First, uneven terrain and microgravity of the Moon cause different dynamics environment from one of the Earth surfaces. Therefore, the mobile platform needs to be developed to guarantee its mobility in the target environment. Traversability over obstacles and rough terrain, and enough drawbar pull on the soft terrain are often used to analyze the performance of the mobile platform.^4,15 Moreover, slip between the rover’s wheel and the soft terrain of the Moon causes issues of state estimation errors. Even if the state estimation would be corrected by equipped sensors, reduction of uncertainty caused by slip important to further improve the estimation.¹⁶

In addition, due to the absence of atmosphere, the rover would be exposed to an excessive change of temperature and radiation. Electronic components are extremely sensitive to working temperature and fragile on radioactive rays. In mechanical aspects, such environment compromises the durability of machine parts and the actuation of the mobile platform can be critically affected by temperature expansion and contraction. One of the solutions regarding the issue is to install the electronic components inside the warm-box of the body, which blocks radiation and protects electronic components from excessive temperature changes more effectively. At the same time, it is necessary to use as fewer electronic components as possible to reduce the complexity of the system and the chance of failure.¹²

Based on the issues stated above, we selected four representative design elements: wheel configuration, suspension, steering method, and actuator placement. In the following subsections, previous and ongoing researches on the development of planetary rovers would be reviewed based on the chosen design elements and compare the mechanism candidates of each element.

The rocker-bogie mechanism with 6-wheel configuration developed by NASA is known to have great traverseability and terrain adaptation on rough terrain without actuation of the chassis. For this reason, 6-wheel configuration with the rocker-bogie mechanism has been applied in many planetary and lunar exploration missions. However, in a lunar surface exploration mission, the rover would traverse soft terrain covered by the lunar regolith so these advantages are less effective and the slip caused by the lunar regolith is a rather more challenging issue.¹¹ Moreover, in the aspect of the cost, 6-wheel configuration requires not only great volume and weight but also increases the complexity of the electronic systems to drive and steer wheels.

Instead, 4-wheel configuration is applied in the mobile platform. It is known that bigger wheel size is more advantage to slip on loose regolith and 4-wheel configuration allows bigger wheel size given with the same volume and payload capacity.¹¹ In addition, by reducing the number of wheels, it requires a smaller number of actuators, and therefore, the overall system of the mobile platform is simplified.

The rover would traverse rough terrain, and therefore, a suspension system takes a critical role to stabilize roll and pitch orientation and to minimize the damage of the system. On the other hand, as the complexity of suspension depends on the stability of the rover system, choice of suspension system must be decided carefully by analyzing the lunar environment where the rover traverses. In general, there are three types of suspension; passive, semi-passive, and active suspensions. The main difference between these three types is the method of damping. The mobility of the rover controlled by sequence-based commands from the ground station would be slow, approximately 1 cm/sec, due to the time delay occurring at its communication and data processing so the dynamics is approximated as to be a quasi-static model,¹⁷ which the advantage of semi-passive suspension is not effective. In the case of active suspension, it may not react to external shock effectively with limited communication and computing power.

Another role of suspension is to ensure all wheels to contact with the ground of uneven terrain. To ensure all wheels to contact with the ground, we selected a passive suspension mechanism that has been applied in many 4-wheeled platforms as shown in Fig. 1: the mechanism consists of a pair of differencing rockers with wheels at their ends.^11,18 In the suspension system, four wheels are installed at the end of the rockers, and the suspension allows each wheel to passively contact with uneven terrain. In terms of geometry, the four wheels consist of up to two contact planes. On uneven terrain, three contact points of wheels define a contact plane and the other wheel passively lie on the terrain defining another contact plane with the adjacent two wheels, which offers good stability with a simple mechanism.

Fig. 1 
Illustration of the passive adaptive suspension

Fig. 2 
Kinematic illustration of a rover’s steering (left: skid-steering, right: explicit-steering)

In a lunar exploration mission, we can consider two methods to change the direction of the rover; spot-turning motion and making a curve. A spot-turning motion allows the rover to change the direction without moving long distance, which optimizes a trajectory in a limited area. On the other hand, making a curve is an effective method to follow a smooth trajectory or to correct the direction. Both methods are essential for the rover to traverse robustly against high uncertainties of the lunar environment.

The skid-steering mechanism performs both steering methods without changing the alignments of the wheels. In skid-steering, each wheel has a fixed rolling direction with respect to the body. Then, by controlling the revolution of each wheel, steering torque can be generated from contact friction and slips with respect to the terrain. A skid-steering mechanism has an advantage of not requiring additional actuators for the wheel alignment but the rover’s motion depends on slips,¹⁹ which causes severe odometry error to affects the position determination of the rover. Considering uncertainties of nonlinear dynamics of rough terrain, sensor error, and communication delay, skid-steering runs risks of control or estimation failure of the rover's state.

On the other hand, to minimize the lateral slip of wheels, the active explicit-steering mechanism aligns every wheel to the tangential direction of the wheel's desired trajectory by using actuators.²⁰ However, as motors for aligning the wheels are added, the system becomes more complex. In addition, considering the cost and limit of payload capacity, the explicit-steering mechanism is less economic than the skid-steering mechanism.

There is a tradeoff between skid-steering and explicit-steering systems: skid-steering more relies on the slip of the wheels while the explicit-steering requires a more complex system. In the present research, we aimed to develop an explicit-steering mechanism that uses a minimized number of actuators to increase stability against the slip of wheels and to reduce the systematic costs of motors at once.

Conventionally, motors to drive wheels are installed directly on the wheels. It implies that the motors and following electronic components are exposed to hostile environments. Subsequently, the system would run a high failure risk due to external effects on electronic components. Hence, it is suggested that every motor is installed inside the body, which requires a more complex mechanical mechanism but protects the motors and the following components from excessive radiation and temperature changes. The thermal expansion problems on mechanical components can be solved by limiting the rover’s operation to the daytime of the Moon and the failure rate of gears caused by external lunar dust can be prevented by utilizing seals.¹³ For this reason, although the design has a tradeoff between the complexity of the actuation system and the reliability of the electronic components, we consider the reliability of electronic components more critical, and the design is expected to improve the stability of the mobility systems. This approach is the main difference between the rover design of the present research and ones of previous and on-going previous or ongoing planetary rovers, such as Opportunity rover, that have motors for their wheel actuation installed on the wheel module.²¹

Let the rover’s state configuration in the inertial frame be (x, y, θ) where x and y are second-dimensional coordinates and θ is the orientation. Define the body frame of the rover such that the origin is the center of gravity (CG) P_B of the rover and the positive x-axis direction is the rover's forward direction. Assume the rover’s CG only moves with the linear velocity v on the x-axis of the body frame. Then, the rover’s state in the inertial frame can be written with respect to the rover’s linear velocity v and angular velocity w in the body frame.

Here, the differential of the rover’s orientation θ˙Iin the inertial frame is equivalent to the angular velocity w on the flat terrain. The instant center of rotation (ICR) is always on the y-axis of the body frame and we can define the coordinate of ICR in the body frame to be P_ICR = (0, r). Then, we can obtain the following equation.

Under the assumption of the non-lateral-slip condition, the ICR is equivalent to one of each wheel. Define the wheel frames such that the ICR is on the y-axis of the wheel frames and the origins of the frames are on the wheels’ CG P_mn, where m = f (forward) or b (backward), n = l (left) or r (right). The indexes of the wheels as shown in Fig. 3. Let δ_mn be the direction of the wheel regarding the body frame. Then, δ_mn is given as the following equation, where L and W are the length and width of the rover’s body, respectively.

Fig. 3 
Illustration of the kinematic model (r < 0)

If the wheels’ radius is large, inward alignments of the wheels cause physical interference between the chassis and the wheels. In addition, it is known that enough surface of the wheels’ contact points should be secured for the rover’s stability on its tipover.²² Therefore, we limit the wheels’ alignment to be outward from the body as δ_mn = (-π/2, π/2). Then, we can find the following relations from Eq. 3.

Note that the rover’s trajectory shows spot-turning with zero linear velocity v = 0 when r = 0.

Define the y-axis coordinate of the ICR in the wheel frame to be l_mn, where m and n are the indexes of the wheel. The symmetry of the rover model allows l_fl = l_bl and l_fr = l_br. Then, l_mn is given with respect to r, as shown in the below equations, where S is the length of the steering offset.

The sign functions are multiplied due to the defined range of δ_mn in Eq. 4. In order to satisfy the pure-rolling condition, a wheel's rolling speed equals to the translation velocity in the rolling direction. Let ω_mn be the angular speed of each wheel and R be the radius of the wheels. Then, from the relation of Eq. 4 of the steering angles δ_mn, the angular velocities are given by the below equation.

Here, the first term on the right side denotes the wheels’ trajectories according to the ICR and the second term denotes the effect of the steering angles’ changes. Since the 4 × 2 matrixes of Eq. 6 are not identical, it is required to realize each term independently. The first term is coupled with respect to wl_fl/R and wl_fr/R and they can be easily controlled by two actuators. The second term depends only on the wheels' alignment rate δ˙fI and δ˙fr and it can be manipulated passively corresponding to the change of wheels’ alignments, which will be described in Subsection 3.2.

From Eq. 3 and 6, the effect of the offsets’ rotation on the wheels' rolling is passively canceled by the rolling compensation and the actuation of the rover's driving is decoupled from the one of the steering’s. Therefore, driving of each wheel can be controlled to its trajectory regardless of the rotational velocity of the wheel's alignment, which simplifies the model of the mobile system. We can find a relation such that driving wl_fl/R and wl_fr/R of the mobile system is similar to the differential wheeled mobile system in terms of DOF but additional 2 actuators for the wheels’ alignments, δ_fl and δ_fr, and mechanical compensation, wδ˙fl/R, and wδ˙fr/R, of driving for explicit steering are added.

In Subsection 3.1, it is presented that a pair of front and rear wheels on the same side is coupled and it can be controlled by two actuators. To demonstrate the issues, we developed a mechanism of the rover’s mobile system. There are two pairs of motors are installed in the rover system: a pair of motors are used for steering and driving of each side of wheels. Due to the fragility of electronic components, all the motors are placed in the rover's body. In particular, each pair of motors are installed on the rotational axis of the rocker. Then, each motor can convey power through the revolution of its bevel gear in the direction of the axis.

Firstly, a motor for aligning wheels, a steering motor, rotates two screw axes through bevel gears as shown in Fig. 4. Note that the screws revolute in the opposite direction of each other to realize Eq. 4. Then, the screws push or pull levers that are installed on the wheel modules in the opposite direction of each other. Define the displacements of the screws to be Δs_l and Δs_r and their positive direction to be outward from the body. The housing of gears and a wheel rotates corresponding to the lever’s revolution as the equations below.

Fig. 4 
Illustration of steering mechanism

These equations yield the following equations from the kinematic relation in Eq. 3 so the required displacement of the steering angle is expressed with respect to the desired angle of the wheels.

Since the linear displacement is proportional to the revolution of the bevel gear, the rover’s steering can be easily controlled by computing Δs_l and Δs_r. This steering system has an advantage of large maximum torques working on the lever. In addition, if the angle offset of the lever is negligible, i.e. δ₀ = 0, computation of Δs_l and Δs_r are simplified as Δsl,r=DL±2r-W.

Secondly, a motor for driving rotates a screw axis through bevel gears, as shown in Fig. 5. Unlike the case of the steering system, only one screw is used and it conveys rolling of the same direction to each wheel. At the end of the screw, a set of worm gears are placed and driving power is conveyed through the revolution of them. However, the gear is designed to rotate independently from the rotation of the wheel's housing. It allows a relative rotation between the axis of the worm gear and the axis of the wheel's driving, which mechanically realizes passive compensation of the wheel’s rolling term caused by the change of the wheel's steering mentioned in Eq. 6. Therefore, the wheel speed is represented in the below equation, where p_n, n = l, r is the motor’s rotation and K is the composite gear ratio for mapping rotational velocity of steering into wheel speed compensation.

Fig. 5 
Illustration of driving mechanism

Here, the ratio K is chosen corresponding to the ratio s/R. Then, Eqs. 6 and 9 become identical. The proportional relation between the wheels’ rolling ω_mn and the motors' rotation p_n are set depending on the requirement of wheel torque.

Note that Δs_l and Δs_r of Eq. 8 and p_l and p_r of Eq. 10 represent the four motor inputs used in the mobile system. Δs_l,r is an input to align a pair of wheels on either left or right side in the tangential directions of the trajectory and p_l,r is for the wheels’ trajectory following corresponding to the rover’s velocity. Δs_l,r depends only on r and, with the given r, w only affects the input for driving, p_l,r.