and the total projected area of the underwater robot’s pad.

4.2. Effects of Seabed Soil Properties on the Landing Process of Underwater Robots

The upper layer of the seabed soil primarily consists of soft clay, while the lower layer is composed of medium-dense sand. For the new underwater robot, the resistance exerted by the seabed soil on the novel underwater robot primarily includes end-bearing resistance (F_b) and side friction resistance (F_f). Due to the different expressions of resistance in various seabed soil types, this study focuses on clay and sandy soils to investigate how the properties of seabed soil affect the initial penetration depth of the underwater robot. The characteristic parameters of seabed soil are shown in

Table 3. Properties of sandy soil and cohesive soil.

Soil Type	Mass Density (kg/m3)	Shear Modulus (Pa)	Bulk Modulus (Pa)
sandy soil	1800	1.18 × 107	1.075 × 108
cohesive soil	1360	1.841 × 106	6.895 × 107

.

In the numerical simulation calculations, the seabed soil model employs the Tresca yield criterion to describe the plastic deformation behavior of the soil. The external boundary of the soil model uses non-reflecting boundary conditions to simulate an infinite region with a finite model. A gravity field is applied to the entire model to replicate real marine conditions.

Figure 8 shows the numerical simulation results under the following conditions: the underwater robot’s footpad initially contacts the soil’s upper surface, with a landing velocity of 3 m/s, maintaining a vertical descent. By varying the seabed soil properties, we obtained the velocity, penetration depth, and contact pressure of the underwater robot under different soil conditions.

In Figure 8a, as the end-bearing resistance and side friction resistance of the seabed soil increase, the robot’s speed continuously decreases, eventually reaching zero after some fluctuations. Compared to soft clay, the underwater robot decelerates more quickly and stops earlier in sandy soil, stabilizing at zero velocity after 0.4 s. This suggests that the higher resistance of sandy soil leads to faster deceleration and earlier penetration cessation.

Figure 8b illustrates that the penetration depth of the underwater robot initially follows a parabolic trajectory, increasing with time. After 1 s, the final penetration depth is 0.38 m in soft clay and 0.03 m in sandy soil. This indicates that increased soil strength significantly reduces the robot’s penetration depth, demonstrating that stronger soil properties (e.g., end-bearing and friction resistance) limit the robot’s ability to penetrate the seabed.

Figure 8c shows that during the initial collision stage, the underwater robot experiences the highest contact pressure, which tests the material’s strength and stiffness. Over time, the contact pressure decreases. The maximum pressure experienced by the robot in soft clay is much lower than in sandy soil, indicating that higher soil strength corresponds to increased maximum pressure.

Figure 9 presents the deformation and pressure contours at the same moment for different soil types. The deeper color at the contact point between the robot’s footpad and the soil indicates ongoing penetration, with the depth increasing over time. Figure 9a,b show that the pressure experienced by the robot is significantly higher in sandy soil than in clay, corroborating the findings from Figure 8c. Figure 9c,d reveal that the deformation in clay is much greater than in sandy soil at the same time, consistent with the penetration depth changes in Figure 8b. These results clearly demonstrate the significant influence of soil properties on the robot’s landing and penetration behavior. In high-strength soils, the robot experiences greater pressure and reduced penetration depth, necessitating enhanced structural strength and design optimization.

4.3. Effect of Bottom Contact Speed on the Landing Process of Underwater Robots

The landing velocity is the vertical speed of the underwater robot at the moment it contacts the seabed. A higher landing velocity generates a greater impact force and contact pressure, which increases the risk of structural damage to the robot. Moreover, landing velocity significantly influences the penetration depth of the robot; excessively high velocities can destabilize the penetration process or even cause the robot to rebound off the seabed soil. The force analysis suggests that the landing velocity of the underwater robot affects its penetration depth both directly and indirectly.

This study uses sandy soil for the seabed, with the soil parameters detailed in Table 3. The chosen landing velocities for the underwater robot are 1 m/s, 3 m/s, and 5 m/s. Simulation results, shown in Figure 10, and the final penetration depths and maximum contact pressures summarized in

Table 4. Effect of landing velocity on penetration depth and bottom contact pressure.

Speed (m/s)	Penetration Depth (m)	Maximum Pressure (N)
1	0.026	24,441
3	0.0315	80,239
5	0.0325	134,593

provide insights into how landing velocity impacts the robot’s penetration behavior. Analyzing these results at different landing velocities allows for a better understanding of the effect of landing velocity on the penetration process of the underwater robot.

Figure 10a,b show that the penetration depth of the underwater robot into the seabed soil increases significantly with higher landing velocities. In the initial phase, the robot rapidly penetrates the soil due to the greater kinetic energy associated with higher speeds. Upon reaching maximum penetration depth, the increased soil resistance causes the robot’s speed to gradually decrease, eventually leading to an upward rebound. The rebound height is positively correlated with landing speed; a higher speed results in a greater rebound amplitude. Ultimately, the robot stops due to the soil resistance.

Figure 10c illustrates that as the underwater robot penetrates the seabed soil, the contact pressure it experiences significantly increases with higher landing velocities. This trend suggests that the increased impact force leads to a rise in contact pressure. According to Table 4, at a landing speed of 1 m/s, the maximum contact pressure is 24,441 N; at 3 m/s, this pressure rises to 80,239 N; and at 5 m/s, it reaches 134,593 N. This demonstrates that as speed increases, the impact force grows exponentially, resulting in a substantial increase in contact pressure. To withstand this higher contact pressure, the underwater robot must use higher-strength materials to maintain structural integrity and ensure operational safety.

To ensure the safety and efficiency of underwater robots, landing speed must be carefully controlled. In practical applications, landing speed should be adjusted based on factors such as seabed soil type, the robot’s structural design, and operational requirements. By optimizing landing speed, potential damage to the robot can be minimized, allowing it to complete its tasks efficiently and safely. This strategy is especially important in complex seabed environments, where a balance between structural strength and operational performance is needed to ensure the underwater robot can operate reliably over an extended period.

Analyzing the pressure variation contour maps provides a clearer understanding of how pressure changes during the underwater robot’s landing process. Figure 11 presents the pressure variation contour maps at three different time points (t = 0.001 s, 0.01 s, and 0.086 s) as the robot lands on sandy terrain at velocities of 1 m/s, 3 m/s, and 5 m/s.

At t = 0.001 s, the four footpads and supporting legs of the underwater robot experience an initial pressure spike, reaching the maximum pressure value, as shown in Table 4. This indicates that the robot undergoes the highest pressure at the moment of landing due to the impact force. As time progresses, the pressure on the underwater robot gradually decreases while the contact area with the compressed soil increases. This decrease occurs because, as the robot penetrates farther into the soil, the expanding contact area allows the impact force’s kinetic energy to be gradually converted into potential energy, resulting in a reduction in pressure. By t = 0.086 s, the pressure on the underwater robot drops to zero, aligning with the results shown in Figure 10c. This finding indicates that the pressure on the robot steadily decreases after landing, eventually reaching equilibrium. Additionally, as the landing velocity increases, the initial pressure experienced by the underwater robot also increases. This is because higher velocities generate greater impact forces, thereby raising the peak pressure. Therefore, the landing speed of the underwater robot directly affects the pressure it experiences—the higher the speed, the greater the impact pressure.

In designing and operating underwater robots, it is crucial to carefully control the landing velocity to achieve the desired penetration depth while minimizing impact force and pressure on the seabed soil. This balance ensures the robot’s stability and the successful completion of its tasks. Excessive landing velocities can lead to higher impact forces and pressures, increasing the risk of structural damage and potentially affecting penetration depth and operational efficiency. Conversely, landing velocities that are too low may result in insufficient soil penetration, reducing operational efficiency.

4.4. The Influence of the Underwater Robot’s Mass on the Bottom Landing Process

In the application of underwater robots, mass is a critical factor that affects penetration depth and contact pressure. Heavier robots can penetrate the seabed soil more deeply because their greater mass provides more initial kinetic energy, increasing the impact force at landing and causing greater deformation of the seabed soil. Additionally, a heavier robot exerts more contact pressure on the seabed, which further affects soil deformation. Therefore, in engineering projects involving the design and operation of underwater robots, accurately assessing and controlling the robot’s mass is crucial to ensure effective penetration depth and stable contact with the seabed.

In this study, the mass of the underwater robot is varied by changing the materials while keeping its volume and contact area with the soil constant. Figure 12 presents the simulation results of the novel underwater robot’s penetration into the seabed soil at different masses, with a landing velocity of 3 m/s and sandy soil as the seabed material. The data for penetration depth and maximum contact pressure are summarized in

Table 5. Influence of underwater robot’s mass on the penetration depth and the maximum contact pressure.

Material	Density (kg/m3)	Mass (kg)	Penetration Depth (m)	Maximum Pressure (N)
steel	7850	451	0.03	80,239
titanium	4500	258.5	0.0236	78,336

.

Figure 12 shows that under low-speed conditions in sandy soil, the velocity change curves for novel underwater robots of different masses follow the same trend, with only minor variations. This indicates that under low-speed conditions, changes in mass have a minimal effect on the robot’s velocity. Additionally, the penetration depth and contact pressure of the novel underwater robot increase with its mass. As shown in Table 5, the penetration depth for a 451 kg underwater robot is 0.03 m, with a maximum contact pressure of 80,239 N, whereas the penetration depth for a 258.5 kg underwater robot is 0.0236 m, with a maximum contact pressure of 78,336 N. This suggests that variations in mass have a relatively small impact on the penetration depth and contact pressure of the novel underwater robot. Figure 13 further supports this conclusion, demonstrating that the differences in penetration depth and pressure contours for robots of different masses at the same moment are not significant.

Thus, changing the shell material of the novel underwater robot has a limited impact on its penetration depth, contact pressure, and velocity changes, but it can significantly alter its compressive strength and other performance characteristics. This suggests that in designing underwater robots, selecting appropriate materials can enhance compressive strength to cope with the complexities of the seabed environment and high-pressure challenges, without excessive concern for how mass changes might affect penetration depth and speed. Moreover, by optimizing materials, designers can maintain the flexibility and stability of the robot while ensuring its structural strength, thereby improving its adaptability and efficiency in diverse marine conditions.

4.5. Effect of Pad Area on the Landing Process of Underwater Robots

The force analysis in Equation (2) indicates that the total projected area of the footpads of the novel underwater robot is directly proportional to the inertial drag resistance of the soil, which in turn affects the penetration depth and contact pressure. To verify this relationship, numerical simulations were performed under specific conditions: the underwater robot descends vertically at a speed of 3 m/s, starting with its footpads in contact with the surface of a sandy seabed. By varying the footpad area (with diameters of 100 mm, 200 mm, and 300 mm), the impact on the landing process was analyzed. The simulation results are summarized in Figure 14, with the final penetration depths and maximum contact pressures presented in Table 1 and

Table 6. Effect of footpad area on penetration depth and bottom contact pressure.

Pad Diameter D (mm)	Penetration Depth (m)	Maximum Pressure (N)
100	0.031	80,239
200	0.0184	214,000
300	0.0182	374,000

.

As shown in Figure 14, variations in the footpad area have a minimal effect on the speed of the underwater robot but significantly influence the time it takes for the speed to reach zero. As the footpad area increases, the time to reach zero decreases. This occurs because a larger footpad area experiences greater end-bearing resistance from the soil, causing the robot to decelerate more rapidly. Additionally, the increased end-bearing resistance reduces penetration depth and increases contact pressure.

Data from Table 6 further support these findings: as the footpad area increases, the penetration depth of the novel underwater robot decreases, while the maximum contact pressure increases. Specifically, for footpad diameters of 100 mm, 200 mm, and 300 mm, the penetration depths are 0.031 m, 0.0184 m, and 0.0182 m, respectively; the maximum contact pressures are 80,239 N, 214,000 N, and 374,000 N, respectively. These results are consistent with the pressure contours shown in Figure 15.

From the results, it can be concluded that increasing the footpad area leads to a decrease in penetration depth. A larger footpad area significantly increases the support force exerted by the soil on the underwater robot, thereby reducing the robot’s penetration depth during landing. This effect is especially pronounced under conditions of high soil strength, where a larger contact area effectively disperses the impact force, limiting further penetration into the soil. While the overall pressure is distributed over a larger area as the footpad area increases, the pressure per unit area (contact pressure) may actually rise, particularly in high-strength soils where contact pressure increases significantly. Additionally, a larger footpad area enhances friction and support from the soil, causing the robot to stop more quickly after landing. This phenomenon indicates that increasing the footpad area effectively reduces the robot’s kinetic energy during impact, thereby limiting its movement range in the soil.

In designing underwater robots, the selection of footpad area must consider factors such as penetration depth, contact pressure, and motion stopping speed. A larger footpad area can enhance the stability and load-bearing capacity of the robot in soft soils but may also increase local contact pressure. Furthermore, due to the rounded and flat design of footpads, underwater robots are prone to being buried in mud and sand during operations, which can complicate their ability to float up after completing a task. A larger footpad area makes it more difficult for the robot to regain buoyancy. Therefore, designers should select the footpad area based on specific application scenarios and operational requirements to optimize both performance and structural stability.

4.6. Selection of New Underwater Robot Materials

Selecting appropriate materials that can withstand pressure is crucial in designing a novel underwater robot. Considerations must include resistance to water pressure, corrosion, strength and stiffness, lightweight properties, and wear resistance to ensure stable underwater operation and fulfillment of various task requirements. This section, in conjunction with the previously discussed simulation results, focuses on analyzing material strength and stiffness to identify those that minimize or prevent damage during collisions with seabed soil, thereby ensuring reliable operation.

Underwater robots typically utilize the following materials: stainless steel, known for its good corrosion resistance and strength but characterized by high density and weight; titanium alloy, which offers high strength, excellent corrosion resistance, and both high- and low-temperature stability, though it is expensive; aluminum alloy, valued for its lightweight, high strength, and good conductivity, but it has poor corrosion resistance; and carbon fiber composite materials, which provide high strength, stiffness, light weight, and corrosion resistance, but are costly and challenging to process.

Table 7. Material strength and stiffness parameter table.

Material	Compressive Strength (MPa)	Bending Strength (MPa)	Elastic Modulus (GPa)	Price ($/kg)
steel	170–205	360–510	193	1–2
titanium alloy	900–1000	800–1500	113	50–80
aluminum alloy	310–450	130–320	71.5	4–8
carbon fiber composite material	1000–2000	1000–2000	100–200	10–25

presents the relevant parameters of strength and stiffness for these materials.

The formula for calculating the compressive strength of the material is as follows:

$$\sigma =F/A$$

(3)

In the equation, σ represents the compressive strength in MPa, F denotes the pressure in N, and A is the cross-sectional area of the material in the direction of the applied force in m².

In this study, the supporting legs are identified as the weak structural components of the novel underwater robot. Therefore, the stress state of the supporting legs is a primary consideration. This can be simplified to an analysis of a cantilever beam structure under load. The formula for calculating the bending strength of the material is as follows:

$${\sigma }_1={\displaystyle \frac{M\cdot y}{I_z}}$$

(4)

In the equation, σ₁ is the bending stress in MPa, M is the bending moment in N·mm, y is the distance from the neutral axis to the outermost fiber in mm, and I_z is the moment of inertia of the beam’s cross-section in mm⁴.

From Table 4, it is evident that as the landing velocity of the novel underwater robot increases, the maximum contact pressure also rises. At a landing velocity of 5 m/s on sandy seabed soil, the maximum contact pressure reaches 134,593 N. Under these conditions, the maximum compressive stress on the robot’s supporting leg is 48.5 MPa, which is within the compressive strength range of the materials listed in Table 7. However, the calculated maximum bending stress is 593 GPa, which significantly exceeds the bending strength of all materials listed in Table 7. At a landing velocity of 1 m/s on sandy seabed soil, the maximum contact pressure is 24,441 N. Here, the maximum bending stress on the supporting leg is 975 MPa, which surpasses the bending strength of stainless steel and aluminum alloy but can be withstood by titanium alloy and carbon fiber composite materials.

To verify the conclusions made above, finite-element analysis of the robot’s structure is conducted. Figure 16 presents the strain distribution of the underwater robot’s overall structure, where supporting legs and footpads made of steel and titanium alloy are studied and two different pressure conditions are applied. At a speed of 5 m/s and a bottom pressure of 134,593 N, both steel and titanium support legs show deformation, but the deformation is significantly greater in the steel legs than in the titanium legs. At a speed of 1 m/s and a bottom pressure of 24,441 N, the steel legs exhibit deformation, while the titanium legs remain mostly unchanged. These results are consistent with previous calculations. The figure shows that the maximum strain occurs in the support legs and their connections to the wings during a collision, indicating that structural design significantly impacts the mechanical properties of the underwater robot. Under the same pressure conditions, the deformation of steel legs is much greater than that of titanium legs, highlighting the importance of material selection on the robot’s strength and stiffness. Therefore, optimizing the mechanical properties of underwater robots requires careful consideration of both structural design and material selection.

Based on the calculations and analysis, the following measures are recommended to ensure the safe operation of the new underwater robot: limit the landing speed to below 1 m/s to reduce contact pressure and bending stress; use high-strength materials, such as titanium alloy or carbon fiber composites, for critical components like support legs to enhance bending strength; increase the cross-sectional area of the support legs to improve bending resistance; and incorporate a curved design at the junction between the support legs and the wing to prevent stress concentration. Additionally, selecting appropriate materials is crucial for the safety of wing panels and other structural components. At the same time, a safety factor for material under different falling speeds can be proposed, which must be taken into account in the robot material selection and structural design process. Using these measurements will significantly enhance the structural integrity and operational safety of the underwater robot and ensure its normal function even after collisions with the seabed.

5. Conclusions

Based on the ALE algorithm in LS-DYNA 2022R1 [27], this study simulates and analyzes the deep-sea landing process of a novel underwater robot. The results reveal that the penetration depth and impact pressure are affected by the seabed soil properties, landing velocity, the robot’s mass, and the footpad area. The following conclusions can be drawn.

(1) 

Seabed soil properties. Higher density and strength of the seabed soil increase the resistance encountered by the underwater robot during penetration, resulting in a shallower penetration depth and higher maximum pressure upon impact. For instance, when the seabed soil density increased from 1360 kg/m³ to 1800 kg/m³, the penetration depth decreased by approximately 92%, and the contact pressure doubled.

(2) 

Landing velocity. A higher landing velocity leads to a greater penetration depth and higher maximum pressure upon impact. For example, increasing the landing velocity from 1 m/s to 3 m/s resulted in a 21% increase in penetration depth and a 2.3-fold increase in contact pressure. Similarly, increasing the velocity from 1 m/s to 5 m/s resulted in a 25% increase in penetration depth and a 4.5-fold increase in contact pressure.

(3) 

Robot mass. An increase in the underwater robot’s mass causes a greater penetration depth and higher maximum pressure upon impact, although this effect is relatively minor. When the robot’s mass increased from 258.5 kg to 451 kg, the penetration depth increased by approximately 27%, and the contact pressure rose by about 2.4%.

(4) 

Footpad area. A larger footpad base area leads to a reduced penetration depth and higher maximum pressure upon impact. For instance, increasing the footpad diameter from 100 mm to 200 mm decreased the penetration depth by about 40.6%, while the contact pressure increased by approximately 1.67 times. Further increasing the footpad diameter to 300 mm resulted in a 41.3% decrease in penetration depth and a 3.67-fold increase in contact pressure.

These conclusions demonstrate that seabed soil properties, landing velocity, and footpad area significantly affect the penetration depth and contact pressure of the underwater robot. In contrast, the robot’s mass has a relatively minor effect on contact pressure. Additionally, it is recommended to construct the supporting legs, which are the weakest parts of the overall structure, from titanium alloy or carbon fiber composites. This would improve their bending and compressive strength, ensuring that collisions do not hinder the robot’s subsequent operations.

This study provides a critical theoretical foundation and reference data for the deep-sea landing process of new underwater robots, offering guidance for their design and application. Future research could expand on several aspects, such as incorporating the presence of water and gas in seabed soil by developing a more accurate multiphase flow model to better simulate the landing process. Additionally, simulating a more realistic ocean environment and considering the effects of other potential variables (such as different ocean conditions and currents) on the penetration process would be beneficial. Employing a more precise nonlinear material model to describe the mechanical properties of seabed soil could help reduce data errors. Furthermore, conducting field tests would help verify the accuracy of numerical simulation results while optimizing the simulation model to enhance its precision. With continued research, it is anticipated that new underwater robots will be used more safely and reliably in deep-sea exploration, resource development, and other fields, thereby contributing significantly to human exploration of the ocean.