Study on an 8Wheel Suspension to Enhance the HillClimbing Performance for a Planetary Exploration Rover
 Author: Eom WeSub, Lee JooHee, Gong HyunCheol, Choi GiHyuk
 Publish: Journal of Astronomy and Space Sciences Volume 31, Issue4, p347~351, 15 Dec 2014

ABSTRACT
Planetary exploration rovers are likely to make a trip on a winding and sloping road of irregular surfaces to the destination in order to accomplish scientific missions. One of the key technologies for rovers is a suspension for traveling and performing exploration missions; the suspension is an essential area of technology for a stable movement of a rover. In this study, an 8wheel suspension is designed to enable efficient climbing of slopes on a passage to the destination. For the two front wheels among the eight wheels, the moment at the pivot connecting two wheels is derived when the distance between the wheels and the torque of wheels are same. A test experiment was performed to compare the magnitude of moment according to the change in tilt angle and the position of the pivot. Finally, a suspension design considering the position of the pivot was proposed to enhance the hillclimbing performance.

KEYWORD
planetary exploration rover , 8wheel suspension , hillclimbing performance , moment at pivot , rockerbogie suspension

1. INTRODUCTION
Planetary exploration rovers travel a road of unknown surfaces to the destination and perform scientific missions, such as, the investigation of geology and climate, the investigation of the existence of water and alien life forms (http://science.nasa.gov/platenaryscience/missions). In order to perform these scientific missions successfully, the rover is developed to ensure the design targets: survival through the mission period and stability of movement to the destination (Eisen 1997, Siegwart et al. 2002, Chen et al. 2009). The typical suspensions applied to a conventional rover is a rockerbogie suspension developed by NASA in 1960s ~ 1970s (Eom et al. 2012a). This suspension was developed for a slowmoving system and 6wheel application is enabled through this suspension structure. The rockerbogie suspension undergoes a passive transformation in response to the shape of surfaces. Also it enables slopeclimbing of 30 degreetilt, and it is possible to maintain static equilibrium at the slope of 40 degreetilt. The suspension of rockerbogie type was applied to the first Mars Exploration Rover, Sojouner to prove its superior driving performance as shown in Fig. 1 through Fig. 3. It was subsequently applied to Spirit/Opportunity (http://marsrover.nasa.gov/home/index.html) and Curiosity (http://mars.jpl.nasa.gov/msl) (Bajracharya 2008, Eom et al. 2012a). Also at present, in addition to USA, developed nations in space technologies, such as, Europe, China, and Japan, etc., have had research projects on the suspension system of a rover lead by government funded research institutes and universities (Seeni et al. 2010, Ding et al. 2011, Trease et al. 2011).
Rovers have sensors to detect obstacles or dangers in forward or backward directions to get to the destination safely. The sensor collects the data of obstacles, such as, height, width, etc., in its way. The rover analyzes the obtained data to evaluate the possibility of stepping over the obstacle, and when it seems efficient in driving stability and power consumption to step over than to circumvent the obstacle, the rover goes on to overcome the obstacle. Therefore, in order to take account of the driving stability and power management at the same time, it is essential to have a suspension design to enable the efficient overcoming of obstacles (Kim et al. 2009, Eom et al. 2012b, Eom et al. 2014).
In this study, an 8wheel suspension is designed to enable efficient climbing of slopes on a passage to the destination considering the pivot location to evaluate the climbing performance. In Section 2, the moment at the pivot connecting the two front wheels of a rover is derived, and in Section 3, in order to compare the hillclimbing performance, a test experiment is performed to compare the magnitude of moment according to the change in the tilt angle and the position of the pivot and the results are described. Finally, conclusion is summarized in the last section.
2. DYNAMIC MODELING OF MOMENT ON PIVOT
In this section, a conceptual outline is described and the necessary parameters are defined, for the proposed suspension. Also, the dynamic modeling on the above mentioned moment which arises during hillclimbing process is described. The outline of the 8wheel suspension for a planetary exploration rover is shown in Fig. 4. The target of dynamic modeling is the center of rotation (the pivot;
C_{f} ) which connects the two wheels in the red rectangle as shown in Fig. 4.For an 8wheeled rover whose suspension system responds passively against tilted surfaces, the two front wheels’ movement is divided into 4 stages as follows during the driving transition from flat surfaces to tilted surfaces. First, all wheels are on the flat surface and Wheel 1 touches the tilted surface to begin climbing the slope. Secondly, Wheel 1 is on the tilted surface and the Wheel 2 is on the flat surface. Thirdly, Wheel 1 is on the tilted surface and Wheel 2 begins climbing the slopes. Finally, both wheels are on the tilted surface to climb the slopes. Among the four stages, the first stage at which the moment start to arise at the pivot is described in this study. The Free Body Diagram (FBD) to derive the moment at the pivot is shown in Fig. 5.
Where,
θ represents the tilted angle of the slopes, and d indicates the vertical distance from the pivot (C_{f} ) to the horizontal axis line connecting Wheel 1 and Wheel 2;l _{1} andl _{2} are distances between the pivot (C_{f} ) and the centers of Wheel 1 and 2, respectively;l _{h1} andl _{h2} represent the horizontal distances between the pivot (C_{f} ) and the centers of Wheel 1 and 2, respectively;α _{1} andα _{2} are angles betweenl _{1} andl _{h1} , and betweenl _{2} andl _{h2} , respectively;F _{h1} andF _{h2} are driving forces acting on Wheel 1 and 2 by the motor torque;F _{w1} andF _{w2} are weights on Wheel 1 and 2;F _{n1} andF _{n2} are normal force acting on Wheel 1and 2, respectively;F _{f1} andF _{f2} are friction force applied to Wheel 1 and 2, respectively;M_{f} is the moment at the pivot (C_{f} ).For ground moving robots, in order to identify the position of a robot, dynamics is derived considering the slipping effect between the wheel and the surface (Kozlowski & Pazderski 2004), however, for planetary exploration rovers, since the sensor type and the methodology of position identification are different from those of ground moving robots, thus, this effect was deemed to be negligible. Moreover, due to the planetary surface environment which consists of irregular particles with various granularities, the friction coefficient term between the wheel and the surface is considered in the design of rover wheels, it is assumed to be same for the simplicity of equations.
From the FBD of Fig. 5, the derivation process of moment (
M_{f} ) at the pivot (C_{f} ) is shown in Equation (1) through (5)where, , , , .
where, , , , .
where, ,
where, ,
The larger the moment (
M_{f} ) as derived in Equation (5) is, the less the friction force between Wheel 1 and the tilted surface. This indicates that the horizontal force acting on Wheel 1 on the slope decreases and the vertical force increases, thus, when climbing the tilted planetary surface of particles with low binding force such as a dry sand dune, the driving performance improves by not changing the shape of road surfaces.3. SIMULATION AND RESULTS
Since the purpose of test experiment is to compare the hillclimbing performance according to the change in the position of pivot under the same driving environment, the effect of wheel slipping is neglected and same friction coefficients are assumed in this experiment. The tilted angle of slope is varied from 0° to 40° by 1°. While rovers are designed to be capable of climbing the slopes of maximum 30° tilt in general (Eom et al. 2012a), the test condition was established considering the requirement to maintain static equilibrium at the slope of 40°. The properties of proposed suspension are summarized in Table 1. For simulations, the flowchart of the moment derivation process using force and position vectors defined in the FBD is shown in Fig. 6. Fig. 7 through Fig. 9 show the moment values (
M_{f} ) according to the change ind ,l _{h1}, andl _{h2} as a function of tilt angle (θ ) in the range of 0°~40°. Fig. 6 displays the behavior of the moment values whenθ varies from 0° to 40° by the 1° interval with fixedl _{h1} of 0.05 m andl _{h2} of 0.15 m for three kinds ofd : 0.0 m, 0.02 m, and 0.04 m. It was found that the larger the value of d is, the bigger the value of the moment is up to the tilt angle of 28°, however, the moment value is larger for smaller d with the tilt angle greater than 28°. The tilt angles giving 0 moment for each d, turned out to be 0°, 17°, and 25°, respectively. Thus, for the tilt angle greater than these, hillclimbing performance is degraded because the moment value becomes negative.Fig. 8 shows the behavior of the moment values when
θ varies from 0° to 40° by the 1° interval with bothl _{h1} andl _{h2} fixed to 0.15 m for three kinds ofd : 0.0 m, 0.02 m, and 0.04m. The figure indicates that the larger the value of d is, the bigger the value of the moment is up to the tilt angle of 35°, however, the moment value is larger for smaller d with the tilt angle greater than 38°. The tilt angles giving 0 moment for each d, turned out to be 16°, 22°, and 24°, respectively. Thus, for the tilt angle greater than these, hillclimbing performance is degraded because the moment value becomes negative.Fig. 9 displays the behavior of the moment values when
θ varies from 0° to 40° by the 1° interval with fixedl _{h1} of 0.15 m andl _{h2} of 0.05 m for three kinds ofd : 0.0 m, 0.02 m, and 0.04 m. It was found that the larger the value of d is, the bigger the value of the moment is up to the tilt angle of 40° which is the upper end of the tilt angle range. The tilt angles giving 0 moment for each d, turned out to be 33°, 34°, and 35°, respectively. Thus, for the tilt angle greater than these, hillclimbing performance is degraded because the moment value becomes negative.4. CONCLUSIONS
In this study, for a planetary exploration rover which is required to overcome the obstacles in its way to the destination, a suspension design to improve the hillclimbing performance is proposed. The moment at the pivot which connects the two front wheels was derived for the proposed suspension system, and the change in the moment values were compared varying the vertical and horizon distance of the pivot according to the change in tilt angle.
According to the result of test experiment, as the pivot position is higher against the midpoint of horizontal line which connects the two front wheels and the pivot position is horizontally closer to the second wheel, hillclimbing performance is improved. However, it is not sufficient to analyze the complete hillclimbing performance by the analysis of hillclimbing at the inception of slope, dynamic modeling for the whole hillclimbing process and simulation will be performed to verify the excellence of current design for further study.

[Fig. 1.] Rover Sojourner.

[Fig. 2.] Rover Spirit and Opportunity.

[Fig. 3.] Rover Curiosity.

[Fig. 4.] Concept of Proposed Suspension for a Rover.

[Fig. 5.] FBD of the Front Suspension.

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[Table 1.] Properties about the proposed suspension.

[Fig. 6.] FBD of the Front Suspension.

[Fig. 7.] Comparison for moments with lh1=0.05m & lh2=0.15m.

[Fig. 8.] Comparison for moments with lh1=0.10m & lh2=0.10m.

[Fig. 9.] Comparison for moments with lh1=0.15m & lh2=0.05m.