Soil embedding avoidance for planetary exploration rovers...

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Proceedings of the 8th ISTVS Americas Conference, Detroit, September 12–14, 2016

SOIL EMBEDDING AVOIDANCE FOR PLANETARY EXPLORATION ROVERS

Ramon Gonzalez, Karl Iagnemma

Robotic Mobility Group, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Bldg. 35, 02139, Cambridge, MA, USA

[email protected], [email protected]

Abstract

This paper contributes a new and novel layer, embedding avoidance, to the traditional navigation control architecture of a planetary exploration rover. In particular, the aim of this new layer is to both maximize traction and and minimize risk of entrapment. This layer is composed of a soil embedding detection algorithm (described in another paper published in this conference) and a traction control strategy. Simulation results demonstrate the suitability of the proposed embedding avoidance layer in realistic challenging conditions. Additionally, several traction control algorithms show the importance of considering both the slip compensation and the kinematic incompatibility problems within the same control strategy. After those experiments the following conclusions are drawn: (i) the proposed traction controllers mean simpler approaches than traditional torque-based optimal controllers, and they demonstrate a proper balance between slip-compensation (lowest mean slip) and reduction of wheels fighting effect (less aggressive control actions); (iii) when no traction control is considered (current solution in NASA’s rovers), simulation results show the rover becomes stuck in one of the proposed scenarios.

Keywords: Traction control, kinematic incompatibility, slip, K-REX rover, ANVEL simulator

1. Introduction

What makes Mars interesting to scientists also makes it challenging to a planetary exploration rover, that is, accessing rough and steep terrain. Notice that steep terrain mobility is not limited only to hard surfaces, but also to loose materials at an angle of response (e.g. dunes, slopes). Even though advanced rover designs have been developed for roving over through challenging conditions, Martian rovers still experienced risky situations. For instance, on sol 4461 (April 26, 2005), the NASA’s Opportunity rover got stuck in a sand dune in Meridiani Planum (http://mars.nasa.gov/mer/missionstatus_opportunityAll_2005.html). It took five weeks for the engineers to extract it from this situation. The rover Curiosity has also faced challenging situations dealing with soft soils [Parnell, 2015].

There is a broad body of literature solving two of the main problems involving off-road robots. The first problem deals with minimizing the soil embedding risk or maximizing the traction, those two issues are directly related to slip. In this context, some approaches try to avoid slip generating control signals such that the soil never fails (Iagnemma and Dubowsky, 2004; Lamon and Siegwart, 2007). These approaches rely on complicated torque-based traction controllers, which involve numerous parameters that are difficult to measure online. Other researchers propose simpler velocity-based slip-compensation controllers (Gonzalez et al., 2014; Helmick et al., 2006). These control strategies adapt the control signals depending on the estimated slip. This main limitation of this paradigm is that in general slip cannot be accurately estimated in a continuous way (Iagnemma and Ward, 2009).

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One of the main drawbacks of the previous strategies, either avoiding slip or compensating slip, is that they do not account for the second major problem related to the mobility of mobile robots in off-road conditions, that is, the wheel “fighting” phenomenon or kinematic incompatibility. This phenomenon is a natural outcome of rover travel over uneven terrain, it explains why the wheels may move at different velocities, which ultimately means a lack of coordination among them. There are not many references solving this issue in the field of mobile robotics (Baumgartner et al., 2000; Peynot and Lacroix, 2003). However, this point constitutes a known problem in the automotive field, and several techniques have appeared such as ABS (Anti-lock Braking System) and ESP (Electronic Stability Program) (Ulsoy et al., 2012). However, these approaches do not take into account the slip derived from the vehicle-terrain interaction (the kind of slip that appears in planetary exploration rovers).

The solution proposed here not only aims at reducing wheel slip by taking the slip estimate from the embedding detection algorithm, but also, by coordinating the velocity among multiple rover wheels in such a way as to reduce wheel “fighting” (kinematic incompatibility). In this sense, this paper contributes a new and novel layer, embedding avoidance, to the traditional navigation control architecture of a planetary exploration rover. In particular, the aim of this new layer is to both maximize traction and minimize risk of entrapment. Notice that the latter component of this layer is further explained in the paper: “Comparison of Machine Learning Approaches for Soil Embedding Detection of Planetary Exploration Rovers”, which is also published in this conference by the same authors.

The performance of the proposed navigation architecture is validated using the advanced robotic simulator ANVEL (Quantum Signal) with a model of the K-REX rover (planetary exploration rover assembled by ProtoInnovations for NASA AMES). More specifically, two challenging scenarios has been set up. In the first scenario, the rover negotiates a combination of sandy rippled soils and rocks. In the second case, the rover climbs on a slope of sandy/rocky terrain. Those scenarios lead to moderate and high slip conditions as well as wheel “fighting”.

This paper is organized as follows. In Section 2, the new soil embedding avoidance layer is described. Section 3 presents the four traction control strategies proposed in this work. Section 4 provides experimental results showing the performance of the soil embedding avoidance layer and the traction control algorithms. Section 5 concludes the paper.

2. Soil Embedding Avoidance Layer

As explained in the previous section, this paper is framed within the context of the investigation of velocity-based traction control strategies to improve all-terrain mobility by optimizing the vehicle response to conditions experienced by the individual wheels. This goal requires of a proper embedding detection method, which feeds back the traction controller with real-time estimation of wheel slip. As shown in Figure 1, a new layer has been added to the traditional navigation architecture. The objective of the traction control module (“TC” in the figure) is to compute the angular velocity of each wheel such that the risk of soil embedding and the deviation from the desired body forward velocity, vbody, are both reduced for an arbitrary rover pose and terrain condition: geometric (e.g. slopes, ripples) or non-geometric (e.g. loose sand, bedrock) condition. To achieve such goal, two problems must be taken into account: (1) minimizing wheel slip and (2) mitigating the kinematic incompatibility phenomenon (“wheel fighting”). The first problem is due to the physical/mechanical properties of the terrain and the rover-terrain interaction. In this regard, the embedding detection module classifies the current slipping conditions according to three categories: low slip (slip ≤ 30 %), moderate slip (30 > slip ≤ 60 %), and high slip (slip > 60 %).

Wheel fighting is a natural outcome of rover travel over uneven terrain: different contact angle for each wheel leads to different projection of the linear velocity on the ground. In order to account for this phenomenon, the current contact angle between the wheel and the soil must be estimated and feeds back to the traction controller, which considers this angle to generate the new commanded velocity. The interested reader is referred to (Iagnemma and Dubowsky, 2004) for an approach to estimate the contact angle.

The main features and limitations of the new embedding avoidance layer are: • The primary purpose of traction control is to reduce the risk of rover entrapment by means of slip

compensation. • The motion control layer should ensure path following accuracy. This layer will consider rover’s pose and may

include information about the surrounding terrain conditions to change the velocity of the rover. This velocity means the input to the traction control layer.

• In order to ensure a fast computation, the traction control strategy must be as simple as possible. For that reason, the control strategies suggested here are derived from kinematic relationships.

• The wheel-fighting problem is solved independently for each wheel. It means that a distributed control strategy is avoided (e.g. message passing).

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• Discrete indication of the slip (low slip, moderate slip, and high slip). This information comes from the embedding detection classifier (article published in this conference).

• Longitudinal slip reduces rover traction; this phenomenon is compensated by increasing the angular velocity of the wheels. This assumption makes sense for sandy soils because the soil becomes stronger as the sinkage increases.

• It bears mentioning that the path planner, motion controller, and localization strategies are beyond the scope of this paper.

• It is assumed that properly tuned PID controllers ensure the velocity commanded by the upper layer generating the right voltage and current signals.

Fig. 1. The control architecture incorporates a novel layer for velocity-based traction control and

embedding detection.

3. Traction control

Traction control constitutes a standard in the automobile community, which is designed to prevent loss of traction of driven road vehicles (under acceleration). When the traction-control system determines that one wheel is spinning more quickly than the others, it automatically “pumps” the brake to that wheel to reduce its speed and lessen wheel slip (Rosenbluth, 2001).

A different reasoning is behind the traction control approaches suggested in this work. Here, the rover does not loose traction (slippage) because of acceleration. Slippage is produced by the nature of the terrain (soil failure). Thus, reducing the velocity may cause the rover to sink and become trapped. In this scenario, a reasonable solution consists in increasing the velocity of the wheels such that the real velocity matches the angular velocity of the wheels. Several publications demonstrate that increasing the input velocity (control action) to the wheels when the vehicle is under moderate slippage on semi-compact surfaces (e.g. dry sand) is beneficial. In contrast, when the vehicle is under the same conditions of slippage but on extremely soft soils this solution is counterproductive (Rohani and Baladi, 1981; Wong and Reece, 1967).

In this research, four traction control algorithms are proposed following the reasoning previously explained. The first solution is based on the kinematic relation between the wheels, and its only goal is to minimize the kinematic incompatibility issue while considering the contract angle of the wheels. The second traction control approach not only takes into account the kinematic relation between the wheels, but also, the slip at each wheel. This slip estimate is assumed to be a continuous variable. The third approach means a trade-off between the two previous solutions and

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needs of a certain threshold to commute between them. The last method leads to the most realistic solution because it minimizes the kinematic incompatibility issue, but also uses a discrete variable representing the slip status (i.e. low slip, moderate slip, and high slip) to compensate it. This discrete value is fed-back by the embedding detection algorithm. Notice that it means a promising solution because online estimation of longitudinal slip is not reliable considering slow-moving rovers (noisy measurements). The use of a discrete variable then represents a much more practical solution.

3.1 Strategy 1. Kinematic incompatibility

The first strategy is based on analysis of the kinematic relations between the wheels of a rover. A new control input for each wheel is computed when a wheel’s contact angle is different than zero. The angular velocity of the wheel can be computed as

v1 =vbodycos(γ1)

!→! ω1 =vbody

Rcos(γ1),

(1)

where ω1 is the control input to wheel 1 and R is the wheel radius. By enforcing this relation, the longitudinal component of the rover wheel velocities is the same. Then, as long as the global motion of the robot (vbody) respects the references, the low-level PID controllers ensure the given set points, and a sensor provides a measure of the rocker configuration (γ1, γ2), the effective velocity of all the wheels will be the same, reducing the risk of slip. Figure 2 illustrates this approach.

Fig. 2. Strategy 1. Analysis of velocities for traction control compensating the kinematic incompatibility (different contact angle).

Observe that vix is the projection in the x-axis of the linear velocity of wheel j.

3.2 Strategy 2. Kinematic incompatibility and slip compensation

The second strategy follows the same general idea as the first one, but in addition to the kinematic relationships between the wheels, it also considers an estimate of the slip at each wheel. In particular, the control input to the wheels is given by

ω1 =vbody

R(1− i1)cos(γ1),

(2)

where i1 is the estimated slip of wheel 1 (continuous value). Finally, the new control input is constrained to the

actual limits of the motor attached to the wheel, that is, the angular velocity of each wheel cannot exceed a maximum (minimum) value, as in: ωm≤ ωi ≤ ωM.

In order to compensate the input tothe low-level controller is updatedto:

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3.3 Strategy 3. Switching policy between kinematic incompatibility and slip compensation

Notice that in Strategy 2, if slip is greater than zero the new control input may lead to a de-synchronization between the wheels. This fact may mean poor tracking performance (the rover deviates from the desired trajectory). Here, a new strategy is proposed based on a trade-off between the compensation of the kinematic incompatibility phenomenon and the slip compensation. More specifically, a switching policy ruled by a fixed threshold, δ, balances between Strategy 1 when slip estimates are coarse or slip is low, and Strategy 2 when slip is greater than such threshold. It bears mentioning that a high value for this threshold might lead to too conservative control actions leading to rover embedding. The control inputs are obtained as

If slip > δ //Strategy 2 (Slip compensation and kinematic incompatibility)

ω1 =vbody

R(1− i1)cos(γ1),

(3)

Else //Strategy 1 (Kinematic incompatibility)

v1 =vbodycos(γ1)

!→! ω1 =vbody

Rcos(γ1),

(4)

3.4 Strategy 4. Switching policy considering discrete slip values

This new configuration of Strategy 3 considers discrete values for the slip, instead of the continuous feedback of the previous algorithms. These discrete values come from the “Embedding Detection” module, see Figure 1. Notice that the control action depends on the contact angle (continuous value), the other terms are discrete or constant. The reasoning behind the representative values used for each slip class is explained subsequently.

If (slip < 0.3) OR (low-slip event is detected) i1 = 0.20, //representative value for this range

ω1 =vbody

R(1− i1)cos(γ1),

(5)

Elseif slip < 0.6) OR (moderate-slip event is detected) i1 = 0.46 //representative value

ω1 =vbody

R(1− i1)cos(γ1),

(6)

Else %slip ≥ 0.6 i1 = 0.83 //representative value

ω1 =vbody

R(1− i1)cos(γ1),

(7)

3.5 Strategy 4. Tuning the representative slip value

As shown in Figure 3, the influence of the slip in the control action obtained while considering Strategy 2 can be grouped into three regions: (1) from 0 to 0.3, an almost constant behavior is observed (ω ≈1); (2) from 0.3 to 0.6, a linear behavior is obtained (ω ≈3.3*slip); (3) lastly from 0.6 to 1, an exponential behavior is obtained (ω ≈ 0.35*i3 -

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1.8*i2 + 3.5*i) being i the slip. This result explains why there are three different cases in Strategy 4, which are related to the three discrete slip events identified by the soil embedding detection algorithm. For each region a constant representative value for slip must be given. A first naïve approach can be: for the first region, slip = 0.2, which means an angular velocity of ~1 [rad/s] (depending on the contact angle); for region 2, slip= 0.46, which means an angular velocity of ~1.5 [rad/s]; and for the third region, slip = 0.83, which leads to ω = ~ 4.7 [rad/s] (close to the maximum velocity in the vehicle considered in the simulations). In the future, a more advanced approach will be investigated, for example, using an adaptive control policy.

Fig. 3. Strategy 2 in terms of slip. Notice that three different regions can be used for representing the angular velocity (control

action).

4. Simulation Results

In order to validate the proposed soil embedding avoidance layer and the different traction control algorithms, the advanced robotic simulator ANVEL has been used (http://anvelsim.com). More specifically, a model of the planetary exploration rover K-REX has been used for running the simulations. Two challenging scenarios have been configured. In the first case, the rover negotiates a combination of sandy rippled soils and rocks. In the second scenario, the rover climbs on a slope of sandy/rocky terrain. For these specific simulations, the desired body velocity was set to 0.2 [m/s], and the angular velocity of the wheels was constrained to {-5.5, 5.5} [rad/s]. The two scenarios are displayed in Figure 4.

It is important to remark that for comparison purposes the rover is also controlled using no traction control, this is the way in which the current Mars rovers are operated. Additionally, Strategy 3 has been tested using two different values for the threshold value. In particular, Strategy 3 with δ = 0.65 and Strategy 3 with δ = 0.35. Recall that, Strategy 4 uses discrete values for slip, which will be provided by the soil embedding detection algorithm during physical experiments. In these simulations, this algorithm is not running, hence, such values are obtained according to the policy explained in Section 3.5.

Slip0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

ω [r

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Contact angle = 10[deg]Contact angle = 0 [deg]Contact angle = 20[deg]

X: 0.3Y: 1.16

X: 0.6Y: 2.031

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(a) Scenario 1 (b) Scenario 2

Fig. 4. Scenarios considered in this work and planetary exploration rover used for the simulations (KREX rover). Notice that in both cases the rover travels over dry sandy terrain, which leads to slippery conditions

4.1 Scenario 1. Sandy rippled terrain

This first illustrative example constitutes a benign scenario because slip is smaller than 20%. However, this scenario will show the advantages and limitations of the compared traction control strategies. In this case, the simulation was run during 70 seconds.

Figure 5a displays the trajectories of the rover when various control strategies were employed (bold blue: no traction control, black: Strategy 1, cyan: Strategy 2, light blue: Strategy 3/variant 1 (δ = 0.65), green: Strategy 3/variant 2 (δ = 0.35), dashed blue: Strategy 4 (discrete slip). Notice that all the strategies allow the rover to reach the target except Strategy 2, because of its aggressive control actions deviate the rover from the desired path. Figure 5b shows the heading of the rover for each traction control strategy. As previously remarked, all the strategies follow closely the reference path except Strategy 2.

Figure 6a shows the control inputs. Observe how the commanded velocity changes depending on the contact angle for every traction control strategy except for the case when no traction control is employed. Looking at this figure, it is easy to understand the wrong result obtained while considering Strategy 2. Recall that this strategy generates the control action according to the current (continuous) value of the slip and the contact angle. It means that even small slip creates de-synchronization among the wheels in the rover. This effect is even augmented along time and distance until a certain point where the rover is uncontrollable. This is exactly what happens after 20 meters from the starting point.

Figure 6b displays the contract angles. Observe the uneven nature of this scenario, because the wheels are always facing a slope (some of them greater than 20 [deg]). Finally, Figure 6c shows the slip estimate in terms of the traveled distance. As explained at the beginning of this section, this scenario represents a benign terrain where slip is always less than 20%. However, a large slip peak is observed when Strategy 2 is employed. This result has been already explained because of the aggressiveness of this strategy.

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(a) Trajectories (b) Yaw angle (rover orientation)

Fig. 5. Performance of the traction control algorithms in terms of the tracked tracjectory. Notice the large deviation of Strategy 2.

(a) Control inputs (b) Wheel contact angles

(c) Estimated slip

Fig. 6. Control inputs generated by the traction controllers depending on the wheel contact angles and the estimated slip. Notice the aggressive control inputs generated by Strategy 2

X [m]-8 -7 -6 -5 -4 -3 -2 -1

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4.2 Scenario 2. Sandy ripples, rocks, and moderate hill made of dry sand

In this illustrative example the rover negotiates a combination of sandy soil, rippled terrain, small rocks, and a moderate hill made of dry sand. This configuration constitutes a real challenging experiment where the rover moves over regions with high slippage (> 60%). As in the previous case, the simulation was run during 70 seconds.

Figure 7a displays the trajectories of the rover when various control strategies were employed (bold blue: no traction control, black: Strategy 1, cyan: Strategy 2, light blue: Strategy 3/variant 1 (δ = 0.65), green: Strategy 3/variant 2 (δ = 0.35), dashed blue: Strategy 4 with discrete slip). Observe that the hill causes the robot to get stuck when no traction control and Strategy 1 are employed. When Strategy 3 and Strategy 4 are applied the rover climbs over the obstacle but it deviates from the desired reference path. Strategy 2 slightly improves the performance of Strategy 3 in terms of path following. However, recall that there is no closed-loop feedback control so there are no steering corrections. In any case, this result shows again the suitability of the traction control layer in the navigation architecture. Figure 7b shows the heading of the rover for each traction control strategy. As previously observed, the four slip compensation strategies show a slight deviation from the reference.

(a) Trajectories (b) Yaw angle (rover orientation)

Fig. 7. Performance of the traction control algorithms in terms of the tracked tracjectory. Notice that when no traction control the large deviation of Strategy 2.

Figure 8a shows the control inputs obtained. When no traction controller is applied a constant velocity profile is given to the wheels, which explains why the rover becomes trapped. In contrast, Strategy 1 slightly increases the velocity when the rover faces the hill (traveled distance = 10 m). However, this tiny increase is not enough to climb such hill. As expected, Strategy 2, Strategy 3, and Strategy 4 lead to more aggressive control actions to compensate the high slip experienced in this challenging scenario. This explains why the rover is able to climb the hill. Additionally, notice that those commanded control inputs saturate to the maximum velocity achievable by the wheels ({-5.5, 5.5} [rad/s]). It is important to remark the interesting behavior obtained with Strategy 4. This results into a smooth profile. As expected, the control inputs only take discrete values (see Figure 9b). In contrast, when the slip is continually fed back, noisy profiles are obtained, which ultimately leads to aggressive control actions and sudden actions (see Figure 9a). Figure 8b displays the contract angles. Observe the uneven nature of the sandy hill; the wheels face different slopes during the experiment (some of them greater than 15 [deg]). Finally, Figure 8c shows the slip estimate in terms of the traveled distance. It bears mentioning the challenging conditions of this scenario, where slip is higher than 80% in some parts of the hill. Observe that when no traction control is applied the rover becomes tapped (slip ≥ 100 [%]). The same situation is experienced when Strategy 1 is used. The slip-compensation traction control strategies solve this challenging condition.

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(a) Control inputs (b) Wheel contact angles

(c) Estimated slip

Fig. 8. Control inputs generated by the traction controllers depending on the wheel contact angles and the estimated slip. Notice the rover becomes stuck when no traction control and Strategy 1 are employed.

(a) Strategy 3 (b) Strategy 4

Fig. 9. Control input generated by Strategy 3 and Strategy 4. Notice that Strategy 4 leads to a smoother input profile (red line). This figures also show the proper performance of the low-level PID controllers (blue line).

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4.3 Discussion

Here, a comprehensive comparison of the performance of each traction control strategy is described. Figure 10 shows the mean value of the total slip in each scenario. In order to test the suitability of the selection of three discrete regions for slip, another configuration for Strategy 4 is compared in this section. In this case, Strategy 4 deals with four discrete regions, namely region 1 (slip ≤ 20 %), region 2 (20 > slip ≤ 40 %), region 2 (40 > slip ≤ 60 %), and region 4 (slip > 60 %).

Observe that Strategy 4 with discrete slip values leads to the best performance and, hence, the lowest embedding risk, that is, this control approach achieves the smallest mean slip in the two illustrative examples. Another significant property of this algorithm is that it results into smooth control actions, which ultimately mean a proper behavior of the rover (avoiding sudden changes, aggressive control inputs, etc.). The two configurations of Strategy 4 (3 slip regions or 4 slip regions) achieve the same performance. However, it is much more difficult to classify the slip events according to four classes (small inter-class distance), for that reason, the case of three slip regions is considered as the most appropriate solution from a practical standpoint.

Another interesting conclusion from this comparison is related to the performance of the Strategy 3, which is similar to Strategy 4 but considering a continuous estimate of slip. However, this strategy is not affordable from a practical standpoint because slip cannot be accurately estimated in real-time, see a discussion about this issue in the paper “Comparison of Machine Learning Approaches for Soil Embedding Detection of Planetary Exploration Rovers”, published in this conference as well.

On the other hand, Strategy 2 means a proper solution when the rover faces challenging conditions (Scenario 2), however, it leads to too aggressive control actions even in benign terrains. This aggressiveness ultimately results into desynchronization of the wheels and instability (see Figure 10a).

Finally, it is important to remark the high embedding risk associated with the current method available in the Mars rovers, that is, when no traction control is employed. As observed in Figure 10b, this strategy leads to the highest values for slip (> 65%). A similar result is obtained with Strategy 1.

(a) Scenario 1. Sandy rippled terrain (b) Scenario 2. Sandy ripples, rocks, and moderate hill

made of dry sand

Fig. 9. Mean slip value of the compared traction controllers for the two scenarios considered in this research

5. Conclusions

This paper presents a novel layer to the traditional navigation architecture of mobile robots. This layer successfully demonstrates a promising performance through realistic simulations. More specifically, when the current no-traction-

Mean

wheel1

wheel2

wheel3

wheel4

slip

[%]

0

5

10

15

20

25

30

35Mean values of slip

Alg0Alg1Alg2Alg3, / = 0.65Alg3, / = 0.35Alg4 (3 regions)Alg4 (4 regions)

Mean

wheel1

wheel2

wheel3

wheel4

slip

[%]

0

10

20

30

40

50

60

70Mean values of slip

Alg0Alg1Alg2Alg3, / = 0.65Alg3, / = 0.35Alg4 (3regions)Alg4 (4regions)

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control policy is applied to a challenging scenario, the rover gets trapped. However, when the traction control algorithms proposed in this paper are employed the rover not only reduces the wheels “fighting” effect (less aggressive control actions), but also, and most important, minimizes the mean slip. Additionally, the proposed traction controllers mean simpler approaches than traditional torque-based optimal controllers (or physics-based traction controllers).

Future efforts will focus on validating the proposed soil embedding avoidance layer and the traction control algorithms through field tests.

Nomenclature

vj Linear velocity of wheel j γj Contact angle of wheel j vbody Global velocity of the robot ωj Angular velocity of wheel j ij Estimated slip of wheel j δ Threshold associated with strategies 3 and 4 R Wheel radius

Acknowledgements

The research described in this publication was carried out at the Massachusetts Institute of Technology under the STTR Contract NNX15CA25C funded by NASA.

References

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