Experimental Investigation of Enhanced Bearing Capacity Due to Vibration on Loose Soils Under Low-Atmospheric-Pressure Conditions ^†

Abstract

Legged rovers are gaining interest for planetary exploration due to their high mobility. However, loose regolith on celestial surfaces like the Moon and Mars often leads to slippage as legs disturb the soil. To address this, a walking technique has been proposed that enhances soil support by transmitting vibrations from the robot’s legs. This approach aims to improve mobility by increasing the ground’s bearing capacity. To evaluate its effectiveness in space-like environments, this study experimentally investigates the effect of vibration on bearing capacity under low atmospheric pressure, which can influence soil behavior due to reduced air resistance. Using Silica No. 5 and Toyoura sand as test materials, experiments were conducted to compare bearing capacities under standard and low pressure. The results demonstrate that applying vibration significantly improves bearing capacity and that the influence of atmospheric pressure is minimal. These findings support the viability of vibration-assisted locomotion for planetary rovers operating in low-pressure extraterrestrial environments.

1. Introduction

1.1. Current Trends in Lunar and Planetary Exploration

Exploration of the Moon and planets is essential for understanding the solar system’s formation and evolution. Studying their geology and surface environments sheds light on Earth’s origin and the conditions for life. Simon et al. (2023) analyzed Mars rover Perseverance samples from Jezero Crater, finding mostly igneous rocks with carbonates and sulfates altered by water-related processes [1], indicating ancient aqueous environments. Returning these samples will enable precise dating and organic analyses to clarify Mars’s geological and hydrological history and its potential for past life. Similarly, analyses of lunar far-side samples from China’s Chang’e-6 mission revealed 2.8-billion-year-old basaltic rocks, showing prolonged volcanic activity and prompting a revision of lunar mantle thermal models [2]. These findings highlight the value of sample-return missions.

The Moon and Mars also serve as critical bases for future human exploration and sustainable space use. Developing in situ resource utilization (ISRU) and long-term habitation technologies under extreme conditions is key to space sustainability and benefits terrestrial tech. NASA’s Artemis program plans to build a lunar base camp near the South Pole by the late 2020s, supporting crews for up to 60 days with habitats, pressurized rovers, and stable power from solar, fuel cells, and compact nuclear reactors [3]. Demonstrations of ISRU aim to reduce Earth resupply needs. Concurrently, NASA’s CHAPEA program simulates Mars habitation on Earth; since June 2023, four crew members have lived in a 3D-printed habitat under Martian-like conditions, gaining insights into resource management, teamwork, and health maintenance [4].

In conclusion, Moon and planetary exploration advances scientific knowledge, drives space technology innovation, and supports sustainable human development.

1.2. Overview of Mobility Systems of Rovers for Extraterrestrial Body Exploration

In lunar and Martian exploration, robotic vehicles known as rovers have been deployed to navigate and perform various tasks on planetary surfaces. Traditional missions have predominantly employed wheeled rovers due to their relatively simple control mechanisms and proven reliability. For instance, NASA’s Perseverance rover, equipped with the Mars Environmental Dynamics Analyzer (MEDA), has collected comprehensive meteorological data—such as atmospheric pressure, wind speed, temperature, humidity, and dust—at Jezero Crater on Mars [5]. These observations have significantly advanced understanding of the dynamic Martian atmosphere and its weather patterns. Similarly, the Chinese lunar rover Yutu-2 conducted topographic surveys of the Von Kármán crater on the Moon’s far side, revealing ejecta distribution and crater floor deformation that inform the geological history of the region [6]. However, wheeled rovers are prone to immobilization when wheels lose traction on soft or unstable terrain, as exemplified by the Mars rover Spirit becoming trapped in loose regolith [7]. Such mobility challenges are especially critical in complex terrains including steep slopes and cratered surfaces, prompting the need for rover systems with enhanced terrain adaptability.

In response, legged robots, particularly multi-legged rovers, have garnered attention as next-generation planetary exploration platforms due to their superior mobility and high degrees of freedom. By independently controlling each leg, these systems can effectively negotiate uneven terrain and overcome obstacles that challenge wheeled designs. Moreover, legged rovers can adjust ground contact pressures through leg articulation, providing stable support on soft or loosely compacted surfaces. NASA’s All-Terrain Hex-Limbed Extra-Terrestrial Explorer (ATHLETE), a six-legged, six-wheeled hybrid rover, exemplifies this approach by enabling high-speed wheeled locomotion on flat terrain and legged walking on rugged surfaces. Each limb also functions as a manipulator for scientific tasks, infrastructure deployment, and in situ resource utilization across various extraterrestrial environments [8]. Additionally, the Space Hopper, developed by Spiridonov et al., is a compact tripod-legged rover designed for low-gravity environments such as asteroids. It utilizes hopping locomotion and leg-based attitude control instead of traditional reaction wheels. With a mass of approximately 5.2 kg and CubeSat-compatible structure, it employs deep reinforcement learning (DRL) for autonomous attitude control, achieving hops up to 6 m with high landing accuracy in both terrestrial and simulated low-gravity conditions [9]. These features position the Space Hopper as a promising platform for exploring rugged, previously inaccessible terrains on the Moon and small bodies.

1.3. Introduction to Our Previous Research

Legged rovers possess an advantage in navigating obstacles, such as rocks, due to the high degree of freedom in their limbs, allowing for the selective placement of feet on the terrain. However, they tend to perform poorly on loose substrates because slippage occurs as the terrain deforms under foot, impeding forward motion. Since the surfaces of the Moon and Mars are characterized by loose granular materials—known as regolith—and uneven landscapes, legged rovers must demonstrate effective locomotion capabilities on such unstable ground. In previous work, we introduced a novel walking strategy that utilizes vibrations to alter the ground state and reduce slippage during movement on loose soils [10]. That study focused on examining how ground properties such as density and shear strength respond under different vibrational conditions. Specifically, the correlation between shear strength, measured using a hand vane tester, and ground density was established. Measurements were conducted before, during, and after the application of vibrations. During vibrations, both density and shear strength decreased. In contrast, vibrations were applied but increased beyond initial levels once vibrations ceased. This indicates that the mechanical state of the soil varies dynamically with the vibration input. Figure 1 schematically represents particle behavior inferred from these observations. Under normal static conditions, soil particles remain in contact with one another and are stabilized by frictional forces (shear resistance). Therefore, prior to vibration, voids exist between soil particles (Figure 1a). When vibration is applied to the soil, repetitive accelerations (inertial forces) act between the particles. In this condition, the ground particles are flowing, as shown in Figure 1b. As the particles flow, the number of interparticle contacts decreases compared to the static state, resulting in a temporary reduction in frictional forces (shear resistance). When vibration is applied, the frictional resistance between particles temporarily decreases, allowing the particles to be more easily mobilized under the influence of gravity. As a result, particles relocate and fill the voids that previously existed within the soil structure after vibrations stop (Figure 1c). This particle rearrangement leads to an increase in bulk density, which in turn enhances the contact area between particles. The increase in interparticle contact promotes higher frictional resistance, thereby contributing to an improvement in the shear strength of the ground.

Building on this understanding, we developed a coordinated walking pattern combining leg motions with timed vibrations to enhance ground reaction forces and minimize slippage. The proposed gait sequence is illustrated in Figure 2. Initially, the leg advances (Figure 2b). Upon ground contact, vibrations are activated (Figure 2c), softening the soil and allowing the leg to penetrate more easily. Subsequently, vibrations are halted to allow soil compaction and density increase (Figure 2d). This compaction results in an increased bearing capacity on the leg due to greater leg sinkage and denser ground, which expands the slip line—the interface separating moving soil particles influenced by the leg from stationary particles (Figure 3a). A longer slip line corresponds to stronger bearing capacity against the leg, as shown in Figure 3b,c. Prior research confirms that slip line length grows with increased leg penetration and soil density [12,13]. To validate this approach, we conducted experiments with a legged prototype traversing inclined loose soil surfaces. Comparative tests between walking with and without vibration demonstrated notable improvements in traversal distance, confirming the efficacy of the vibration-assisted gait.

The experimental environment used to evaluate the proposed walking method using vibrations in the previous study differed slightly from the actual conditions on the Moon and other planets. For example, the experiment in the previous research was conducted at Earth’s standard atmospheric pressure. To evaluate whether the proposed walking method is helpful in actual space exploration missions, investigating the increased bearing capacity by imparting vibration is essential in simulated environments, such as those on the Moon and other planets, particularly in conditions with low atmospheric pressure.

1.4. Research Overview

A previous investigation proposed a walking strategy for legged space exploration rovers that utilizes vibrations to prevent slippage. Building on this, the present study investigates how vibrations impact bearing capacity in low-pressure environments, such as those on Mars and the Moon. The experimental setup involved placing the apparatus within a chamber simulating reduced atmospheric pressure, where the bearing capacity was measured. During the tests, a rod was sunk into the soil and subjected to vibrations and then dragged across the surface to evaluate the bearing capacity. Measurements were conducted under both normal and low-pressure conditions for comparison. The findings confirmed that vibration effectively enhances bearing capacity regardless of atmospheric pressure, with only minor differences observed between standard and low-pressure conditions. These results suggest that low-pressure conditions have minimal impact on the vibration-induced improvement in bearing capacity, indicating that vibration-assisted locomotion is a viable approach for traversing loose soils in extraterrestrial environments.

This paper is structured as follows: Section 2 details the experimental apparatus and procedures, Section 3 presents the results and discusses the influence of vacuum conditions on bearing capacity enhancement through vibration, and Section 4 concludes this study.

2. Methods

2.1. Explanation of Increasing Bearing Capacity by Vibration

Vibration-based ground compaction is commonly applied in civil engineering, particularly for building foundation construction. Numerous studies have explored how compaction equipment interacts with varying ground conditions. For example, Gao et al. analyzed the compaction behavior of soil using an internally vibrating probe, focusing on its underlying mechanism [14]. Since the probe operates by transmitting vibrations directly within the soil, it has been shown to enhance compaction efficiency. Pistrol et al. proposed an improved method for calculating the Intelligent Compaction Meter Values (ICMV), incorporating machine characteristics and operating conditions based on a drum–soil contact model [15]. The method enables integrated analysis of factors such as soil stiffness, vibration frequency, speed, and amplitude. Experiments on gravelly soils showed higher sensitivity to deformation and more stable evaluation than conventional methods.

In vacuum pressure environments such as those on the Moon or Mars, the influence of atmospheric pressure on the ground is significantly smaller than on Earth. Under such conditions, it is possible that the ground behavior associated with vibration—previously observed and characterized in terrestrial studies—may change. In particular, the reduction in air pressure leads to a decrease in air resistance within the soil pores, which may enhance the transmission of vibrations. This may result in more effective compaction of the ground and, consequently, an increase in bearing capacity. Conversely, since air resistance contributes to bearing capacity under atmospheric pressure, its absence under vacuum conditions may lead to a reduction in bearing capacity. Therefore, it is essential to investigate whether the application of vibration under vacuum conditions—simulating planetary exploration environments—can lead to an increase in bearing capacity and to clarify the underlying mechanisms.

Figure 4 is a schematic diagram of how the bearing capacity changes when a leg is dragged across the soil surface. This figure is illustrated based on the experimental result from a previous study [10]. Initially, the bearing capacity rises due to the leg’s motion compressing the soil. Once the bearing capacity reaches its maximum, it begins to decline as the soil starts to break apart. When vibration is applied (as shown in Figure 4), the peak bearing capacity is higher. This is attributed to the vibration further compacting the soil, thereby increasing its density.

2.2. Introduction to the Related Research

Understanding how ground conditions behave under low-pressure conditions is crucial for developing exploration rovers. Several research teams have examined rover locomotion mechanisms within vacuum chambers that replicate low-pressure environments. For instance, Sutoh studied the wheel mobility of a planetary rover under vacuum conditions [17]. In this study, a soil bed was prepared inside a vacuum chamber, and experiments were conducted using a single wheel of a planetary rover. By varying the type of sand used as the ground material and the rotational speed of the wheel, the relationships among traction force, slip ratio, and sinkage were investigated. The results indicated that atmospheric pressure conditions had a negligible influence on these parameters. The findings provide important insights by quantitatively demonstrating the influence of wheeled rover mobility in low-pressure and deformable terrain environments, such as those found on the lunar or Martian surface. Similarly, Reiss et al. assessed the performance of a hopper designed to transport lunar and Martian soil [18]. Their setup was also housed in a vacuum chamber, which was flown aboard an aircraft to simulate reduced gravity during parabolic flight. Comparative experiments conducted under vacuum and atmospheric pressure conditions revealed that ambient pressure significantly affects the flow stability of lunar regolith simulants, as evidenced by sudden dust ejections observed during material flow under vacuum. These findings provide essential design insights for the development of transportation and handling systems in future in situ resource utilization (ISRU) applications on the Moon and Mars. In another study, Sakatani et al. explored the thermal conductivity of lunar regolith simulant (JSC-1A) in a vacuum environment using a dedicated vacuum chamber [19]. As a result of the analysis, it was demonstrated that JSC-1A can effectively simulate the thermal behavior of lunar surface regolith.

As these examples illustrate, experiments replicating space-like conditions often involve storing the test setup inside a vacuum chamber. Following this approach, we conducted bearing capacity measurements under low-pressure conditions by placing our test setup within such a chamber.

2.3. Experiments

Figure 5a illustrates the experimental apparatus, comprising a vacuum chamber, a test setup, and a vacuum pump. A more detailed view of the test setup is presented in Figure 5b, which includes a soil container, a cylindrical rod, and a force measurement sensor. The dimensions of the soil container were 90 mm in length, 150 mm in width, and 70 mm in height. The rod was dragged along the container’s longitudinal axis. The soil used in the test bed consisted of Silica No. 5 and Toyoura sand, both of which are widely used in research related to extraterrestrial robotic mobility. The physical properties of these materials are summarized in

Table 1. Soil parameters.

Item	Silica No.5 [11,22]	Toyoura Sand [23,24]
Size of particle	106–600 $\mathrm{\mu }\mathrm{m}$	106–300 $\mathrm{\mu }\mathrm{m}$
Density	1490 $\mathrm{kg}/{\mathrm{m}}^3$	1400 $\mathrm{kg}/{\mathrm{m}}^3$
Internal friction angle	40.2$°$	30.2$°$
Related research that uses the soil as the simulated one of exterraserestial bodies	Mori and Ishigami (2015) [25], Shirai and Ishigami (2015) [26], Sutoh (2021) [17]	Kobayashi (2021) [27], Ono (2021) [28], Oe (2024) [29]

. The cylindrical rod used for the test (shown in Figure 6) had a diameter of 32 mm and was modeled based on prior studies involving legged rovers for planetary exploration [10,20,21]. The vibration mechanism embedded in the rod included a DC motor (TP-2528C-24, Three Peace Co., Ltd.), which produced vibration through rotation of an eccentrically mounted mass. The resulting oscillatory force was tangential to the motor’s rotational path, as depicted in Figure 6. For the experiment, the motor operated at 30 V, producing a vibrational force of approximately 11.9 N at a frequency of 233 Hz. A summary of the test setup is provided in

Table 2. Summary of the test setup.

Item	Condition (Value)
Vacuum chamber	1-5800-01, AZ ONE Corp., Osaka City, Japan
Vacuum pump	TA150SW-K, Ichinen TASCO Co., Ltd., Osaka City, Japan
Vibration motor	TP-2528C-24, Three Peace Co., Ltd., Kobe City, Japan
Force sensor	Load cell SC133-2kg, Sensor and Control Co., Ltd., Fuzhou, China
Type of sand	Silica No.5 and Toyoura sand

.

The procedure for measuring bearing capacity is outlined in Figure 7. The soil surface was first homogenized and leveled, after which the rod was inserted into the soil to a depth of 30 mm. Prior to testing, shear strength was measured using a handheld vane tester to assess initial ground conditions. This value served as an indicator of compaction and bulk density, and the target shear strength was maintained between 0.30 and 0.60 cN·m. If the measured shear strength fell outside this range, the soil was remixed. Following ground preparation, the chamber was evacuated to a pressure of 13 hPa. After reaching the desired vacuum condition, vibration was applied to the rod in the horizontal (xy-plane) direction for 30 s. Upon cessation of vibration, the rod was dragged through the soil at a constant speed of 1.67 mm/s for another 30 s, during which the force sensor recorded the reaction force from the ground. This test was performed under both standard and low-atmosphere conditions, with five repetitions conducted for each experimental condition. The experimental conditions are provided in

Table 3. Experimental conditions.

Item	Condition (Value)
Number of trials	5
Sinkage of the rod	30 mm
Dragged speed	1.67 mm/s
Dragged time	30 s
Supply voltage for vibration motor	30 V
Vibration time	30 s
Vibration force	11.9 N
Vibration frequency	233 Hz
Atmospheric pressure	Standard atmosphere (1013 hPa), Low atmosphere (13 hPa)

.

3. Results and Discussion

3.1. Experimental Results Using Silica No.5

Figure 8 and Figure 9 illustrate the relationship between shear displacement and bearing capacity in the absence and presence of vibration, respectively. Each plot represents the average of five experimental trials. In the case without vibration (Figure 8), bearing capacity increased initially and then reached a plateau. In contrast, when vibration was applied (Figure 9), the bearing capacity rose at first but then declined before stabilizing. Notably, the trends observed under both ambient and low-pressure environments appear comparable in both figures. These results suggest that imparting vibration also increases the bearing capacity under low-pressure conditions.

Figure 10 presents the peak bearing capacities recorded under each condition, with associated standard errors derived from five replicates. Across all pressure conditions, the application of vibration consistently led to higher peak bearing capacities compared to tests without vibration. A comparison between standard and low-atmospheric conditions reveals a difference of 0.23 N in the no-vibration case and 0.31 N when vibration was applied. Given the small magnitude of these differences, it can be inferred that the atmospheric pressure has minimal effect on the enhancement of bearing capacity through vibration.

Root Mean Square Error (RMSE) values for each condition are provided in

Table 4. RMSE value in each experimental condition using Silica No.5.

Condition	Value
Without vibration	0.185 N
With vibration	0.274 N

. The RMSE value was calculated from Equation (1).

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}\sum _{i=1}^n{|y_s\left(i\right)-y_v\left(i\right)|}^2}$$

(1)

Here, n is the amount of measured bearing capacity data from the start to the end of the time that the rod was dragged. $y_s\left(i\right)$ and $y_v\left(i\right)$ are the values of the bearing capacity under standard atmospheric pressure and under low atmospheric pressure when the data number was i. A lower RMSE value indicates a higher degree of agreement in the change in bearing capacity during traction between standard-atmosphere and low-atmosphere conditions.

Without vibration, the RMSE is 0.185 N, while with vibration it increases to 0.274 N. These relatively low RMSE values indicate that the bearing capacity responses to shear displacement remain consistent between standard and low-atmospheric environments.

3.2. Experimental Results Using Toyoura Sand

Figure 11 and Figure 12 illustrate the relationship between shear displacement and bearing capacity in the absence and presence of vibration, respectively. Each plot represents the average of five experimental trials. In both cases—without and with imparted vibration—the variation in bearing capacity with respect to the dragging distance exhibited a similar trend to that observed in the experiments using Silica No. 5. In the case without vibration (Figure 11), the trends observed under both ambient and low-pressure environments appear comparable. On the other hand, the bearing capacity at standard atmospheric pressure was larger than that at low atmospheric pressure in the case with vibration.

Figure 13 presents the peak bearing capacities recorded under each condition, with associated standard errors derived from five replicates. Similar to the experiment using Silica No.5, across all pressure conditions, the application of vibration consistently led to higher peak bearing capacities compared to tests without vibration. A comparison between standard and low-atmospheric conditions reveals a difference of 0.018 N in the no-vibration case and 1.22 N when vibration was applied. From these results, it is evident that the atmospheric pressure condition does not affect the increase in bearing capacity without vibration. However, it is possible that the bearing capacity with vibration became small due to a low atmospheric pressure.

Although no significant difference in bearing capacity was observed prior to vibration, a distinct divergence emerged after vibration, suggesting that post-vibration ground conditions differ between low-atmospheric-pressure and standard-atmospheric-pressure environments. One potential explanation for this difference is the relationship between particle size and particle mobility; smaller and lighter soil particles are generally more susceptible to movement under external forces. Toyoura sand, having finer particles than Silica No. 5 sand (Table 1), is presumed to exhibit a lower bearing capacity due to the increased mobility of its constituent particles. Furthermore, the observed reduction in bearing capacity for Toyoura sand under vacuum conditions may be attributed to the decreased air resistance, which facilitates greater particle movement. These two factors—particle size and reduced air resistance—are considered to jointly contribute to the variation in bearing capacity between vacuum and atmospheric conditions. To clarify the mechanisms behind these observations, Particle Image Velocimetry (PIV) will be employed to analyze the behavior of soil particles both during vibration and under post-vibration loading. This approach aims to determine whether differences in particle motion arise between standard and reduced-pressure environments.

The RMSE values under each condition are presented in

Table 5. RMSE value in each experimental condition using Toyoura sand.

Condition	Value
Without vibration	0.197 N
With vibration	0.898 N

. Without vibration, the RMSE was 0.197 N, whereas with vibration, it increased to 0.898 N. The lower RMSE value in the non-vibration condition indicates that there was minimal difference in bearing capacity during traction between the standard and low-atmospheric conditions. In contrast, the higher RMSE observed under the vibration condition suggests that the application of vibration caused a variation in bearing capacity due to the low-atmospheric environment.

4. Conclusions

This research explored how vibration affects the bearing capacity of ground surfaces under low-pressure environments, similar to those on the Moon and Mars. The experimental setup involved a sealed chamber with reduced atmospheric pressure. Inside, a rod was sunk into the ground and subjected to vibration. The bearing capacity was then evaluated as the rod was dragged across the surface. Results demonstrated that even under low-pressure conditions, vibration contributed to an increase in bearing capacity. Furthermore, the measured capacities under both standard and low-pressure conditions were nearly identical. This tendency was confirmed when using two kinds of soil (Silica No.5 and Toyoura sand). This indicates that low atmospheric pressure has minimal effect on the enhancement of bearing capacity due to vibration. These findings support the idea that vibration is a useful method for traversing soft or loose soil in extraterrestrial environments.

Future research will focus on developing a predictive model for bearing capacity under vibratory loading. This model will incorporate the effects of low atmospheric pressure observed in this study. Additionally, experiments will be expanded to examine a wider range of parameters, including various soil types such as regolith simulant, to gain deeper insight into performance in low-pressure environments. It is particularly important to conduct experiments using a lunar regolith simulant, as actual lunar regolith has not been subjected to atmospheric weathering. Consequently, it is composed of highly angular particles, in contrast to the rounded grains commonly found in terrestrial sands. Moreover, the particle size of lunar regolith is significantly smaller than that of the soils used in conventional terrestrial studies, necessitating material-specific considerations in evaluating compaction behavior.

A distinct divergence emerged after vibration using Tyoura sand, suggesting that post-vibration ground conditions differ between low-atmospheric-pressure and standard-atmospheric-pressure environments. To clarify the mechanisms of changing bearing capacity under vacuum pressure, Particle Image Velocimetry (PIV) will be employed to analyze the behavior of soil particles both during vibration and under post-vibration loading. This approach aims to determine whether differences in particle motion arise between standard and reduced-pressure environments.