Enhancing Consistent Ground Maneuverability by Robot Adaptation to Complex Off-Road Terrains
Authors: Sriram Siva
Maggie Wigness
John Rogers
Hao Zhang
Venue: CoRL2021 Oral (2021)
Keywords: Robot Learning
Off-road Navigation
Terrain Adaptation

Abstract: Terrain adaptation is a critical ability for a ground robot to effectively traverse unstructured off-road terrain in real-world field environments such as forests. However, the expected or planned maneuvering behaviors cannot always be accurately executed due to setbacks such as reduced tire pressure. This inconsistency negatively affects the robot's ground maneuverability and can cause slower traversal time or errors in localization.  To address this shortcoming, we propose a novel method for consistent behavior generation that enables a ground robot's actual behaviors to more accurately match expected behaviors while adapting to a variety of complex off-road terrains. Our method learns offset behaviors in a self-supervised fashion to compensate for the inconsistency between the actual and expected behaviors without requiring the explicit modeling of various setbacks. To evaluate the method, we perform extensive experiments using a physical ground robot over diverse complex off-road terrain in real-world field environments.  Experimental results show that our method enables a robot to improve its ground maneuverability on complex unstructured off-road terrain with more navigational behavior consistency, and outperforms previous and baseline methods, particularly so on challenging terrain such as that which is seen in forests.

Enhancing Consistent Ground Maneuverability by Robot A Adaptation to Complex Off-Road Terrains
Sriram Siva', Maggie Wigness", John
John G. Rogers", , and Hao Zhang'
CColorado School of Mines, Golden, CO 80401, USA
{s fsivasr ram, hzhang ) [eminess nes edu
U.S. Army Research Laboratory, Adelphi, MD 20783, USA
fmaggie wigness. civ, john. g.. rogers59 civ)earnm mil
Abstract: Terrain adaptation is critical ability for ground robot to effectively traverse unstructured off-road terrain in real-world field environments such as forests. However, the expected or planned maneuvering behaviors cannot always be accurately executed due to setbacks such as reduced tire pressure. This inconsis- tency negatively affects the robot's ground maneuverability, and can cause slower traversal time or errors in localization. To address this shortcoming, we propose a novel method for consistent behavior generation that enables a ground robot's s actual behaviors to more accurately match expected behaviors while adapting to a variety of complex off-road terrains. Our method learns offset behaviors in a self-supervised fashion to compensate for the inconsistency between the actual and expected behaviors without requiring the explicit modeling of various setbacks. To evaluate the method, we perform extensive experiments using physical ground robot over diverse complex off-road terrain in real-world field environments. Ex- perimental results show that method enables robot to improve its ground mancuverability on complex unstructured off-road terrain with more navigational behavior consistency, and outperforms previous and baseline methods, particularly so on challenging terrain such as that which is seen in forests.
Keywords: Robot Learning, Off-road Navigation, Terrain Adaptation
Introduction
Over the past several years, autonomous ground robots have been increasingly deployed in off- road field environments address real-world applications, including disaster response, home- land defense, and planetary exploration [1, 2, 3]. Field environments are challenging for ground robots navigate over because the terrain is un- structured and cannot be fully modeled before- hand, as depicted in Fig. 1. Terrain adaptation, the robot's 's ability to adjust its behaviors to per- ceived terrains, is therefore an essential ability to traverse over unstructured terrains [4, 5].
Expected belaavior
Actual behavtor
Grovdi
Wooddon Frees
Off-road environments such as forests unstructured and exhibit variety of character- isties, including changing terrain types and slopes. When ground robots are deployed in these environ- ments, their actual behaviors often do not match the expected behaviors, e.g., due to wheel slip. The inconsistency often causes slower traversal time errors in robot state estimation. Therefore, the capability of consistent behavior generation is es- sential for maneuverability while ground robots navigate over unstructured off-road terrains.
Figure 1:
Given its importance, robot terrain adaptation has recently been widely investigated. Previous barning-based methods be divided into two broad categories: terrain classification and ter- rain adaptation. The first category uses a robot's exteroceptive and proprioceptive sensory data to classify terrain types and estimate traversability
for robot navigation over the terrain [6, 7, 8, 9, 10). This category also includes techniques that model
terrain complexity for navigation planning [5, 11]. The second category of methods focus on directly
5th Conference on Robot Learning (CoRI. 2021), London, UK.

---

generating adaptive behaviors according to terrain in order to successfully complete navigation tasks [5, 12, 13. 14]. Specifically, learning from demonstration (LfD) widely used to transfer human expertise to robots in order to achieve human-level robot navigational control [15, 14, 16).
However, the expected navigational behaviors generated by previous approaches cannot always be executed accurately by ground robot when traversing over unstructured off-road terrain, i.c., the actual and expected behaviors may not be consistent. This inconsistency is mainly caused by setbacks [17, 18] that are defined as factors that increase the difficulty for ground robot to achieve its expected behaviors. Example setbacks include wheel slip, reduced tire pressure, and heavy payload. Existing learning-basse based methods for robot navigation generally ignore these setbacks, which often leads to the robot not being able consistently execute the learned behaviors. The challenge of how to learn consistent navigational behaviors in supervieeee fashion has not been well addressed.
To address this shortcoming, we develop an approach for consistent navigational behavior generation. Our approach learns offset behaviors in a self-supervised fashion, allowing the robot to compensate for the inconsistency between the actual and expected behaviors without explicitly modeling the setbacks, while also adaptively navigating over changing terrain. In addition, our method is able to integrate nulti-modal features characterize terrain and estimate the importance of features to enable terrain-aware ground navigation. This is all implemented in a unified regularized optimization framework with theoretical convergence guarantee.
The key novelty of this paper is the introduction of a method to enhance consistent ground maneuver- ability, which advances the state-of-the-art by enabling ground robot's s actual behaviors accurately match its expected behaviors while adapting to a variety of complex unstructured off-road terrain. The specific novel contributions include:
We propose novel mathematical formulation to generate consistent navigational behaviors by learning offset behaviors in self-supervised fashion. We also introduce new regulariza- tion terms to learn important terrain features from multi-sensory observations and fuse them together to improve robustness of robot adaptation to unstructured terrain.
We propose a new optimization algorithm address the formulated regularized optimiza- tion problem with dependent variables and non-term regularization terms, which holds a theoretical guarantee to effectively converge to the global optimal solution.
As experimental contribution, we provide a comprehensive performance evaluation of learning- based terrain adaptation methods by designing a set of robot navigation scenarios over a wide variety of individual and complex unstructured off-road terrains.
2 Related Work
Related research on robot terrain adaptation can be broadly classified into two categories, including terrain classification and robot adaptation.
Terrain classification methods use sensory data from a robot to classify the terrain. Many earlier methods were developed to address the specific needs of larger vehicles [19, 20] and the classification process was typically performed in manual or pre-selected fashion. Some methods used a pre- existing terrain map and terrain ruggedness data to achieve high-speed terrain navigation [6. 7, 9, 10, 21, 22]. Learning-based methods are commonly used to classify terrain for navigation. Color-based terrain classification was performed to generate navigational behaviors by labeling obstacles [23]. More recently, semantic segmentation neural network architectures [24] have been successfully used to classify off-road terrain [25, 26] and perform robot navigation tasks accordingly. However, these methods rely discrete categorization of terrain types. The methods typically do not characterize complex unstructured oof-road terrain well and cannot directly enable robot adaptation in real- world environments, where environments have a wide variety of characteristies (as seen in Fig. 1).
Robot adaptation methods focus on enabling robots to intelligently adapt to various unstructured ter- rain. The general problem of robot adaptation is commonly studied in robotics [27, 28, 29, 30, 31, 32] using high-level behavior models. Earlier works considered ground speed as the optimization variable and formulated method for trading progress and velocity with changing terrain characteristics [33, 34]. L.aariig-bbased methods for terrain adaptation have gained attention because of their effectiveness and ficxibility [35]. Early work addressed terrain adaptation from the perspective of

---

online learning that updates model parameters in the execution phase [36, 37, 38). However, these methods lacked the ability to quickly adapt sudden terrain changes. Accordingly, methods were developed that generate navigational behaviors using open-loop controllers according to the predicted terrain characteristics [39]. Methods to mimic expert controls were also developed aiming to achieve human-level maneuverability [15, 14]. Recently, navigational affordances are learned from experts for off-road navigation [40]. External disturbances were also considered in the learning-
methods [41, 42, 43J. However, these methods often require modeling of robot dynamics or explicit human demonstrations, and cannot generate consistent ground navigation that adapt to diverse terrains.
3 Approach
Notation: We denote scalars using lowercase italic letters (e.g.. m E R), vectors using boldface lowercase letters (e.g., m E IR",, matrices using boldface capital letters, e.g., M- {m]] E R with its i-th row and j-th column denoted m' and mj, respectively. We use boldface capital Buler script letters to denote tensors (i.e., 3D matrices), e.g., M = {mm, (()(())) RRxaxr_ Unstacking tensor M along its height (p), width (q) and depth (r) provides slices of matrices M' E &R R E Rgxr and ( E RPx0, respectively [44].
3.1 Problem Formulation for Terrain-Awary Navigation
As a robot traverses over terrain, at each time step, we extract multi-modal features from observations acquired from multiple sensors installed on the robot including visual camera, LiDAR, and IMU. We concatenate all features extracted at time step t into vector and denote it as x()) E R where = Σソ= d and d' is the dimensionality of the j-th feature modality with m as the number of modalities. We stack features extracted from a sequence of consecutive e time steps into a matrix and represent it as terrain feature instance denoted as X ;x(=) E Rd We further denote the set of feature instances that are obtained as robot traverses over various terrains, and denote this set as a terrain feature tensor
[X,,... X,,] E Rddxxx.
We use Y= ly1...., .Yn] E R='" to denote the robot's expected navigational behaviors associated with X, where y; IR" is vector of behaviors corresponding to X,. Behaviors encoded by the control variables (e.g., linear and angular velocities) that decide the robot's 's motion at the present time f. Due to momentum, a robot often has continuous motion and observations; thus, considering history of past e observations can provide more information to generate navigational behaviors at the
present time. Accordingly, estimate the robot's behaviors y, using X; [x[" :x!")...::] :x((-))], taking
into account the history of e observations. Then, the problem of navigational behavior generation can be formulated as:
min I 03 X Y 1 + X1 |allar W
(1)
where We E Rexexxe is a weight tensor used to encode the importance of each element in X' towards
i(k) E V denotes the weight of the i-th estimating navigational behaviors. Each tensor element w
terrain feature from the k-th past time step to recognize the j-th behavior type. The operator @ denotes the tensor product and 83 is defined as the tensor product that performs the sum of mode-3 multiplication [44] between feature tensor X and W. In Eq. (1), the tensor product 0g takes each terrain feature instance X; E X, and multiplics it with the weight tensor W.
The first term in Eq. (1) is a loss function that encodes the error of using terrain features in X' to estimate the robot behaviors, through the learning model parameterized by W. Furthermore, our loss function encodes the non-linear nature of robot navigational behavior generation as a linear function of terrain features X. This can achieved because: i) for short periods of time (i.e., c = [1,30] 30)), the dynamics of the robot do not dramatically change [45, 46) and thus the non-linearity in the robot is not severe, and ii) with high-dimensional features (e.g., >> 10000), learning non-linear tasks can be lifted to a linear space [47, 48). The second term in Eq. (1) is regularization term named the feature modality norm and is mathematically defined as:
m
m
W M
Σ
W
==
Σ
W ((k) (1))) ((w)))((())))) (w()))
(2)
3

---

where ||-Ile is the Frobenius norm and W E R is the slice of the matrix obtained by unstacking the weight tensor W along its height d. The feature modality norm groups together weights within feature modality and enforces sparsity among different modalities, thus, identifying the most descriptive features for behavior generation. This critical capability for ground robot navigation since different features typically capture different characteristics of the unstructured terrains (e.g.. color, slope, and roughness), and have different effects toward generating navigational behaviors. The trade-off hyperparameter A in Eq. (I) is used to balance the loss and the regularization term.
The problem formulation in Eq. (1) allows ground robots to adapt their navigational behaviors according to different terrain features. However, due to setbacks that reduce the effectiveness of robot navigation, such as wheel slip, heavy payload, and reduced tire pressure [49]. the robot's actual behaviors may not match the expected behaviors.
3.2
Consistent Navigational Behavior Generation
W
The key novelty focuses principled method for ground robots to generate consistent naviga- tional behaviors that adapt unstructured ter- rain. As illustrated by Fig. 2, besides generating terrain-aware expected behaviors, our method monitors the difference between the actual and expected navigational behaviors caused by set-
())
[W
[W
Consistent Navipational Behaviors
X
w
W
Behavior
Expected
5%
wingghts
Y
iialances
Ai-oi (i-m y%
Dist
Offeet Behavior
backs, and computes an offset to reduce the dif-
AITIORENCE
instances
ference. This allows our approach to achieve consistent robot behaviors without the require- ment of explicitly modeling all of the setbacks.
n-Jaclan for
gitls
Figure 2: Overview of our proposed approach.
Mathematically, we denote the actual behaviors A [ai, ..... an)] R where a; E Rr denotes the actual behaviors executed by the robot when observing the i-th terrain feature instance X,. The actual robot behaviors can be estimated using a pose estimation technique, c.g., based on SLAM or visual odometry [50]. Setbacks can cause the robot's 's actual behaviors to not match its expected behaviors. This difference in navigational behaviors over the past c-time steps is computed as E = [(a(t)- -y(");:... (a(t-o) -y((=))] E R and the behavior differences for all the instances in X' is denoted as behavior difference tensor E = [EI,.... Em] E Rrxnxe.
We then introduce loss function to encode consistent behavior generation as follows:
min W 33 X + u @3 & A Wl
(3)
U.W
where 44 = -U" U'1 E Rexexe is a weight tensor with U E Rexe indicates the importance of behavior differences E towards generating the j-th offset behaviors. Using data from a history of time steps allows our method to consider inertia (i.e., resistance to change in behaviors) during navigation. Mathematically, this implies that (k)), k 1,...,c; c; has non-zero elements as opposed to each element in (k) being 1 at k = and O at k A 1 when robot inertia is not considered.
The loss function in Eq. (3) models the actual behavior by considering both terrain features X' and the behavior differences& E to achieve consistent navigational behaviors. Because of inertia, historical data from different past time steps may contribute differently towards generating offset behaviors (c.g., a heavier robot with larger inertia often needs to consider a longer history). Thus, we propose new regularization term to explore which time steps in the historical data are more important for generating the offset behaviors. We name this regularization term the temporal norm, which is expressed by:
U
u
(4)
A=1
E Re is the weight matrix, and u indicates the importance of the j-th behavior difference a. y (k) from ke past time step towards generating offset behaviors. This norm groups together weights for the vector of behavior differences at each time step, and
where (A)) = [u]
enforces sparsity between weights at different time steps to identify the most important time steps.

---

Algorithm 1: Our algorithm to solve the regularized optimization problem in Eq. (5).
Input :X' E [gdxaxc A E _ and & E IRTx,Xx
Output :The weight tensors W E Egdrrx and E R
Initialize W E Rdxrxe and E IRrxrxe;
while converge do
Calculate each block diagonal matrix Q(+) with i-th diagonal block given as 2i lat
Compute the matrices ((k) according to Eq. (8);
Calculate the block diagonal matrix with the k-th diagonal block as 2| U L,
Compute the matrices ( according Eq. (10):
return: W E _xxxxxe and U E xx*xxx
Using both norms to generate consistent robot navigational behaviors while identifying important feature modalities and historical time steps, the final objective function becomes:
min U.W
I 33 X + u &3 3 - All- + A + A ||
(5)
where A1 2 and X2 2 0 are trade-off papee--aramtter..
After computing the optimal values of the weight tensors W and U according to Algorithm 1, in the training phase, a rohot can apply our self-reflective terrain-aware adaptation method to generate consistent navigational behaviors during execution. At each time step to in the execution phase, the robot extracts multi-modal features Xt, from observations obtained from on-board sensors over the past c-time steps. Then, the robot also estimates the corresponding actual behaviors (measured using a pose estimation technique based upon SLAM or visual odometry [50]) and computes the matrix of behavior differences at time to E.,. Then our approach can be used by the robot to generate consistent actual navigational behaviors as:
W 03 X
+ X3 Et
The first term in Eq. (6) generates the expected navigational behaviors according to the terrain traverses, which allows ground robot to adapt its navigational behaviors to unstructured terrains. The second term in Eq. (6) provides offset behaviors based on monitoring the difference between actual and expected behaviors in order to compensate for the setbacks.
4 Optimization Algorithm
The optimization problem in Eq. (5) is challenging to solve because the regularization terms are not smooth and because the objective function includes dependent variables. Thus, we derive new iterative optimization algorithm to obtain the optimal solution to Eq. (5). This algorithm is shown in Algorithm 1, which provides an alternating minimization algorithm that alternatively updates the parameter tensors in each iteration until convergence.
To solve for the optimal weight tensor W, we minimize Eq. (5) with respect to (k) resulting in:
2x (1) (1)) W(k) (R) 2X 03 A + 2(U @3 T)T 83 X + X (+() =
(7)
where each (A) E R4xd, is diagonal matrix with the i-th diagonal block computed by 2 lll Las and L is identity matrix. Then, compute each (kk) as:
W = (2x X ( + i - (2X 0g A 2(4 @3 E) O2
(8)
Because each of the block-diagonal matrices (k) are dependent on W and also each slice of matrix (kk); dependent on corresponding ((k), an iterative algorithm is required to compute them.
To compute the optimal 24, we calculate the derivative of the objective function in Eq. (5) with respect to ((k) and set the equation to zero as:
2B (k) (E (k) T U(() 2A 8g E + 2(W @3 X) E + (k) = 0
(9)
5

---

Figure 3: Individual types of unstructured terrain used in the experiments.
where P E RR'x" is a diagonal matrix with the k-th diagonal block 2 I, with I, being an identity matrix. Then, we compute each Utk) in a closed-form solution as:
U (2E ( + A2P)
(2A 83 3 2(W Go X) & E)
(10) Q(k) and W, and U are
This 4 is then used to caleulate W the next iteration. Similar to Q interdependent. Thus, we develop an iterative algorithm to solve the formulated optimization problem, which is described in Algorithm 1.
Convergence. Algorithm is guaranteed to converge to the global optimal solution to the formulated regularized optimization problem in Eq. (5). The proof is provided in the supplementary material.
Complexity. As the optimization problem in Eq. (5) is convex, Algorithm converges fast (e.g.. within tens of iterations only). In each iteration, computing Steps and is trivial. Steps and can be computed by solving a system of linear equations with quadratic complexity.
Experiments
We utilize the Clearpath Husky robot in our field experiments. The robot is equipped with an Intel Reasense D435 color-depth camera and Ouster OS1-64 LiDAR. The robot also has variery of sensors to measure its internal states, including IMU readings, wheel odometry, motor speed, and battery status. Linear interpolation is used to get a steady 30 Hz frame rate from all sensors.
To represent unstructured terrain, we implement multiple visual features extracted from color images describe different terrain characteristics, including Histogram Oriented Gradients (HOG) [51] to describe the shape and Local Binary Patterns (LBP) [52] to describe texture. We also compute an elevation map [53] from LiDAR data to represent robot-centric grid-wise elevation of the terrain. During training, expected navigational behaviors are provided by remote control to navigate the robot over unstructured terrains as fast as possible while maintaining safety. In the training and execution phases, actual behaviors are estimated from LiDAR-based SL.AM [50] as robot pose. We use sequence of 15 frames (i.e., e = 15), and \₁ 0.1 and X2 for all experiments. More details on our implementation and training/testing procedures are provided in the supplementary material.
We compare our approach with several previous state-of-the-ard learning- robot navigation techniques, including Learning from Demonstration (LfD) for robot navigation [16], multi-modal LfD (MfD) [54], and Terrain Representation and Apprenticeship Learning (TRAL) [15]. To quantitatively evaluate the performance of robot navigation, we use four metrics:
Failure Rate (FR): This metric is defined the number of times the robot fails complete the navigation task across a set experimental trials. If robot flips or stopped by a terrain obstacle, it is considered failure. Lower values of FR indicate better performance.
Table I: Quantitative results based ten for scenarios when the robot traverses over individual
types of instructured terrain. Successful runs (with no failures) are used to calculate the metrics of traversal time, inconsistency and jerkiness.
Failure Rate (/10)
Traversal Time (s)
Inconsistency
Jerkiness (m/s
Terrain
MID TRAL
MiD TRAL Ours
LiD
MiD
TRAL
LtD
MiD
TRAL
Ours
Grass
0
0
0
0
17.9
18.2
17.4
17.5
2.82
3.06
1.84
2.11
79.59
81.42
75.18
76.50
Sand
0
1
0
0
15.3
12.7
15.9
13.1
4.72
4.62
4.67
4.55
71.14
73.74
65.32
64.22
Gravel
0
0
0
0
22.9
24.1
20.4
20.2
4.12
4.63
3.81
3.04
44.95
48.27
40.26
39.48
M.R
1
33.2
36.9
29.4
28.4
9.59
4.21
2.41
141.48
144.22
111..3411..1
L.R
6
37.855.3
63.4
60.9
24.79
28.50
9.51
7.84
52.55
54.30
49.50
48.36

---

Medutiii Boo
Grass Large Picks
Moxd Terrai
Figure 4: Complex unstructured off-road terrains used in the experiments.
Traversal Time (TT): This metric is defined the time taken to complete the navigation task over given terrain. Smaller values of TT indicate better performance.
Inconsistency: This metric is defined as the error between the expected behavior and the actual behavior in terms of robot poses (linear position and angular). Lower values of inconsistency indicate better performance.
Jerkiness: This metric is defined as the average sum of the acceleration derivatives along all axes, with lower values indicating better performance. Jerkiness indicates how smooth robot can traverse over a terrain. Because state estimatiin and SLAM methods (e.g., based Kalman filters) may assume smooth robot motions, jerkiness jerkiess is useful metric.
5.1 Navigating over Individual Types Unstructured Terrain
In this set of experiments, the robot navigates over individual terrain using off-road tracks. Each track is made up of one type of terrain and is approximately ten meters long. Five types of terrain used our experiments, which are illustrated in Fig. 3. Our approach is trained on data collected while the robot is manually controlled by expert traverse the terrain. Then, the learned model is deployed on the robot to autonomously navigate over the terrain. Evaluation metrics for each method computed across trials each type of individual terrain track.
The quantitative results achieved by our approach and the comparison to other methods are presented in Table 1. For simple individual terrains, such as grass and gravel, all methods allow the robot to successfully traverse over the terrain. However, for more challenging terrain, especially large rocks, both LfD and MfD have high failure rate, whereas, TRAL and approach have low failure rate. Our approach only has one failure over the difficult targe-rock terrain and outperforms other tested methods. The presented traversal time is computed by averaging the traversal time across all successful runs, i.c., it excludes the failed trials captured by the FR metric. methods have similar traversal time. In successful runs, both Lff methods show less traversal time compared to other methods over rocky terrain, although they also have a much higher failure rate. Thus, the emphasis on high-speed traversal used by both the LfD methods produces unreliable system when the robot traverses unstructured off-road terrain in real-world field environments.
observed that all
Table I also presents the quantitative results for the inconsistency and jerkiness metrics, We observe that both LiD and MfD methods do not perform well and have higher values of inconsistency over individual types of terrain, especially on the large-rock terrain. TRAL has lower inconsistency and performs the best over the grass terrain. Our proposed method outperforms the previous approaches and obtains the lowest averaged inconsistency value. Finally, also evaluate the tested methods using the jerkiness metric. An observation that the medium-rock terrain causes the largest jerkiness measure. This is because medium-rocks terrain compared the large-rocks produce much more vibrations for even slow maneuvers.
Table 2: Quantitative results for scenarios when the robot traverses over complex unstructured off off-road terrain shown Fig. 4.
Failure Rate (/10)
Traversal Time (s)
Inconsistency
Jerkiness (m/s")
Terrain
ADMMIDITRALOUR
LtD MLDDTRLL
LtD
MtD
TRAL
Ours
LtD
MrD Ours
Gr..R
5
7
1
22.0
19.7
27.5
23.1
15.62
17.28
14.54
12.31
65.01
58.36 51 51.93
Gr.L.R
8
3
27.2
27.4
29.4
28.8
68.87
51.16
34.9640.51 28.22 24.55
M.T-I
17.9
18.2
19.4
18.9
3.97
5.38
4.91
3.39
72.37
70.36 68.58
M.T-II
5
23.1
18.1
30.2
28.5
93.37
95.47
80.43
78.82
54.1377.49 47.93

---

5.2 Navigating over Complex Off-road Unstructured Terrains
In the second set of experiments, we evaluate our approach when the robot navigates over complex off- road unstructured terrain. The tracks in these experiments either show transitions between different terrain types (i.e., grass to large rocks: Gr.L..,, and grass to medium rocks: Gr.M.R) or a mixture of different terrain types real off-road environments (i.e., Mixed Terrain I: M.T-I and Mixed Terrain II: M.T-II), as shown in Fig. 4. In the experiments, no additional training is performed and the previously trained model from individual types of unstructured terrains used directly.
Table 2 presents the quantitative results obtained by our approach and the comparison with other methods. is observed that each of the methods have much higher failure rate in general, especially over the M.T-II and the Gr...R terrains. Our approach significantly outperforms LfD and MfD in terms of failure rate. Similar to the experiments over individual types of terrain, observe that both Lff) methods have slower traversal time for successful runs, but they have a significantly higher failure rate. Moreover, L.fD and Mfl) outperformed with respect inconsistency and jerkiness, with MID performing worst among all tested methods, especially on the jerkiness metric.
Although both TRAL and our method obtain promising performance, as the main goal is to enhance consistent maneuverability, our approach obtains average of 15.83% less inconsistency over TRAL (with 7.66% less over traversal time, 4.50% less over failure rate, and 4.56% less jerkiness). The p-value for inconsistency improvement is 0.004, indicating that the improvement is statistically significant. This improve- ment is most likely to be caused by the closed loop feedback, it is the biggest fundamental difference between the methods.
7.43
4.0
6.0
6.00
0.32
412
130
5.03
131
1M
1.4
1.3
5.3 Discussion
Figure Hyperparameter Analysis.
Hyperparameter Analysis:
The hyperparameters λ₁ and A2 in Eq. (5)
are implemented to balance the loss function and regularization terms. Fig. 5 depicts how the inconsistency metric changes given varying X values based on cross-validation during training. It is observed that A E (0.1, 10) and A2 E (1, 10) result in good performance in general.
Inconsistency
The best result is obtained when A 0.1 and X2 10. These values of hyperparameters are then used for all the experiments.
Dependence on Frame Sequences: Our approach uses sequence of historical frames with length generate consistent behaviors. Fig.
35
6 shows the change of the inconsistency metric according to c. It is observed that our approach generally performs well when c E (15, 20).
Figure 6: Seq. length.
and we observe that the inconsistency metric is worst when either small number (c 5) or big number (c 30) is used under the sensing framerate of 30 Hz. These values can be mainly affected by the robot's ss speed and can differ between robotic platforms.
Objective Value
Convergence: Experimental results in Fig. 7 illustrate the fast, mono- tonically decreasing convergence of Algorithm I, which validates our theoretical analysis.
Iterations
Conclusion
Figure 7: Convergence.
In this paper, we introduce novel approach for consistent behavior generation that enables ground robots' actual behavior more accurately match expected behaviors while adapting variety of unstructured off-road terrain. Our approach learns offset behaviors in a self-superviser fashion to compensate for the inconsistency between the actual and expected navigational behaviors without the need to explicitly model various setbacks, and learns the importance of the multi-modal features to improve the representation of terrain for better adaptation. Our proposed approach is extensively evaluated in real-world off-road environments. Experimental results have shown that our approach enables a robot to improve ground maneuverability when traversing over complex unstructured off-roo road terrain with more behavior consistency and smoothness compared to previous methods.
8

---

Acknowledgements
This work was partially supported by the NSF CAREER Award IIS- NSF CNS-1823245. and ARL SARA Program W911NF-20-2-0107.
References
[1] A. A. Hmoudi. Robotics for Disaster Warning and Response in the UAE. Journal of Environ- mental Science and Engineering, 9:215-221, 2020.
[2] L.. Bruzzone and Quaglia. Locomotion systems for ground mobile robots in unstructured environments. Mechanical Sciences, 3(2):49 2012.
[3] H. T. L. Chiang, B. HomChaudhuri, L. Smith, and L. Tapia. Safety, challenges, and performance of motion planners in dynamic environments. Robotics Research, pages 793-808. Springer, 2020.
[4] G. Sartoretti, Shaw, K. Lam, N. Fan, M. Travers, and H. Choset. Central pattern generator with inertial feedback for stable locomotion and climbing in unstructured terrain. In International Conference on Robotics and Automation, 2018.
[5] D. Silver, J. A. Bagnell, and A. Stentz. Learning from demonstration for autonomous navigation in complex unstructured terrain. International Journal of Robotics Research, 29(12):1565-1592 2010.
[6] L. G. Bermudez, R. C. Julian, D. W. Haldane, P. Abbeel, and R. S. Fearing. Performance analysis and terrain classification for legged robot over rough terrain. In International Conference on Intelligent Robots and Systems, 2012.
[7] C. A. Brooks and K. lagnemma. Vibration-based terrain classification for planetary exploration rovers. Transactions on Robotics, 21(6):115--119 2005.
[8] E. Devjanin, V. Gurfinkel, E. Gurfinkel, V. Kartashev, A. Lensky, A. Y. Shneider, and L. Shtilman. The six-legged walking robot capable of terrain adaptation. Mechanism and Machine Theory, 18(4):257-260, 1983.
[9] E. M. DuPont, C. A. Moore, and R. G. Roberts. Terrain classification for mobile robots traveling various speeds: An eigenspace manifold approach. In International Conference on Robotics and Automation, 2008.
[10] R. Hudjakov and M. Tamre. Aerial imagery terrain classification for long-range autonomous navigation. In International Symposium on Optomechatronic Technologies, 2009.
[11] T. Peynot, S. T. Lui, R. McAllister, R. Fitch, and S. Sukkarieh. Learned stochastic mobility prediction for planning with control uncertainty unstructured terrain. Journal of Field Robotics, (1(6))969 995, 2014.
[12] F. Han, X. Yang, Y. Zhang, and H. Zhang. Sequence-based multimodal apprenticeship learning for robot perception and decision making. In International Conference on Robotics and Automation, 2017.
[13] P. Pastor, H. Hoffmann, T. Asfour, and S. Schaal. Learning and generalization of motor skills by learning from demonstration. International Conference on Robotics and Automation, 2009.
[14] M. Wigness, J. G. Rogers, and L. E. Navarro-Serment. Robot navigation from human demon- stration: Learning control behaviors. In International Conference on Robotics and Automation, 2018.
[15] S. Siva, M. Wigness, J. Rogers, and H. Zhang. Robot adaptation to unstructured terrains by joint representation and apprenticeship learning. In Robotics: Science and Systems, 2019.
[16] Ge, Moore, and M. Antolovich. Learning from Demonstration Using GMM, CHMM and DHMM: A Comparison. In Australian Joint Conference Artificial Intelligence, 2015.

---

[17] C. D. B. Borges, A. M. A. Almeida, I. C. P. Junior, and J. J. d. M. S. Junior. A strategy and evaluation method for ground global path planning based on aerial images. Expert Systems With Applications, 137:232-252, 2019.
[18) R. Knight, F. Fisher, T. Estlin, B. Engelhardd, and S. Chien. Balancing deliberation and reaction, planning and execution for space robotic applications. In International Conference on Intelligent Robots and Systems, 2001.
[19] A. Jumikis. Introduction to Terrain-Vehicle Systems. Soil Science, 110(1):77, 1970.
[20] C. Urmson, J. Anhalt, M. Clark, T. Galatali, J. P. Gonzalez, J. Gowdy, A. Gutierrez, S. Harbaugh, M. Johnson-Roberseee H. Kato, et al. High speed navigation unrehearsed terrain: Red team technology for grand challenge 2004. Robotics Institute Carnegie Mellon University, 2004.
[21] M. Spenko. Y. Kuroda, Dubowsky, and K. lagnemma. Hazard avoidance for high-speed mobile robots in rough terrain. Journal of Field Robotics, 23(5):311-331) 2006.
[22] D. Sadhukhan, C. Moore, and E. Collins. Terrain estimation using internal sensors. In International Conference on Robotics and Automation, 2004.
[23] R. Manduchi, A. Castano, A. Talukder, and L. Matthies. Obstacle detection and terrain classification for autonomous off-road navigation. Autonomous Robots, 18(1):11-02,, 2005.
[24] J. Long, E. Shelhamer, and T. Darrell. Fully convolutional networks for semantic segmentation. In Conference on Computer Vision and Pattern Recognition, pages 3431-3440, 2015.
[25] P. Jiang, P. Osteen, M. Wigness, and S. Saripalli. RELLIS-3D Dataset: Data, Benchmarks and Analysis, 2020.
[26] M. Wigness, S. Eum, J. Rogers, Han, and H. Kwon. A RUGD dataset for autonomous navigation and visual perception in unstructured outdoor environments. In International Conference on Intelligent Robots and Systems, 2019.
[27] B. He, S. Wang, and Y. Liu. Underactuated robotics: a review. International Journal of Robotics Research, 16(4), 2019.
[28] S. Nikolaidis, Y. X. Zhu, D. Hsu, and S. Srinivasa. Human-robot mutual adaptation in shared autonomy. In International Conference on fluman-Robot Interaction, 2017.
[29] P. Papadakis. Terrain traversability analysis methods for unmanned ground vehicles: A survey. Engineering Applications of Artificial Intelligence, 26(4): 1385, 2013.
[30] L. E. Parker. L-ALLIANCE: Task-oriented multi-robot learning in behavior-based systems.
Advanced Robotics, 11(4):305-322 1996.
[31] L. E. Parker. Lifelong adaptation in heterogeneous multi-robot teams: Response to continual variation in individual robot performance. Autonomous Robots, 8(3):239 267, 2000.
[32] Watson and F. Marir. Case-based reasoning: A review. The Knowledge Engineering Review, 1994.
[33] D. Fox, W. Burgard, and S. Thrun. The dynamic window approach to collision avoidance. Robotics and Automation Magazine, 4( 4(1):23-33, 1997.
[34] S. Nabulsi, M. Armada, and H. Montes. Multiple terrain adaptation approach using ultrasonic sensors for legged robots. In International Conference Climbing and Walking Robots. 2006.
[35] S. Thrun. Lifelong learning algorithms. In Learning to Learn. Springer, 1998.
[36] A. Kleiner, M. Dietl, and Nebel. Towards life-long learning soccer agent. In Robot Soccer World Cup, 2002.
[37] S. J. Yi, B. T. Zhang, and D. Lee. Online learning of uneven terrain for humanoid bipedal walking. In Proceedings of the Association for the Advancement of Artificial Intelligence, volume 24, 2010.
10

---

[38] A. Koppel, J. Fink, G. Warnell, E. Stump, and A. Ribeiro. Online learning for characterizing unknown environments in ground robotic vehicle models. In International Conference on Intelligent Robots and Systems, 2016.
[39] C. Plagemann, S. Mischke, S. Prentice, K. Kersting, N. Roy, and W. Burgard. Learning predictive terrain models for legged robot locomotion, In International Conference on Intelligent Robots and Systems, 2008
[40] G. Kahn, P. Abbeel, and S. Levine. BADGR: an autonomous self-super farming-based navigation system. Robotics and Aulomation Letters, 6(2):1312-1319, 2021.
[41] K. Pereida and A. P. Schoellig, Adaptive model predictive control for high-accuracy trajectory tracking in changing conditions. In International Conference on Intelligent Robots and Systems, 2018.
[42] S. Jeong and D. Chwa. Coupled multiple sliding-mode control for robust trajectory tracking of hovercraft with external disturbances. Transactions on Industrial Electronics, 65(5):4103-411 13,, 2017.
[43] A. Altan and R. Hacroğlu. Model predictive control of three-axis gimbal system mounted on UAV for real-time target tracking under external disturbances. Mechanical Systems and Signal Processing, 138: 106548, 2020.
[44] H. Lu, K. N. Plataniotis, and A. N. Venetsanopoolos.. A survey of multilinear subspace learning for tensor data. Pattern Recognition, 4477):1550-1551 2011.
[45] Y. Tassa, T. Erez, and E. Todorov. Synthesis and stabilization of complex behaviors through online trajectory optimization. In International Conference on Intelligent Robots and Systems, 2012.
[46] Y. Alothman and D. Gu. Quadrotor transporting cable-suspended load using iterative linear quadratic regulator (iLQR) optimal control. In Computer Science and Electronic Engineering, 2016.
[47] J. L. Proctor, S. L. Brunton, and N. Kutz. Generalizing Koopman theory to allow for inputs and control. Journal on Applied Dynamical Systems, 17(1):909-930) 2018.
[48] I. Abraham and T. D. Murphey. Active learning of dynamics for data-driven control using Koopman operators. Transactions on Robotics, 35(5):1071-108; 2019.
[49] N. Sidek and Sarkar. Exploiting wheel slips of mobile robots to improve navigation perfor- mance. Advanced Robotics, 27()):627-639, 2013.
[50] T. Shan and B. Englot. LeGO-LOAM: Lightweight and Ground-Optimized Lidar Odometry and Mapping on Variable Terrain. In International Conference on Intelligent Robots and Systems, 2018.
[51] N. Dalal and B. Triggs. Histograms of oriented gradients for human detection. In Conference on Computer Vision and Pattern Recognition, 2005.
[52] T. Ahonen, A. Hadid, and M. Pietikainen. Face description with local binary patterns: Appli- cation face recognition. Transactions on Pattern Analysis and Machine intelligence, (12): 2037-2041, 2006.
[53] P. Fankhauser, M. Bloesch, C. Gehring, M. Hutter, and R. Siegwart. Robot-centric elevation mapping with uncertainty estimates. In Mobile Service Robotics, pages 433-440 World Scientific, 2014.
[54] Y. Wu. R. Wang, L. F. D'Haro, R. E. Banchs, and K. P. Tee. Multi-modal robot apprentice- ship: Imitation learning using linearly decayed dmp+ in a human-robot dialogue system. In International Conference on Intelligent Robots and Systems, 2018.


Reviews:
[{"review_id": "oQCbrYkFxPa", "reviewer": "Reviewer_M3C8", "summary": "This paper presents a method for navigation with ground robots in unstructured outdoors environments. The method in this paper is based on learning from demonstrations, where the goal is to reproduce recorded navigation behaviors conditioned on multi-modal sensor data. To do so, the paper describes an algorithm maps 3d tensors of features extracted from sensor streams, representing a time window of past sensor readings,  to control signals through a linear operator (mode-3 tensor product). Control signals to be executed by the robot are thus computed as a linear combination of  sensor features, with weights learned from demonstrations.  The approach introduces an extra term to deal with divergence of executed robot behaviours from demonstrated behaviours, and regularization terms that ensure that the executed behaviours are temporally consistent. The paper describes an iterative optimization algorithm to solve for the weight tensors, with theoretical analysis for its convergence and an experimental comparison against other learning from demonstration methods applied to the task of navigation over various terrains with a real ground robot.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "The paper provides a  clean and simple method for learning to navigate unstructured environments from demonstrations. The paper is well written, with thorough theoretical analysis and experimental validation. \n\nThe paper could do a better job in describing the implementation details of the algorithm. While some of this information is available in the appendix, it doesn't explain very well how the training and execution phases are carried out. The video shows a failure case of the approach, but it would be better if some discussion of the limitation of the approach was added to the paper. There is no  discussion about the computational requirements and the final performance of the algorithm as a function of dataset and temporal window size, which would make this paper a stronger contribution.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "This paper  presents an approach for solving the difficult task of unstructured navigation. The theoretical analysis and experimental validation make this a good contribution for this conference.", "technical_quality": "Very Good:  Convincing.", "clarity_of_presentation": "Good: Minor revision needed to improve organization or clarity.", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"impact": "3: The work is incremental and unlikely to have much impact, even though it may be technically correct and well executed.", "reviewer_expertise": "Very good: Comprehensive knowledge of the area"}, "extra_text": {"issues": "The paper is not clear in a couple implementation details. For instance, is algorithm 1 executed periodically at test time to include new data points for the actual robot behaviours? or does this happen in an offline data collection phase to construct A with the same size as Y? In terms of computational cost, how does the algorithm's performance scale with varying temporal window size c, and number of demonstrated trajectories n.\n\nLine 36 therefor\nLine 162 y(t) -y(t)"}}, {"review_id": "WGKey9orjTX", "reviewer": "Reviewer_1Tow", "summary": "This paper considers the problem of terrain adaptation for ground robots to traverse unstructured off-road terrains. The authors motivate the work by observing that in realistic scenarios, robots often fail to execute behaviors due to unexpected and difficult to model aspects such as wheel slip, reduction in tyre pressure etc. Hence, this paper presents a data-driven approach that learns to predict control inputs from observed features such that the robot is able to correct for unexpected observations and still consistently perform the behavior. The authors frame the problem as learning a weight tensor that associates a particular terrain feature captured at a time step with a particular behavior type. The optimization objective implicitly encodes an adaptation for correcting the behaviors online. Experiments are carried out in realistic outdoor settings on a data set captured in a certain types of unstructured terrains with features derived from multiple modalities. ", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths\n- The authors tackle and important problem of robust execution of navigation behaviors with a data-driven approach. \n- The proposed model is demonstrated on a realistic and a challenging data set. \n- The authors have provided the code and a video demonstrating the results on a ground robot. \n\nWeaknesses\n- The authors rely on a certain predefined feature sets such as HOG, Locally Binary Patters etc. Is it possible to ameliorate the need for feature extraction by using a neural-style approach that can learn feature  representations. \n", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "Overall, the paper addresses a practical problem and provides strong results. However, the technical exposition can provide further details on how the paper advances the state of the art. Such an explanation is necessary for wider adoption of this approach. Otherwise the results are convincing. ", "technical_quality": "Very Good:  Convincing.", "clarity_of_presentation": "Fair: Major revision needed to improve organization or clarity.", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"impact": "4: The work contains interesting new ideas that will potentially have major impact in robotics or machine learning.", "reviewer_expertise": "Very good: Comprehensive knowledge of the area"}, "extra_text": {"issues": "Issues\n- I would request the authors to provide details on how the work advances the state of the art and highlight the novelty of the approach.  \n- The authors are also requested to explicitly state the assumptions made in the problem formulation. This would help understand the generality of the method. \n- Does the approach assume that all sensor measurements are available at all times? Can the approach work when one of the sensors fails or when the sensor data arrives at different periodicities. "}}, {"review_id": "4p7Y5htxBXv", "reviewer": "Reviewer_cgkr", "summary": "The core contribution of this work focuses on enabling ground robots to make consistent navigation behaviors in unstructured terrains including grass, sand, gravel, and various rocks. By taking in terrain features from the environment, their method learns to monitor the difference between the expected and actual navigation behaviors to compute an offset that reduces the difference.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "The paper is easy to read for a broad robotics audience. While I am not as familiar with the problem addressed in this work, the problem definition, related works, and results are discussed in a manner that brings someone from outside the community up to speed quickly and shows convincing improvements relative to prior methods. Additionally, the notation provided in the approach is helpful to interpret this work and build upon it.\n\nIt might be helpful to some readers to understand your approach at a high-level before getting into the details in section 3.2A by providing a diagram describing all the interacting tensors, inputs, outputs, critical variables and transformations. For something like object detection, that usually translates into a network architecture. However, that might be different in your case. While the paper is tight on space, the first figure is communicating a familiar to most roboticists (i.e. actual behavior deviating from expected due to unaccounted variables). Perhaps combining that figure with a high-level diagram would be beneficial.\n", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "The paper is well organized, mentioning relevant related work. The paper clearly defines all notation, the problem definition, and approach. The paper presents a set of unstructured terrain traversal experiments including various terrain types and complexities. Additionally, the paper shows how the proposed method outperforms prior baselines from related work, considering multiple metrics including success, consistency, and others. I think the paper would be an excellent addition to CoRL and enjoyable to readers.", "technical_quality": "Excellent: Very convincing and thorough.", "clarity_of_presentation": "Very Good:  Well organized and clear.", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"impact": "4: The work contains interesting new ideas that will potentially have major impact in robotics or machine learning.", "issues": "Incorporating a high-level diagram as mentioned in strengths/weaknesses along with text describing it might be helpful to some readers.", "reviewer_expertise": "Good: General knowledge of the area"}, "extra_text": {}}, {"review_id": "0K2QkrHWAID", "reviewer": "Reviewer_7mFQ", "summary": "This paper investigates off-road ground robot navigation, particularly aiming to learn a control policy that provides offsets to provided vehicle commands such that the vehicle does not get stuck as often. The technical contribution is an algorithm for updating the weights of the control policy using self-supervision (i.e. learning from windows of (state, expected trajectory, actual trajectory) tuples). The authors numerically compare the proposed method with three baseline algorithms on a husky robot in various off-road terrains.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "Strengths:\n- Navigating off-road is a challenging and important problem, and the authors motivate and explain the problem nicely. The paper is written well and it was enjoyable to read.\n- The ability to learn in a self-supervised manner (without requiring annotation) is a great attribute of the approach\n- The hardware experiments are indeed extensive: several runs of several baseline algorithms are compared on various terrains on a real hardware platform in several real off-road environments. That is a lot of work!\n\nWeaknesses:\n- It isn't obvious to me how novel the optimization algorithm is. It looks like a fairly standard regularized loss, and the authors propose to iteratively update the two weight matrices by taking the derivative and setting it to zero. If the convergence guarantee is novel then it would make sense to have it in the main text or at least a sketch of how the proof is done.\n- The improvement over TRAL is rather small, and for n=10, are the differences statistically significant? \"The clear performance improvement obtained by our approach is because of the closed-loop capability that considers robot states along with terrain characteristics when adapting to terrains.\" -- there's no ablation, so how to justify this claim?\n- The quality/quantity/diversity of the training data is arguably the most important design \"parameter\" for the algorithm, so it would be great if the authors could provide some discussion on insights or impacts of these factors on the results.", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "The paper is solving an important and relevant problem, seems technically sound, and provides extensive hardware evaluation which can provide insights to future research in this direction. However, the technical novelty is not as clear to me, in terms of how unique the self-supervised formulation is, how unique the optimization algorithm is, and to what extent this is better than approaches such as actually modeling things like wheel slip/payload weight, off-road learning methods from Kahn et al, learning other types of offset terms (eg from Schoellig et al).", "technical_quality": "Very Good:  Convincing.", "clarity_of_presentation": "Excellent: Enjoyable to read.", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"impact": "2: Unsure, difficult to assess.", "reviewer_expertise": "Very good: Comprehensive knowledge of the area"}, "extra_text": {"issues": "Minor issues:\n- The introduction repeats itself a few times\n- The related work begins \"Related research on robot terrain adaptation...\" but this seems incomplete. The related work should better align with the paper's claimed contributions, such as a self-supervision methods, learning offset behaviors (e.g. Schoellig's work with UAVs), optimization methods with guarantees, state-of-the-art in off-road experimental validation, etc. What about the work of Kahn at Berkeley?\n- \" Due to momentum, we know the robot’s behaviors at the present time are dependent on previous time steps\" -- ? depends on what is in the state vector\n- \" learning of non-linear tasks can be lifted to linear space\" -- provide support for this claim?\n- \" for short periods of time (i.e., c = [1, 30]), the dynamics of the robot do not dramatically change and thus, the non-linearity in the robot is not severe\" -- questionable... \n- \"behavior\" should be defined more clearly as it is used throughout the paper. Is it a trajectory? or something more?\n- Is this really \"adaptation\" as the title suggests? It's more of learning an offset policy. Adaptation suggests an online component."}}]

Author rebuttal:

Meta-review: This paper presents a method for navigation with ground robots in unstructured outdoor environments. All the reviewers agreed on the good quality of the contribution. The reviewers particularly appreciated extensive robot experiments. 
- Several reviewers have pointed out the need for clearly highlighting the novel contributions of the proposed approach and how it advances the state-of-the-art. 
- Providing more details about the algorithm, training procedure, and the training/test datasets can significantly strengthen the paper. 
Besides addressing the major issues mentioned above, the authors should also revise the manuscript according to the other clarifications
requested and the suggestions provided. 

===== Post rebuttal ===== 
The authors have sufficiently addressed reviewers' concerns. All reviewers agree that the paper is well written and a good contribution. I recommend an acceptance.
Decision: Accept (Oral)