In situ identification of shearing parameters for loose lunar soil using least squares support vector machine
Introduction
Unmanned Ground Vehicles (UGVs) are an important method of data collection for conducting scientific research during lunar or Mars exploration missions. The planetary surfaces of the Moon and Mars are very rough, covered by loose regolith composed of dust and rock, which impedes the mobility of UGVs. For example, the Sprint and Opportunity rovers became deeply embedded in loose sand during their explorations of Mars [1], [2]. Fortunately, after several weeks of attempts, the Opportunity rover was finally freed from Purgatory on Sol 484. The driving force generated by the wheels thrusting through soil is insufficient to overcome the resistance created by this kind of loose terrain, causing the slip ratio and sinkage to increase. Understand soil mechanics, such as the internal friction angle φ, cohesion c and shear deformation modulus K, is an important task for researchers. It is desirable to estimate terrain parameters online, since such knowledge, combined with a wheel–terrain interaction dynamic model, allows researchers to predict vehicle drawbar pull, which can be used for trafficability prediction, traction control and risk assessment [3]. Also, knowledge of terrain parameters would assure a safe landing for planetary lander [4].
Two main methods can be used to obtain planetary soil mechanics. The first method, which can provide exact information, is to collect samples of the planetary soil and return them to earth. The second method is in situ observation, which allows the soil mechanics to be obtained in the absence of planetary soil. Many research groups conduct research on soil mechanics through the online estimation of planetary soil based on terramechanics for planetary rovers.
Researchers from NASA and JPL have performed investigations to identify the parameters of Martian soil. They used Sojourner and MER rover wheels as a shear test device and the Mohu–Coulomb failure criteria to identify soil cohesion and internal friction angle [5], [6], [7], [8], [9], [10]. However, this method not only exacerbates wheel wear, but could also threaten the safety of mobile systems. Also, the method was an offline analysis technique. Since the communication time delays from Earth to Mars is about 3–21 minutes in a one-way transmission, the method may limit the UGV's autonomy and reduce its efficiency.
Based on the classical terramechanics equations proposed by Bekker [11] and Wong and Reece [12], [13], [14], Iagnemma [15], [16], [17], [18] used a linear-least squares estimator to estimate terrain parameters such as cohesion and internal friction angle using onboard sensors. However, at least two unique datasets combined with large-scale slip were required to estimate terrain parameters and shear deformation modulus should be pre-determined. Hutangkabodee [19], [20], [21], [22] used Newton Raphson method to identify lumped pressure sinkage coefficient, internal friction angle and shear deformation modulus, while cohesion was set to 3 kPa. This method required at least three sets of measured data to identify three soil parameters. Cui [23] used Newton's iterative method for computing terrain parameters such as internal friction angle and press–sinkage parameter. However, the method also required a reasonable cohesion to be determined beforehand. Ding [24], [25], [26], [27], [28], [29] proposed a set of closed-form analytical equations to identify three groups of planetary soil parameters: contact angle coefficients, bearing performance parameters and shearing performance parameters. A cyclic iterative parameter identification approach was applied to estimate the three sets of parameters step-by-step, using measured data obtained from a wheel–soil interaction test system. In this process, drawbar pull DP should be used as input data when calculating the contact angle coefficients. However, it is difficult to acquire precise DP information directly during planetary exploration missions [17]. Cross [30], [31] proposed a trained neural network for estimating cohesion and internal friction angle online for a rigid wheeled rover. However, the terrain parameter of the shearing deformation modulus should be set to a suitable value before computing DP. A vibration-based technique was employed to classify terrain type but not to estimate terrain parameters [32]. Based on Newton–Raphson method, Tan [33] and Yousefi Moghaddam [34] done a lot of work to estimate terrain parameter online, however their application was for excavation and not based on wheel–terrain interaction.
The purpose of this study is to develop a method for predicting terrain-shearing parameters online. The multiple-outputs Least Squares Support Vector Machines (LS_SVM) method is used to map engineering data based on simplified classical terramechanics equations. The input data for the LS_SVM comprise wheel load W, torque T and slip ratio s, and output data include three terrain-shearing parameters: cohesion c, internal friction angle φ and shearing deformation modulus K. This method can be used to estimate for [] with a set of data [], which can allow a vehicle to autonomously traverse the planetary surface and ‘feel’ changes of rough terrain in real time during traveling through deformable terrain. Using terrain-shearing parameters, DP and tractive efficiency η can be calculated, which can also be used for optimal route planning, traction control and traversability prediction of a vehicle on off-road terrain.
Section snippets
Mechanics of vehicle
Shear stress distribution acting on a point along a wheel rim can be obtained from the following Eq. (1) [14], [35]: where is shear stress, is normal stress, r is wheel radius, θ is an angular location, and is entrance angle.
Fig. 1 shows a free-body diagram of a driven rigid wheel of radius r and width b traveling through deformable terrain, where z is sinkage. Fig. 1 shows normal distribution under the action of a driven wheel
Soil bin testbed
A series of experiments was performed in a laboratory soil bin, shown in Fig. 3(a), to explore the interaction between the wheel and different lunar soil simulants. The test signal system can collect and store information from the sensors, including the vertical wheel sinkage, torque, slip ratio and drawbar pull. The griddle net wheel used in this experiment had 24 grousers, and the wheel diameter and width were 0.15 m and 0.15 m, respectively, as shown in Fig. 3(b). And the wheel was all
Prediction results under slip ratios
Fifty experimental data sets were used to estimate the terrain-shear parameters. W was set to 30 N, and then 50 N, and the constant s were approximately 0.2, 0.3, 0.4, 0.5 and 0.6. These two values, combined with T value obtained from the test, were entered into the trained LS_SVM model. The output of the model provides the estimates of simultaneously, as shown in Fig. 4, Fig. 5, Fig. 6, respectively.
In Fig. 4, estimated φ is generally between 28.73° and 29.76° with an average of 29.40°
Conclusions
This study investigated a trained multiple-output LS_SVM method for online and real time terrain-shearing parameters estimation, including the cohesion, internal friction angle and shear deformation modulus, for a UGV traversing unknown terrain. Experimental results from a single-wheel testbed operating in JLU_2 lunar soil simulant show that DP predicted from the estimated terrain-shearing parameters are shown to be in good agreement with the measured values with a correlation coefficient (R)
Conflict of interest statement
No conflict of interest.
Acknowledgements
The authors thank the anonymous reviewers for their critical and constructive review of the manuscript. This study was co-supported by the National Natural Science Foundation of China (No. 51375199), Science Fund of Shanghai Key Laboratory of Spacecraft Mechanism (No. SHKLSM201412005), National Defense Pre-research Foundation of Jilin University (No. JDXJY20130207) and Research Founds of Key Laboratory of Bionic Engineering of China (No. K201406).
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