High–slip wheel–terrain contact modelling for grouser–wheeled planetary rovers traversing on sandy terrains

doi:10.1016/j.mechmachtheory.2020.104032

Mechanism and Machine Theory

Volume 153, November 2020, 104032

https://doi.org/10.1016/j.mechmachtheory.2020.104032 Get rights and content

Highlights

•
Wheel-terrain contact modelling and experimental verification for high-slip scenarios were performed.
•
Wheel-terrain contact angles were measured using a developed apparatus and computer-vision-based algorithm.
•
Wheel travelling performance was predicted accurately using established closed-form analytical models.
•
Mean value of relative error of in-situ estimated drawbar pull can be captured within 6.0%.

Abstract

Grouser-wheeled planetary rovers will continue to be used to cruise Mars in lined up missions. Active perception of wheel–terrain contact mechanics under high slip is necessary to manage time delays in teleoperations in order to prevent rovers from becoming stuck. Owing to severe soil particle flows, existing wheel–terrain contact mechanics models cannot be extended to predict the travelling performance of a driving wheel affected by high slips. Hence, wheel–terrain contact angles are measured using both a newly developed apparatus and computer-vision-based algorithm. The typically accepted entrance angle is considerably larger than the actual one, and the magnitude of ratio of the leaving angle to the actual entrance angle increases linearly with the slip ratio. Based on the actual entrance and leaving angles, wheel travelling performance can be predicted accurately using improved closed-form analytical models. Compared with experimental data, the mean value of relative error of an in-situ estimated drawbar pull can be reduced from 36.88% to 4.73%.

Introduction

CNSA, NASA, and ESA plan to explore Mars using landing wheeled planetary rovers (WPRs) in 2020 [1]. To manage time delays in teleoperations, the rovers included in the next wave of Mars exploration must traverse a significant distance with low or zero supervision of Earthbound operators. Additionally, they require greater on-board autonomy and all computations should be performed on board [2], [3], [4].

Owing to excessive sinkage, NASA's Spirit rover became stuck in a Martian patch of soft soil called “Troy” in 2009, as shown in Fig. 1(a). The Mars Exploration Rover team at NASA's Jet Propulsion Laboratory performed a series of tests using a test rover to assess possible solutions to remove Mars rover Spirit from ‘Troy’, as depicted in Fig. 1(b). Finally, they gave up the effort to free Spirit, indicating that thorough studies regarding wheel–terrain contact mechanics, particularly under high slip conditions, must still be conducted to prevent rovers from becoming stuck.

The slip ratio of high-slip conditions was restricted to the range of from 0.6 to 0.9, whereas the extreme case of in-situ rotation without moving forward (i.e. the slip ratio is equal to 1.0) is not the focus of this study. The objective of this study is to establish high-fidelity closed-form analytical wheel–terrain contact mechanics models for high–slip conditions.

Information regarding high-slip conditions for planetary exploration rovers is scarce. To detect the wheel slippage and immobilisation of WPRs, Gonzalez et al. proposed a novel methodology based on machine learning and proprioceptive sensing using IMU sensors [5]. Various slip levels (i.e. low, moderate, and high) can be detected with high success rates even the slip ratio is larger than 0.6, whereas the sophisticated wheel–terrain contact mechanics under high-slip conditions was not considered.

For low- and moderate-slip conditions, extensive studies have been conducted. Iagnemma et al. established an online terrain parameter estimation method for a planetary rover prototype traversing on a sandy terrain [6]. Only the internal friction angle and cohesion can be estimated accurately, whereas classical values were used for terrain pressure-sinkage characteristic parameters.

Ray proposed a multiple-model estimation method rooted in Bayesian statistics to estimate terrain parameters and a drawbar pull traversing on a sandy terrain [7]. Based on the estimated terrain parameters, the computed drawbar pull can track the truth with reasonable accuracy except at high-slip conditions.

Sutoh et al. modelled wheel–terrain contacts based on Bekker's normal stress equation [8] and Janosi's shear stress equation [9] to estimate a WPR's travelling performance when the slip ratio ranged from 0 to 0.8 [10]. The difference between the simulation and experimental results increased with slip ratio. For a wheel with a diameter of 327 mm and a width of 150 mm, when the slip ratio was 0.3, the relative error of the estimated drawbar pull was approximately 40%. Finally, they concluded that the travelling performance of lightweight planetary rovers could not be accurately estimated based on traditional wheel–terrain contact mechanics theories.

Moreover, the authors developed high-fidelity models to analyse the impact of various physical effects, such as wheel lug, slip sinkage, wheel radius and width, and vertical load effects, on the wheel–terrain contact mechanics [11]. Compared with experimental data, the maximum relative error of an offline predicted drawbar pull after the wheels entered steady states was less than 10% when the slip ratio ranged from 0.05 to 0.6. Owing to the sophisticated nature of wheel–terrain contact mechanics, in addition to traditional terrain mechanical parameters, 11 additional empirical parameters are required for modelling. These 11 parameters can be determined using an iterative optimisation algorithm, and the selection of their initial values requires an in-depth understanding of their effects on wheel–terrain contact mechanics. Moreover, if the slip ratio is larger than 0.6 (i.e. at high-slip conditions), the increase in the drawbar pull cannot be predicted accurately.

The complexity of traditional wheel–terrain contact mechanics theories requires expensive computation, thereby severely limiting the autonomy of WPRs. To overcome this issue, based on the proposed linear normal and shear stresses, the authors established closed-form analytical models that can be used to estimate equivalent terrain mechanical properties and drawbar pull on board for low- and moderate-slip conditions [12]. However, if the slip ratio is larger than 0.6, the performance of these analytical equations becomes unacceptable.

The focus of this study is the high–slip wheel–terrain contact modelling of grouser–wheeled planetary rovers. The limitations of existing high–fidelity wheel–terrain contact models and closed–form analytical models for low– and moderate–slip scenarios when extended to high slip conditions was first investigated. Subsequently, the effect of severe soil particle flow induced by high slips on wheel–terrain contact angles was investigated using both a developed multifunction wheel and a computer–vision–based algorithm. Based on actual wheel–terrain contact angles, high–slip closed–form analytical models were finally established and then validated using single wheel experiments.

The remainder of this article comprises four parts. Part 2 introduces the limitations of high-fidelity models and closed-form analytical models for low and moderate slips when applied to high-slip conditions. The effect of severe soil particle flows under high-slip scenarios is investigated in Part 3. The improved wheel–terrain contact modelling and experimental verification are presented in Part 4. Finally, the summary and discussion of this study are presented in Part 5.

Section snippets

Limitations of existing wheel–terrain contact mechanics theories

Wheel–terrain contact mechanics experiments under various slip ratios conducted in soil bins can be used to reveal the contact mechanics between a wheel and a terrain. The slip ratio s is defined as a function of the theoretical forward velocity rω and actual forward velocity v, as shown in Eq. (1). Longitudinal slip conditions can be categorised into four classes, i.e. low slip (0 ≤ s ≤ 0.3), moderate slip (0.3 < s ≤ 0.6), high slip (0.6 < s ≤ 0.9), and becoming stuck (s = 1.0). $s = 1 - \frac{v}{r ω} 0 \leq s \leq 1$

Wheel–terrain contact angle measurement

In the proceeding analysis, the wheel sinkage z₁ used to compute the entrance angle θ₁ was measured using a linear displacement sensor, which employs an undisturbed soil surface as a reference. The photograph of the wheel–terrain interactions under the slip ratio of 0.8 is shown in Fig. 11. As shown in Fig. 11, owing to the severe soil particle flow, a soil mound higher than the undisturbed soil surface behind the wheel was formed, as shown in Fig. 11(a). Moreover, because of this phenomenon, a

Improved modelling considering actual wheel–terrain contact angles

The equivalent wheel–terrain contact stresses distributed along the equivalent wheel radius r_e, as shown in Fig. 5. The actual leaving angle θ₂ computed in SubSection 3.2 and the lug effect on wheel sinkage Δz_G estimated in SubSection 2.2 can be substituted into Eq. (20) to compute the equivalent leaving angle θ_2e. $θ_{2 e} = - arccos \frac{r \cos θ_{2}}{r_{e}} = - arccos \frac{r \cos θ_{2}}{r + Δ z_{G}}$

Considering both the equivalent entrance angle θ_1e and equivalent leaving angle θ_2e, the coefficients k_1e, k_2e, and k_3e as shown in Eq. (13) can

Conclusions and discussions

This paper focuses on wheel–terrain contact mechanics modelling for high-slip scenarios that can be used to estimate wheel travelling performance accurately. Under the experimental conditions reported herein, the findings of this study can be summarised as follows:

(1)
If the effect of severe soil particle flow on wheel–terrain contact mechanics is not considered, then the high-fidelity and closed-form analytical models for low- and moderate-slip scenarios cannot be extended to predict high-slip

Funding

This study was supported in part by the National Natural Science Foundation of China [Grant No. 51,905,119, 51,822,502, 51,705,096], Fundamental Research Funds for Central Universities [Grant No. HIT.NSRIF.2020090], and Self-Planned Task of State Key Laboratory of Robotics and System [Grant No. SKLRS202003C].

Declaration of Competing Interest

None.

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Research paperHigh–slip wheel–terrain contact modelling for grouser–wheeled planetary rovers traversing on sandy terrains

Highlights

Abstract

Introduction

Section snippets

Limitations of existing wheel–terrain contact mechanics theories

Wheel–terrain contact angle measurement

Improved modelling considering actual wheel–terrain contact angles

Conclusions and discussions

Funding

Declaration of Competing Interest

Mech. Syst. Signal Process

Robot. Auton. Syst.

J. Terramech.

Mech. Mach. Theory

Mech. Syst. Signal Process

J. Terramech.

J. Terramech.

Mech. Mach. Theory

J. Terramech.

J. Terramech.

Mech. Mach. Theory

Robot. Auton. Syst.

ARDEA—An MAV with skills for future planetary missions

J. Field Robot.

SLAM for autonomous planetary rovers with global localization

J. Field Robot.

Research paper
High–slip wheel–terrain contact modelling for grouser–wheeled planetary rovers traversing on sandy terrains