Stochastic Occupancy Grid Map Prediction in Dynamic Scenes
Authors: Zhanteng Xie
Philip Dames
Venue: CoRL 2023 Poster (2023)
Keywords: Environment Prediction
Probabilistic Inference
Robot Learning

Abstract: This paper presents two variations of a novel stochastic prediction algorithm that enables mobile robots to accurately and robustly predict the future state of complex dynamic scenes. The proposed algorithm uses a variational autoencoder to predict a range of possible future states of the environment. The algorithm takes full advantage of the motion of the robot itself, the motion of dynamic objects, and the geometry of static objects in the scene to improve prediction accuracy. Three simulated and real-world datasets collected by different robot models are used to demonstrate that the proposed algorithm is able to achieve more accurate and robust prediction performance than other prediction algorithms. Furthermore, a predictive uncertainty-aware planner is proposed to demonstrate the effectiveness of the proposed predictor in simulation and real-world navigation experiments. Implementations are open source at https://github.com/TempleRAIL/SOGMP.

Stochastic Occupancy Grid Map Prediction in Dynamic Scenes
Zhanteng Xie
Philip Dames Department of Mechanical Engineering Temple University United States pdames@temple. edu
Department of Mechanical Engineering Temple University United States zhanteng. xie@temple. edu
Abstract: This paper presents two variations of novel stochastic prediction algo- rithm that enables mobile robots to accurately and robustly predict the future state of complex dynamic scenes. The proposed algorithm uses a variational autoencoder to predict range of possible future states of the environment. The algorithm takes full advantage of the motion of the robot itself, the motion of dynamic objects, and the geometry of static objects in the scene improve prediction accuracy. Three simulated and real-world datasets collected by different robot models are used to demonstrate that the proposed algorithm is able to achieve more accurate and robust prediction performance than other prediction algorithms. Furthermore, a predictive uncertainty-awant planner is proposed to demonstrate the effectiveness the proposed predictor in simulation and real- navigation experiments. Im- plementations are open source at https://githeee comm/eemmleRAAI//OOM..
Keywords: Environment Prediction, Probabilistic Inference, Robot Learning
1 Introduction
Autonomous mobile robots beginning to enter people's lives and try help provide different last-mile delivery services, such moving goods in warchouses hospitals and assisting grocery shoppers [1-3]. To realize this vision, robots are required to safely and efficiently navigate through complex and dynamic environments that are full of people and/or other robots. The first prerequisite for robots to navigate and perform tasks is to use their sensors to perceive the surrounding environment. This work focuses on the next step, which to accurately and reliably predict how the surrounding environment will change based on these sensor data. This will allow mobile robots to proactively act avoid potential futurre collisions, a key part of autonomous robot navigation.
Environment prediction remains an open problem as the future state of the environment is unknown, complex, and stochastic. Many interesting works have focused on this prediction problem. Traditional object detection and tracking methods [4, 5] use multi-stage procedures, hand-designed features, and explicitly detect and track objects. More recently, deep learning (DL)-based methods that are detection and tracking- free have been able to obtain more accurate predictions [6-11]. Occupancy grid maps (OGMs), the most widely successful spatial representation in roboties, common environment representation in these DL-based methods. This transforms the complex environment prediction problem into an OGM prediction problem, outlined in Figure 1. Since OGMs can be treated as images (both are 2D arrays of data), the multi-step OGM prediction problem can be thought of as a video prediction task, a well-studied problem in machine learning.
the most
The most common technique for OGM prediction uses recurrent neural networks (RNNs), which widely used in video prediction [12-14]. For example, Ondruska and Posner [6] first propose an RNN-based deep tracking framework to directly track and predict unoccluded OGM states from raw sensor data. Itkina et al. [7] directly adapt PredNet [13] to predict the dynamic OGMs (DOGMas) in urban scenes. Furthermore, Toyungyernsub et al. [8] decouple the static and dynamic OGMs and
7th Conference Robot Learning (CoRL. 2023), Atlanta, USA.

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DWV
Figure I: A simple illustration of the OGM prediction problem.
propose double-prong PredNet to predict occupancy states of the environment. Schreiber al. [9, 10] embed the ConvLSTM units in the U-Net to capture spatiotemporal information of DOGMas and predict them in the stationary vehicle setting. Lange et al. [11] propose two attention-augmentee ConvLSTM networks to capture long-range dependencies and predict future OGMs in the moving vehicle setting. However, these image-based works only focus on improving network architectures and just treat the OGMs as images, assuming their network architectures can implicitly capture useful information from the kinematics and dynamics behind the environment with sufficient good data.
There are other DL-based approaches that explicitly exploit the ego-motion and motion flow of the environment to improve the OGM prediction accuracy. By using input placement and recurrent states shifting to compensate for ego-motion, Schreiber et al. [15] extend their previous image-based works [9, 10] to predict DOGMas in moving vehicle scenarios. By extending the deep tracking framework [6] with a spatial transformer module to compensate for ego-motion, Dequaire et al. [16] propose a gated recurrent unit (GRU)-based network to predict future states moving vehicle settings. estimate the forward/backward motion
Song al. [17] propose GRU-based LiDAR-FlowNe flow between two OGMs and predict future OGMs. Thomas et al. [18] directly encode spatiotemporal information into the world coordinate frame and propose 3D-2D feedforward architecture to predict futures. By considering the ggo-motion and motion flow together. Mohajerin and Rohani [19] first use the geometric image transformation to compensate for ego-motion, and then propose a ConvLSTM based difference learning architecture to extract the motion difference between consecutive OGMs. However, most of these motion- based works are designed for autonomous vehicles and cannot be directly deployed on mobile robots with limited resources. Furthermore, all the above-described works assume that the environmental state is deterministic and cannot estimate the uncertainty of future states, which we believe is key to helping robots robustly navigate in dynamic environments.
In this paper, we propose two versions of a variational autoencoder (VAe)-based stochastic OGM predictor for resource-limited mobile robots, namely SOGMP and SOGMP++, both of which predict a distribution of possible future states of dynamic scenes. The primary contribution of our approach is that we fully exploit the kinematics and dynamics of the robot and its surrounding objects to improve prediction performance. Specifically, we first develop simple and effective ego- ago-motion compensation mechanism for robot motion, then utilize ConvLSTM unit to extract the spatiotemporal motion information of dynamic objects, and finally generate local environment map to interpret static objects. Another key contribution is that by relaxing the deterministic environment assumption, our proposed approaches are able to provide uncertainty estimates and predict a distribution over future states of the environment with the help of variational inference techniques. We demonstrate the effectiveness of our approaches by using both computer vision metries and multi-target tracking metrics three simulated and real-world datasets with different robot models, showing that our proposed predictors have a smaller absolute enror, higher structural similarity, higher tracking accuracy than other statc-of-the-ar approaches, and can provide robust and diverse uncertainty estimates for future OGMs. Note that while all other published works only evaluate the image quality performance of the predicted OGMs, to the best of our knowledge, we are the first to employ a multi-object tracking metric, optimal subpattern assignment metric (OSPA) [20], to more fully evaluate OGM prediction performance in terms of tracking accuracy. In addition, we propose predictive uncertainty-aware planner by integrating the predicted and uncertain costmaps from predictor, and demonstrate its superior navigation performance in dynamic simulated and real-world environments.

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Figure 2: System architecture of the SOGMP+ predictor (SOGMP omits the Static Objects block).
2 Stochastic Occupancy Grip Map Predictor
2.1 Problem Formulation
In complex dynamic environment with both static and dynamic obstacles, the robot is equipped with lidar sensor sense its surroundings and uses the OGM to represent the environment. We assume each grid cell in the OGM is either occupied or free, i.e., a binary OGM. We assume that the robot is able to obtain relatively accurate estimates of its own pose and velocities from its odometry sensors or other localization algorithms over short periods of time (on the order of 1 s). We denote the pose and control velocity of the robot at time t by x, = [zz yr 0,]" and u, = [U, wy]" respectively. Let y: = [rx b, denote the lidar measurements (range and hearing time Giving a history of lidar measurements Yr-r:t and robot states {xt-rits Ue-rit). the robot needs predict the future state (i.e.. OGM) of the environment 0 Then, this environment prediction problem can be formulated as prediction model:
time t, and o, denote the OGM
po (o VV-rrtiX--re U.-ra),
where 9 are the model parameters. The goal is to find the optimal @ to maximize (1).
Note that in this paper, we set r = 10, the sampling rate is 10 Hz, and limit the physical size of OGMs to [0, 6.4] m along the x axis (forward) and [-3.2, m along the y axis (left). We use a cell size of 0.1 m, resulting in 64 x 64 OGMs. These settings are consistent with other works on mobile robot navigation [21]. All data o, y y are represented the local coordinate frame of the robot.
2.2 System Overview
Before describing our proposed SOGMP and SOGMP++ methods, we first briefly discuss image- based prediction methods. The prediction model (1) of image-based approaches is rewritten as
Po(0 Yi-ritxXe Xe-rit: up-ra) = fo(o,-ra),
Or- c(y:-ra):
(2)
where fa(.) is the neural network model, and c(-) is the conversion function to convert the lidar measurements to the binary OGMs in the robot's local coordinate frame. From this image- based model (2), we can easily see that image-based methods explicitly ignore the kinematics and dynamics of the robot and surrounding objects (i.e., assuming they can implicitly captured by very powerful network architectures and enough good data), and fail to provide range of possible and reliable OGM predictions (i.e., assuming a deterministic future).
Based these limitations, we argue that: 1) the future state of the environment explicitly depends on the motion of the robot itself, the motion of dynamic objects, and the state of static objects within the environment; 2) the future state of the environment stochastic and unknown, and a range of possible future states helps provide robust predictions. With these two assumptions, we fully and explicitly exploit the kinematic and dynamic information of these three different types of objects, utilize the VAE-based network to provide stochastic predictions, and finally propose two novel stochastic OGM predictors (i.e., SOGMP and SOGMP++, shown in Figure 2) to predict the future state of the environment. Since the only difference between the SOGMP and SOGMP+ is that the

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SOGMP++ considers the static objects and the SOGMP does not, we mainly describe the SOGMP+ model. The prediction model (1) of our SOGMP++, outlined in Figure 2, can be rewritten as
po Yt-rit X2 rtt :; -e:t:)) = pe(0 1 m),
(3a)
o h h(o,ra)) Ou-rit c(y ((y--7d)
(3b)
g(y
(3c)
Yt-ri klye-rit, Xt-r:t; ut-ra).
(3d)
The VAE predictor module corresponds to (3a). The dynamic object's module corresponds (3b),
where h(-) is the time series data processing function for dynamic objects, c(-) is the conversion function like (2), and R denotes the local coordinate frame of the robot predicted time + n. The
static object's module corresponds to (3c), where g(.) is the occupancy grid mapping function for static objects. Finally, the robot motion module corresponds to (3d), where k(-) is the transformation function for robot motion compensation. Note that this prediction model (3) only predicts future states at the next time step + and is used for training. To predict a multi-step future states at time t ++ n, we can easily utilize the autoregressive mechanism and feed the next-step prediction back 0++1 our SOGMP/SOGMP++ network (3a) for time steps to predict the future states at time step t + n. Note that the prediction horizon could theoretically be any time step.
2.3 Robot Motion
To account for the robot motion in dynamic scenarios, we propose a simple and effective ego-motion compensation mechanism &(-) ()- to mitigate its dynamic effects and allow the environment dynamics to be consistent in the robot's 's local coordinate frame. To predict the future OGM state in the robot's local future view, we consider the robot's future ego-motion and transform the observed OGMs Og-r:f to the robot's local coordinate frame prediction time step + So, our proposed ego- motion compensation mechanism can be divided into two steps: robot pose prediction and coordinate transformation. To account for the robot's future ego motion, we first use constant velocity motion model to predict the robot's future pose. Then, we use a homogeneous transformation matrix to transform the robot poses X and lidar measurements yt-rit to the robot' local future coordinate frame R and compensate for ego-motion (see Appendix A.l and Appendix A.2 for details).
2.4 Dynamic Objects
Since we use the OGM to represent the environmental state, we first need to implement a conversion function c(-) to convert the compensated lidar measurements y(-y. to the corresponding OGMs Op-rat by using coordinate to subscript conversion equations (see Appendix A.3 for details).
Tracking and predicting dynamic objects such pedestrians the hardest part of environmental prediction in complex dynamic scenes. It requires some techniques to process set of time series data to capture the motion information. While the traditional particle-based methods [5] require explicitly tracking objects and treat each grid cell as an independent state, recent learning- based methods [7-11, 15-17, 19] prefer to use RNNs to directly process the observed time series OGMs. Based on these trends, we choose the most popular ConyLSTM unit to process the spatiotemporal OGM sequences Or-rst- However, while other works [8, 14] explicitly decouple the dynamic and static/unknown objects and use different networks process them separately, we argue that the motion of dynamic objects is related their surroundings, and that explicit disentangling may lose some useful contextual information. For example, pedestrians walking through narrow corridor are less likely to collide with or pass through surrounding walls. To exploit the useful contextual information between dynamic objects and their surrounding, we directly feed the observed OGMs Og-rat into a ConvI unit ((-) and implicitly predict the future state 6.+1 of dynamic objects.
2.5 Static Objects
While predicting dynamic objects plays a key role in environmental prediction, paying extra attention to static objects is also important to improve prediction accuracy. The main reason is that the

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area occupied by static objects is much larger than that of dynamic objects, as shown in Figure 2. where static objects such as walls are consistently clustered together, while dynamic objects such as pedestrians are sparse and scattered point clusters. Another reason is that static objects contribute to the scene geometry and give a global view of the surroundings, where these static objects maintain their shape and position over time. To account for them, we utilize local static environment map m prediction for future static objects, which is key contribution of our work. We generate this local environment map m using the standard inverse sensor model [22]. This Bayesian approach generates robust estimate of the local map, where dynamic objects are treated as noise data and removed over time. We speed up this step by implementing a GPU-accelerated OGM mapping algorithm g(-) that parallelizes the independent cell state update operations (see Appendix A.4 for details).
2.6 VAE Predictor
If we treat the dynamic prediction function (3b) and the static prediction function (3c) as the prediction step of Bayes filters, then the VAE predictor (3a) is the update step of Bayes filters. It fuses the predicted features of static objects from (3c) and dynamic objects from (3b), and finally predicts a distribution over future states of the environment. A range of possible future environment states allows the robot to capture the uncertainty of the environment and enable risk-aware operational behavior in complex dynamic scenarios. To represent the stochasticity of environment states, we assume that environment states Op-r:t+n are generated by some unobserved, random, latent variables that follow prior distribution po (z). Then, our VAE predictor model (3a) be rewritten as
po 6 m) po(2))o(O441 z, 6,41, m)dz.
(4)
Since we are unable to directly optimize this marginal likelihood and obtain optimal parameters 0, we use VAE network parameterize our prediction model pe (o(01+1 6 m), outlined in Figure where the inference network (encoder) parameterized by & refers the variational approximation (z(z 6 m). the generative network (decoder) parameterized by 0 refers the likelihood po(Or+1 z, 0 m), and the standard Gaussian distribution (O,, 1) refers to the prior pa (z). Then, from work [23], we can simply maximize the evidence lower bound (ELBO) loss [(B, o; o++1) to optimize this marginal likelihood and get optimal 6:
(5) The first term on the right-hand side (RHS) is the expected generative error, describing how well the future environment states can be generated from the latent variable z. The second RHS term is the Kullback-Leibl (KL) divergence, describing how close the variational approximation is to the prior.
[(O, Φ; 0.+1) = E (x|6,4 [log (0 z, 6,+1, m)] KL (Lo( 6 m) (z)).
Finally, we use mini-batching, Monte-Carlo estimation, and reparameteriizttion tricks calculate the stochastic gradients of the ELBO (5) [23], and obtain the optimized model parameters ó and A. Using them, our VAE predictor can integrate the predicted features (6.+1, m} of dynamic and static objects, and output probabilistic estimate of the future OGM states with uncertainty awareness.
3 Experiments and Results
To demonstrate the prediction performance of our proposed approaches, we first test our algorithms on a simulated dataset and two public real-world sub-datasets from the socially compliant navigation dataset (SCAND) [24]. Second, we characterize the uncertainty of proposed predictors across different sample sizes and numbers of objects. Finally, propose predictive uncertainty-awarc planner by using the prediction and uncertainty information from our predictor to demonstrate how it improves robot navigation performance in crowded dynamic simulated/rel-woolld environments. See also Appendix B.1 for experimental evaluation of the run time of different prediction algorithms.
3.1 Prediction Results
Dataset: To train networks and baselines, collected an OGM dataset, called the OGM- Turtlebo22 dataset, using the 3D human-robot interaction simulator with 0.8 m/s Turtlebot2 robot [25,
5

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(i) OSPA: OGM-Spot
Figure 3: Average WMSE, average SSIM, and average OSPA of 10 different prediction time steps for all tested methods on 3 different datasets. Note that the shadows for SOGMP NEMC, SOGMP and SOGMP++ approaches are plotted with 95% confidence interval over 32 samples. For all curves for WMSE and OSPA, lower is better. For all curves for SSIM, higher is better.
26). We collected a total of 94,891 (x, y) tuples, where 17,000 tuples are used for testing. In addition, fairly evaluate all networks and examine performance the real world, we extracted two real-world sub-datasets (i.e., (x, y, tuples) from the public SCAND [24] dataset: OGM-Jackal dataset (collected by 2m/s Jackal robot) and OGM-Spot dataset (collected by 1.6m/s Spot robot). These two real-world datasets are only used for testing. See Appendix A.5 for more details.
Baselines: We compare our proposed SOGMP and SOGMP+ algorithms with four DL-based baselines: ConvLSTM [12), DeepTracking [6], PhyDNet [14], and an ablation baseline without the ego-motion compensation module (i.e., SOGMP NEMC). Note that all networks were implemented by PyTorch framework [27] and trained using the self-collected OGM- Turtlebtle dataset.
3.1.1 Quantitative Results
We evaluate all test OGM predictors on the three datasets from above by evaluating the absolute eиror, structural similarity, and tracking accuracy (see Appendix A.6 for details). Figure shows the detailed results obtained from these tests, from which we can observe four phenomena. First, our proposed SOGMP predictors with ego-motion compensation achieve significantly better average WMSE, SSIM, and OSPA than the SOGMP NEMC baseline without ego-motion compensation in all test datasets, which illustrates the effectiveness of ego-motion compensation. Second, the average WMSE of our proposed SOGMP predictors different prediction time steps is lower than the other image-based basclines in all three test datasets collected by different robots. This shows that the

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(b) Entropy vs. Number of objects
Figure 4: Average entropy of our SOGMP and SOGMP++ predictors at 5th prediction time step.
proposed SOGMP predictors utilizing kinematic and dynamic information are able to predict more accurate OGMs (i.e., smaller absolute error) than the statc-of-art amage-based approaches. Third, while our SOGMP predictors achieve the highest average SSIMs in all test datasets, it is interesting that the average SSIM our SOGMP++ with a local environment map is significantly higher than that of SOGMP without a local environment map in long-term predictions over multiple time steps. This indicates that the local environment map, which accounts for static objects, helps for longer-term prediction. Finally, the average OSPA errors of proposed SOGMP predictors significantly lower than that of the other four baselines, especially in longer prediction time steps. This further demonstrates the preferential performance of our proposed motion-base methods in tracking or predicting environmental states (i.e., localization and cardinality) over other image-based methods. However, the average OSPA errors of our proposed SOGMP and SOGMP++ predictors are almost the same. We believe that this is because static objects are more persistent than dynamic objects, so the static map does not provide significant benefits here. See also Appendix B.2 for examples of predicted OGMs and qualitative analysis.
3.1.2 Uncertainty Characterization
One of the biggest differences of our proposed methods compared to other previous baseline works that they can provide uncertainty estimates. To demonstrate the diversity and consistency of uncertainty estimates, we run two experiments to characterize and analyze the output distribution of our SOGMP/SOGMP++ predictors. One is to show how the entropy of the final probabilistic OGM changes as the number of OGM samples increases, with the hypothesis that will level off some value well below that of the entropy of uniform distribution. The other is to show how the entropy of the final probabilistic OGM changes the number of objects in the OGM increases, with the hypothesis that it will increase with the number of objects in it. Figure 4 shows the entropy results of these experiments on the OGM-Turtlebot2 dataset, which validates our hypotheses and demonstrates consistency of our VAE-based predictors. See Appendix A.7 for experimental details.
3.2 Navigation Results
We next test the applicability of our proposed methods to practical robotics applications. Figure shows our planner, where we add two new costmaps to the standard ROS [28] navigation stack using the outputs of our SOGMP predictor: one for the predicted scene and one for the uncertainty of the scene. See Appendix A.8 for additional details about the experimental setup.
3.2.1 Simulation Results
Using the Turtlebot2 robot in simulated lobby environment with different crowd densities, as in [25, 26), compare proposed predictive uncertainty- planner (i.e., DWA-SOMGP-PU with five navigation baselines: supervisec-leerming based CNN [25], deep reinforcement learning-

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Figure 5: System architecture of the predictive incertainty-awan navigation planner.
Table 1: Navigation results at different crowd densities
Environment
Method
Success Rate
Average Time (s)
Average Length (m)
Average Speed (m/s)
CNN [25)
14.30
5.40
A1-RC [29]
0.77
16.81
6.89
0.41
Lobby world,
DWA [30]
0.82
14.18
5.15
0.36
36 pedestrians
Trackkng
0.84
13.93
5.10
0.37
DWA-SOMGP-PP
0.86
13.79
5.12
0.34
DWA-SOMGP-PU
5.12
0.34
CNN [25]
0.79
16.65
5.62
0.34
[29]
6.28
Lobby world.
DWA [30]
0.77
15.39
5.16
0.34
45 pedestrians
DWA- MWA--eeppTaccee Tracking-P P
0.78
15.23
5.14
0.34
DWA-SO WWA-SSMMP-.P
0.79
14.84
5.14
0.35
DWA-SOMGG-PU
0.82
15.96
5.17
0.32
based AI-RC [29], model-based DWA [30]. and two ablation baselines without the uncertainty costmap (i.e., DWA-Deep DWWA-DeeTrraking-PP and DWA- WWA-SSGMM-P), Table summarizes these navigation results. As can seen, our DWA-SOGMP-PU policy has the highest success rate in each crowd size. while having almost the shortest path length. This shows that the prediction costmap from our SOGMP predictor is able help the traditional DWA planner to provide safer and shorter paths, and combining it with its associated uncertainty costmap achieve much better navigation performance than other baselines. It demonstrates the effectiveness of our proposed predictors in helping design safe robot navigation policies in crowded dynamic scenes. See Appendix B.3 for examples of paths planned by each approach and qualitative analysis.
3.2.2 Hardware Results
Besides the simulated experiments, we also conduct real-world experiment to demonstrate the applicability our DWA- SWA--SOGM-PUL policy the real world. Specifically, we deploy our SOGMP predictor and DWA-SOGMP-PU control policy to real Turtlebot2 robot with 2D Hokuyo lidar and Nvidia Jetson Xavier computer, and let it navigate through a crowded dynamic corridor in natural condition. From the attached Multimedia, it can be seen that the robot can safely navigate to its goal points among crowded pedestrians without any collision, which demonstrates the real-world effectiveness of our proposed SOGMP predictors and DWA-SOGMP-PU planner.
Limitations and Future Work
In this paper, we propose two versions of novel VAE-based OGM prediction algorithm that provides mobile robots with the ability to accurately and robustly predict the future state crowded dynamic scenes. In addition, integrate our predictors with the ROS navigation stack to propose predictive uncertainty- crowded navigation. We found that the prediction accuracy of SOGMP predictors was poor when: 1) the robot moves erratically or rotates rapidly; 2) the robot's 's field of view is occluded by large obstacle. We also were not able to compare against any of the DL-based ego-motion compensation methods [15-17, 19] as they do not have apen-source implementations and our attempts to recreate the results were not successful. Our future work will leverage more accurate robot motion models and correct jump steering angles overcome these limitations. We will continue to explore how to integrate uncertainty-awe predictors into learning- bearning-based control policies further improve robot navigation performance in crowded dynamic scenes.
planner and demonstrate its effectiveness the problem of robot

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Acknowledgments
This work was funded by NSF grant 1830419 and Temple University. This research includes calculations carried out HPC resources supported in part by the National Science Foundation through major research instrumentation grant number 1625061 and by the US Army Research Laboratory under contract number W911NF-16-2-0189
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---

A Additional Implementation Details
A.1 Robot Pose Prediction
To account for the robot's future ego-motion, we need to predict the future pose of the robot at prediction time step t + n.. Since the constant velocity motion model is the most widely used motion model for tracking [31] and often outperforms more state-of-the-an methods in general settings [32], we use it as our robot motion model and assume that the robot keeps constant motion in a relatively short period (i.e., less than 1 second). Note that other more suitable robot motion models specific to particular robot models predict the future pose of the robot X prediction time step using the robot's current pose X, and velocity u,
be used provide better robot pose predictions. Then,
easily
Zt+n
Te cos (oe) Ut sin (e) W2
Tx
Mt++
y/e
nãt
(6)
8t+n
8t_
00_
where At the sampling interval, (.) is the Gaussian noise.
A.2 Coordinate Transformation
To compensate for the ego-motion of the robot, we first use a homogeneous transformation matrix to transform the robot poses Xt-rat to the robot's local future coordinate frame R:
2
R
Tst
Toos (fe+n)
sin(Oetn)) sin (Oe+n) cos(Or+n)
Iitn Vt+n
Tt-Trit
yi
R
Tit
yt-
(7a)
1
0 O2
O2 Octn
(7b)
Then, by adding these ego-motion displacements, we convert the observed lidar measurements yt-rat from Polar Cartesian coordinates:
R I
cos((b--:te + A r:t) sin 0 ((rr))
y yi-ra
r:t Ui-rat
Pe-rit
Finally, we implement the transformation function (3d) and obtain set of observed lidar measure- ments y at the robot's local future coordinate frame R. The benefit of ego-motion compensation that we can treat these lidar measurements from a moving lidar sensor as observations from stationary lidar sensor at This significantly reduces the difficulty of OGM predictions and improves accuracy.
A.3 GPU-accelerated Conversion Function c(-)
Algorithm shows the pseudo-code for the GPU-accelerated conversion function c(-) (i.e. (3b)) to convert the lidar measurements to the binary occupancy grid maps.
Algorithm 1: Converting lidar points to OGMs
Input: compensated lidar measurements y Input: grid cell size
Input: the physical size of the OGMs S
Input: the lower left corner the OGMs (æo, yo)
Output: OGMs O
initialize: 01-7:1- 0
2: for all parallel beams E R do
3: i [a zn)
4: j=
j= 80 /s
5:
if S/ss) then
6:
7:
end if
8:
end for
12

---

A.4 GPU-accelerated OGM Mapping Algorithm g(-)
Algorithm 2 shows the pseudo code for the GPU-accelerated and parallelized OGM mapping algo- rithm g(-) (i.e., (3c)) that parallelizes the independent cell state update operation.
Note that 4 is the log odds representation of occupancy in the occupancy grid map m [22]. Algorithm 2: GPU-accelerated OGM mapping
Input: compensated lidar measurements y
Output: local environment map
1: for all time steps n from 1 - to / do
2: for all parallel grid cells m, in the perceptual field of y do
log p(m, vy.) 1-p(m,
p(m,)
3: 4
log I-p(m.)
4: end for
5: end for
A.5 Dataset Collections
We collected three OGM datasets to evaluate our proposed prediction algorithm, one self-collected from the simulator (i.e., OGM-Turtlebot2) and two extracted from the real-world dataset SCAND [24] (i.e., OGM-Jackal and OGM-Spot). Note that all three datasets are open source and available online [33].
A.5.1 OGM-Turtlebot2 Dataset
simulated Turtlebot2 equipped with a 2D Hokuyo UTM-30LX lidar navigates around an indoor environment with 34 moving pedestrians using random start points and goal points, as shown in Figure The Turtlebot2 uses the dynamic window approach (DWA) planner [30] and has maximum speed of 0.8 m/s. The Turtlebot2 robot environment to collect the OGM-Turtlebot2 dataset. The moving pedestrians in the human-robot interaction Gazebo simulator [25, 26) are driven by a microscopic pedestrian crowd simulation library, called the PEDSIM, which uses the social forces model [34, 35] to guide the motion of individual pedestrians:
up navigate autonomously in the 3D simulated lobby
Fp = Edes + Fobs + Fper + Frob
where Fp is the resultant force that determines the motion of pedestrian; Edes pulls pedestrian towards destination; Fobs pushes pedestrian away from static obstacles; Fper models interactions with other pedestrians (e.g., collision avoidance or grouping); and Frob pushes pedestrians away from the robot, modeling the way people would naturally avoid collisions and thereby allowing our control policy learn this behavior. More details can be found in Xie and Dames [26].
We collected the robot states {x, ub and raw lidar measurements at a sampling rate of 10 Hz. We collected a total of 94,891 (x, y) tuples, dividing this into three separate subsets for training (67,000 tuples), validation during training (10,891 tuples), and final testing (17,000 tuples).
A.5.2 OGM-Jackal and OGM-Spot Datasets
Figure 7 shows the real-world outdoor environment at UT Austin and the Jackal robot used to collect the raw SCAND dataset to construct the OGM-Jackal dataset. Figure 8 shows the real-world indoor environment at UT Austin and the Spot robot used to collect the raw SCAND dataset to construct OGM-Spot dataset. Note that the SCAND dataset was collected by humans manually operating the Jackal robot and the Spot robot around the indoor/outdoor environments at UT Austin, More details can be found in Karnan al. [24].
wwt.grrddmapiinttorrreeee torch
13

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Hukuyo Labie
Figure 6: Gazebo simulated environment, where the Turtlebot2 robot was used to collect the OGM- Turtlebot2 dataset.
Weldy Lidar
Whew Ditomiiry
Figure 7: Outdoor environment at UT Austin, where the Jackal robot used to collect the OGM-
Jackal dataset.
A.6 Experiment Details for OGM Prediction
A.6.1 Evaluation Metrics
To comprchensively evaluate the performance OGM predictors, we define the predicted OGM and the ground truth OGM as and use the following three metrics:
Weighted mean square error (WMSE) [36]:
>
Wi (o; oz)²
WMSE
(10)
where N is the number of cells in the OGM, and w, is the weight for the cell in the OGM, calculated by the median frequency balancing method [37]. This metric is used to evaluate the weighted absolute errors (balancing the imbalance in the percentage of occupied and free cells) between the predicted OGM and its corresponding ground truth OGM, describing the predicted quality of single OGM cell.
14

---

LABOVE THE
Velodyne Lider
RGB Camera
JoinAngic
Visual coumetry
Crnyorada Camaras
Figure 8: Indoor environment at UT Austin, where the Spot robot was used to collect the OGM-Spot dataset.
Structural similarity index measure (SSIM) [38]:
SSIM = (2Po/t + C1) (26 + C2)
(11)
(pō p + C1) +g
where ((-) and )(.) denote the mean and variance/covariance,, respectivel, and C() denotes constant parameters to avoid instability. We use C₁ = 1e-4 C2 = 9e-4. This metric is used to evaluate the structural similarity between the predicted OGM and its corresponding ground truth OGM, describing the predicted quality of the scene geometry.
Optimal subpattern assignment metric (OSPA) [20]:
1 min Σ do + d( m) TL FEIT,
OSPA
(12)
where is the cutoff distance, is the norm associated distance, (ō o) min (c, ||ō oll), and II, is the set of permutations of 21.2...., n..,....... n). We use 10 (i.e., m) and 1. This metric is used to evaluate the target tracking accuracy between the predicted OGM and its corresponding ground truth OGM, describing the predicted quality of multi-target localization and assignment.
It is worth noting that while other OGM prediction works [7-11, 15-17, 19] only use the computer vision metrics (e.g., MSE, F1 Score, and SSIM) to evaluate the quality of predicted OGMs, we are the first to evaluate the predicted OGMs from the perspective multi-target tracking (i.e., OSPA). We believe that since it takes into account multi-target localization error and cardinality error, it can give more accurate and comprehensive evaluation than only evaluating the image quality.
A.6.2 Evaluation Pipeline for Calculating OSPA Error on OGMs
This evaluation pipeline about how to extract targets from OGMs to calculate their OSPA errors is shown in Figure 9. First, we binarize the predicted OGMs with an occupancy threshold Pfrce = 0.3. which set by referencing the occ_thresh default parameter of 0.25 from the gmapping ROS package. Second, we use density-based spatial clustering of applications with noise (DBSCAN) [39] algorithm to cluster the obstacle points in the OGMs. Finally, we use the mean position of each cluster as the target calculate the OSPA error (with cutoff distance 10 cells, m). Note, get the ground truth target by applying the same process the ground truth OGMs.
15

---

Binerize
DBSCAN
Mean
Truth
Binarized
Clusters
Targets
OSPA
Binarize
Moan
Prediction
Binarized
Clusters
Targets
Figure 9: Evaluation pipeline for calculating OSPA error on predicted OGMs.
A.7
Experiment Details for Uncertainty Characterization
A.7.1 Evaluation Metrics
To comprehensively characterize the uncertainty information of our SOGMP and SOGMP++ pre- dictors, we define the predicted OGM as and the ground truth OGM as o and use the Shannon entropy [40] the metrie:
N o log + (1 o;) log(1 - 6;]];
H
(13)
N
where N the number of cells in the predicted OGM 6, and oj is the value of the cell in the predicted OGM ó.
A.7.2 Experiment Setup
Since our SOGMP/SOGMP++ network predicts bunch of binary OGM samples (i.e., cell value is 0 or 1) rather than probabilistic OGM, we first combine these binary OGM samples to create single probabilistic OGM and then use Shannon entropy to characterize its uncertainty, Note that the number of samples we draw can be scaled according to the robot's available computational resources. Before we conduct our uncertainty experiments, we first compute the number of objects in each input sequence of the OGM-Turtlebt pipeline shown in A.6.2, where classify these input sequences into 12 categories according the number of objects in them. Then, randomly select 20 input sequences for each number of objects (i.e., from to 12) and generate a total of 1,024 OGM samples for each input sequence at the 5th prediction time step.
dataset the 5th prediction time step using the evaluation
To analyze the relationship between the entropy of the predicted OGM and its sample size, use all selected test sequences and calculate the average entropy over the number of samples growing as an exponential power of 2. To analyze the relationship between the entropy of the predicted OGM and the number of objects in it, we first use 1,024 OGM samples for each input sequence to generate the final probabilistic OGM and then calculate the average entropy over the number of objects from to 12.
A.8
Experiment Details for Robot Navigation
A.8.1 Evaluation Metrics
To comprehensively evaluate the performance of navigation control policies, we use the following four metrics from [25, 26]:
Success rate: the fraction of collision-free trials.
Average time: the average travel time of trials.
16

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Average length: the average trajectory length of trials.
Average speed: the average speed during trials.
A.8.2 Experiment Setup
For the robot navigation experiments, we use the Turtlebo12 robot with a maximum speed of 0.5 m/s, equipped with a Hokuyo UTM-30LX lidar and an NVIDIA Jetson AVG Xavier embedded computer. Considering the computational resources of the Turtlebot2 robot, we use the SOGMP predictor to generate predicted OGM samples at the 6th prediction time step (i.e., 0.6 Based on these predicted OGM samples, generate a prediction map (mean) and uncertainty map (standard deviation), which are used to generate the prediction costmap layer and uncertainty costmap layer respectively for predictive uncertainty- Figure 5. Note that each costmap grid cell has an initial constant cost, and we map each occupied grid cell of the prediction costmap and uncertainty costmap to a Gaussian obstacle value rather than "lethal" obstacle value. This is because the predicted obstacles and uncertainty regions are not real obstacle spaces.
planner (i.e.. DWA-SOGMP-PU),
shown in
17

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B Additional Results
B.1 Inference Speed Results
Before we focus on quantitative results on the quality of these OGM predictions, first talk about the inference speed and model size of these predictors. This is because robots are resource-limited and smaller model sizes and faster inference speeds mean robots have faster reaction time to face and handle dangerous situations in complex dynamic scenarios.
Table 2 summarizes the inference speed and model size of six predictors tested on an NVIDIA Jetson TX2 embedded computer equipped with 256-core NVIDIA Pascal @ 1300MHz GPU. We that although DeepTrackee
[6] has the smallest model size, proposed SOGMP models are about 1.4 times smaller than the ConvLSTM [12] and 4 times smaller than the PhyDNet [14], and their inference speed is the fastest (up to 24 FPS).
Table 2: Inference Speed and Model Size
Models
ConVLSTM [12]
PhyDNet [14)
DeepTracking [6]
SOGMP NEMC
SOGMP
SOGMP++
FPS
2.95
4.66
5.32
24.83
23.29
10.68
# Params
12.44 M
37.17 M
0.95 M
8.84
8.84
8.85
B.2
Qualitative Prediction Results
Figure 10, Figure 11, Figure 12, and the accompanying Multimedia illustrate the future OGM predic- tions generated by our proposed predictors and the baselines. We observe two interesting phenomena. First, the image-based baselines, especially the PhyDNet, generate blurry future predictions after 5 time steps, with only blurred shapes of static objects (i.e. walls) and missing dynamic objects (i.e., pedestrians). We believe that this is because these three baselines are deterministic models that less expressive network architectures, only treat time series OGMs as images/video, and cannot capture and utilize the kinematics and dynamics of the robot itself, dynamic objects, and static objects. Second, the SOGMP++ with local environment map has sharper and more accurate surrounding scene geometry (i.e., right walls) than the SOGMP without local environment map. This difference indicates that the local environment map for static objects is beneficial and plays key role in predicting surrounding scene geometry.
In addition, Figure 13 shows diverse set of prediction samples from SOGMP++ predictor. The red bounding boxes highlight the ability of our SOMGP+ predictor to provide diverse and plausible potential future predictions for stochastic and dynamic environments.
B.3 Qualitative Navigation Results
Figure 14 shows the difference of nominal paths and costmaps generated by three different planners the simulated lobby environment. The default DWA planner [30] only cares about the current state of the environment and generates a costmap based on the perceived obstacles. The predictive DWA planner (i.e., DWA-SOGMP-P) using the prediction map of our proposed SOGMP predictor can generate costmap with predicted obstacles. The predictive uncertainty- awwae DWA planner (i.e., DWA-SOGMP-PUL using both the prediction map and uncertainty map of our proposed SOGMP predictor can generate a safer costmap with predicted obstacles and uncertainty regions. These additional predicted obstacles and uncertainty regions of our proposed DWA-SOGMP-PUL planner enable the robot to follow safer nominal paths and reduce collisions with obstacles, especially moving pedestrians. See the accompanying Multimedia for detailed navigation demonstration.
18

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n-2
n23
n:4
A=7
nZB
R:0
50GMPH4 Ground
ConcETI DeepTrokknng SOOUP JOWC SOGNP
Phychet
Figure 10: A prediction showease of the six predictors tested on the OGM-Turllebot2 dataset over the prediction horizon. The black area is the free space and the white area is the occupied space.
n=2
n*3
n#d
R
n*7
x*8
n*B
50
Ground trdd
SRGNPH4
SOCMI
Ceeptracking SOCIP JEMC
CONLLTTM
PhyOhet
Figure 11: A prediction showcase of the six predictors tested on the OGM-Turtlebot2 dataset over the prediction horizon. The black area is the free space and the white area is the occupied space.
19

---

Goued
50GMPH+
SOCIP
Deep Trocking SOCaP, NEMIC
PhycMe Cont STT
Figure 12: A prediction showcase of the six predictors tested the OGM-Turlebot2 dataset the prediction horizon. The black area the free space and the white area is the occupied space.
Sumple
Sample 2
Sample 3
Sample 4
Figure 13: A diverse set of prediction samples of our SOGMP++ predictor tested on the OGM- Turtlebo22 dataset the 5th prediction timestep. The black area the free space and the white area is the occupied space. The red bounding boxes show multiple possible predictions.
2
(a) DWA [30]
(b) DWA-SOGMP-P
(c) DWA-SOGMP-PL
Figure 14: Robot reactions and their corresponding costmaps generated by different control policies in the simulated lobby environment. The robot (black disk) is avoiding pedestrians (colorful square boxes) and reaching the goal (red disk) according to the nominal path (green line) planned by the costmap (square white map).
20


Reviews:
[{"review_id": "YuciyboRBLI", "reviewer": "Reviewer_iQee", "summary": "", "questions": "", "limitations": "", "rating": 2, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "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": "The paper presents an approach to occupancy grid map (OGM) prediction that extends prior work by (1) generating stochastic prediction using a VAE and (2) compensating for ego robot motion. The method is evaluated on a collected simulated dataset for simulated crowd navigation, SCAND-Jackal and SCAND-Spot, as well as in the real-world on a TurtleBot robot platform in a real-world setting.", "summary_of_recommendation": "Overall, the paper is well written and presents a relevant extension to OGM prediction using generative models. The real-world evaluation is appreciated. My biggest concerns with the paper center around the empirical evaluation. Overall, it is not really completely clear that the uncertainty component helps the planner. Majorly, the lack of stochastic generated prediction qualitative evaluation and the lack of SOTA baseline comparisons for OGM prediction weaken the message of the paper. As it stands, I am leaning towards rejecting the paper at this time. That being said, I think this is a promising paper, and with some improvements to the evaluation it will make a good contribution.", "technical_quality": "Fair: Significant additional evidence required to support the claims.", "clarity_of_presentation": "Good: Minor revision needed to improve organization or clarity.", "potential_impact": "", "robotics_focus": "Sufficient demonstration on hardware", "quality_of_limitations": "Limitations are addressed clearly", "questions_for_rebuttal": "In addition to the weaknesses listed above, I am hoping the authors can address the following clarifications during the rebuttal period.\n1. I think I missed the history and the prediction time horizons. Could you clarify this/point me to where in the paper it is stated?\n2. The paper claims that previous observation-based approaches do not account for robot motion compensation. However, the assumption in those methods is that the robot motion is compensated for by the neural network relative to the local frame of reference. Then the claim here becomes that it is easier for the neural network to work with a predefined structure for the robot motion. But the chosen predefined structure seems pretty straightforward (linear). Do you think a more expressive/powerful neural network architecture would circumvent for the robot motion compensation? Or is there a fundamental limitation that cannot be bridged?\n3. Could you clarify what is meant by the statement in line 124: \"mitigate [the robot's] dynamics effects\"?\n4. Are $\\hat{o}_{t+1}$ only dynamic objects? How are they identified? By filtering them out for the static map?\n5. The argument in Sec. 2.5 in favor of the separate static map component states that static objects take up a large proportion of the occupied grid cells. Why would weighting the cross-entropy loss to account for the data imbalance be insufficient?\n6. Is the local static map a local map? Is its size also 6.4x6.4 m?\n7. Should the prior in the VAE be conditioned on the history of observations? See [D], for example.\n\n[D] M. Itkina, et al. \"Multi-agent variational occlusion inference using people as sensors.\" ICRA, 2022.\n\n8. Do you have a sense for why the WMSE is better without the static map (Fig. 3)?\n9. In the video, there is a lot of shaking in the proposed method as compared to the baselines. Why do you think that is?", "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": "Strengths:\n* The paper is very well written and structured.\n* The topic is timely and interesting. The problem is well-motivated and the literature review does a good job of contextualizing the paper in prior work.\n* The mapping in Sec. 2.6 from the proposed approach to a Bayes filter was insightful.\n* The evaluation in the loop with a planner strengthens the message of the paper.\n* The analysis in the appendix provides further context for the method and the claims made in the main paper.\n\nWeaknesses:\n\n* The literature review is missing the following line of work:\n\n[A] T, Hugues, et al. \"The Foreseeable Future: Self-Supervised Learning to Predict Dynamic Scenes for Indoor Navigation.\" arXiv, 2022.\n\n[B] T. Hugues, et al. \"Learning Spatiotemporal Occupancy Grid Maps for Lifelong Navigation in Dynamic Scenes.\" ICRA, 2022.\n\n[C] B. Lange et al. \"LOPR: Latent Occupancy PRediction using Generative Models.\" arXiv, 2022.\n\n* The current use of binary 0/1 OGMs means that occlusions are not accounted for and some probabilistic elements are ignored as well.\n* Fig. 1 could be made more informative by creating a color/numbering scheme to track different people through the different stages of the OGM prediction process.\n* The size of the considered OGM is quite small (6.4x6.4 m). Prior work looked at bigger OGMs (40-50 m per side). However, the current setting is looking at a small mobile robot rather than an AV, so a smaller OGM may be acceptable. Could you provide a citation for why this is a reasonable size?\n* A major contribution in the paper is the VAE architecture that allows for \"a range of possible and reliable OGM predictions\". However, as far as I could tell, there were no experiments showing the diverse predictions generated by the prediction network. At a minimum, qualitative diverse samples should be presented that show diverse but reasonable potential future predictions.\n* It seems that only the simulation data is used for training, unless I misunderstood something. Generally, evaluating human behavior prediction in simulation is suboptimal as simulators provide much cleaner, simpler behaviors than the real-world. The real-world results do seem to indicate reasonable transfer.\n* One of my biggest concerns with the paper is that there are no modern OGM prediction methods considered as baselines. For example, [8, 11, A-C] seem like relevant methods to compare against.\n* From the quantitative results in Table 1, there does not seem to be a significant difference between the uncertainty and no uncertainty planning performance.\n* The claim that moving objects disappear solely due to a lack of stochastic modeling is not entirely true. Disappearance also occurs due to less expressive architecture choices as found by [8, 11]. Potentially, considering more expressive baselines would at least in part circumvent this issue.\n\nThe following is a list of minor typos as well as consistency issues I found:\n1. What is the github link at the end of the abstract?\n2. Line 37: should be 'DOGMs' and in previous work 'DOGMas' [7].\n3. The references have some consistency issues. For example, conferences should be capitalized (e.g., [12]) acronyms are sometimes included (e.g., ICRA in [1]) and sometimes not (e.g., [2]). When possible, the conference venue should be cited instead of ArXiv (e.g., [13]). The references should in general be proofread (e.g., [7] lists the year and IEEE twice, LSTM is not capitalized (e.g., [12])).", "extra_scores": {"impact": "4: The work contains interesting new ideas that will potentially have major impact in robotics or machine learning."}, "extra_text": {}}, {"review_id": "DuCeBZe04j", "reviewer": "Reviewer_QuXe", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "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": "This paper tackles the problem of probabilistic prediction of local maps in the presence of dynamic objects around a robot. It formulates the problem as a conditional inference problem, with a sliding window history of observations and robot states. The conditional prediction is performed using a variational autoencoder.", "summary_of_recommendation": "Overall the paper presents a reasonable approach (ego-motion compensation + VAEs) to predicting dynamic local maps. The results are good, but the approach could be a bit better explained, and the related work coverage could be expanded.", "technical_quality": "Good: Generally convincing, but some additional experiments or analyses needed.", "clarity_of_presentation": "Good: Minor revision needed to improve organization or clarity.", "potential_impact": "", "robotics_focus": "Sufficient demonstration on hardware", "quality_of_limitations": "Limitations are addressed clearly", "questions_for_rebuttal": "It would be good to clarify the math notation questions above. ", "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": "Review summary:\nThe paper is well motivated, and the proposed solution is clearly described. The probabilistic problem formulation is very clear, and the simulation results are compelling, using an off-the shelf navigation planner. The real-world robot video is also very compelling. However, the proposed algorithm could be a bit better explained, and some additional qualitative results would help.\n\nDetailed comments:\n* Shouldn't the LIDAR conversion function depend on the robot state? Specifically, in eq. 2, shouldn't $c(y_{t-\\tau:t})$ be $c(y_{t-\\tau:t}, x_{t-\\tau:t}, u_{t-\\tau:t} )$?\n* The functions in eq.3 could be better explained. What exactly is $h(\\cdot)$ doing? Is it a learned function, or a geometric operation? Is $k$ just a coordinate transformation? It would help to relate the math notation to the system diagram in fig. 2.\n* The paper claims that the primary contribution is the use of the kinematics and dynamics of the robot. The ablation studies seem to support this, but a qualitative analysis of a few test cases showing the difference that this makes would be good. This would help provide an intuition of what kinds of cases this would make a significant difference.\n* There is a related field on prediction of tracks of moving objects - while the representation of this problem is different, they both solve the same problem. It would be good to include this in the related work, and ideally also include them in the comparison. Here are two recent example papers from the field:\nKamenev, Alexey, et al. \"Predictionnet: Real-time joint probabilistic traffic prediction for planning, control, and simulation.\" 2022 International Conference on Robotics and Automation (ICRA). IEEE, 2022.\nChen, Yuxiao, Boris Ivanovic, and Marco Pavone. \"Scept: Scene-consistent, policy-based trajectory predictions for planning.\" Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. 2022.", "extra_scores": {"impact": "3: The work is incremental and unlikely to have much impact, even though it may be technically correct and well executed."}, "extra_text": {}}, {"review_id": "Af0yMJ6UVve", "reviewer": "Reviewer_Kpfb", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "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": "The work proposes a method to predict the future state of an occupancy grid map (OGM) for robot navigation in 2D. The core contribution of the work is the use of the motion of the robot and dynamic obstacles in its surrounding via ego-motion compensation. The result of the OGM prediction is evaluated on three different platforms, using one simulated scene and two real scenarios. Further, the authors integrate the predicted OGM into a planner and demonstrate this in a real-world navigation scenario.", "summary_of_recommendation": "Some properties, such as the impact of choosing a grid resolution and an alternative OGM method for navigation, have not been discussed and it is therefore difficult to conclusively judge the impact of the work. However, the paper has been well written and clearly shows an advantage of incorporating ego-motion into the prediction of future OGM states. The navigation experiment on the Turtlebot2 helped a lot to assess the applicability of the method in a realistic scenario.", "technical_quality": "Very Good:  Convincing.", "clarity_of_presentation": "Very Good:  Well organized and clear.", "potential_impact": "", "robotics_focus": "Sufficient demonstration on hardware", "quality_of_limitations": "Additional details required", "questions_for_rebuttal": "- 'u' is commonly used for the control input. Is 'u' here the ideal commanded target velocity or the actual measure velocity?\n- While the Turtlebot2 and Jackal are skid-steering platforms where the 2D motion model with 2D position with yaw/heading can be applied, the Spot has 6 DoF where this motion model cannot be applied just like that. How is the 6DoF motion mapped onto the 2D motion model and how does this deal with lateral or vertical movement?\n- How do the runtime and prediction performance change with higher and lower grid map resolutions and history lengths?\n- It is unclear if the OGM evaluation in Section 3.1 runs in realtime (i.e. at 2.95 Hz for ConvLSTM, 5.3 Hz for DeepTracking, 10.68 Hz for SOGMP++, ...) on the Jetson TX2 or offline frame-by-frame. Given the fixed history size (τ=10), wouldn't methods with a slower updated rate, e.g. ConvLSTM, have a longer history (1/2.95 Hz * τ = 3.39 s), and therefore better data, than the proposed faster method SOGMP (1/23.29 Hz * τ = 0.43 s)?\n- The navigation experiments only evaluate the proposed OGM method. How would the navigation perform when using the baseline OGM methods in place of SOGMP?", "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": "The manuscript is well written and easy to follow. The prediction of future states of scenes for navigation is generally relevant for robotics. The attached video with the navigation experiment helps to judge the applicability of this work.\n\nMy main concerns with the manuscript are:\n1. The significance of the chosen OGM method for navigation has not been discussed. It is unclear if any of the other baseline OGM methods would achieve a similar navigation performance.\n2. The grid resolution (0.1 m) and history length (10) appear low. While experiments show that this is sufficient for navigating with a smaller robot (Turtlebot2) in simulation and a real scenario, the impact of choosing those has not been discussed.\n\nFurther, some of the OGM baseline methods are quite old (2 of the 3 are from 2015 and 2016 respectively). While the relation of components in Figure 2 with equations 3 is described in the text, it would help a lot if equations or sections could be referenced directly in the figure.", "extra_scores": {"impact": "3: The work is incremental and unlikely to have much impact, even though it may be technically correct and well executed."}, "extra_text": {}}, {"review_id": "5vsVd7kASI", "reviewer": "Reviewer_M8W2", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "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": "The paper proposes a novel stochastic prediction algorithm that uses a variational autoencoder to predict a range of possible future states of the occupancy grid. The algorithm takes full advantage of the motion of the robot itself, the motion of dynamic objects, and the geometry of static objects. Three simulated and real-world datasets collected by different robot models are used. A predictive uncertainty-aware planner is proposed to demonstrate the effectiveness of the proposed predictor in simulation and real-world navigation experiments.", "summary_of_recommendation": "My main concern is related with the assumption of constant velocity, which over-simplifies the problem. Therefore, more complex cases where the objects don't have constant velocity should be investigated (especially on simulation, since the velocity profiles can be adjusted).", "technical_quality": "Good: Generally convincing, but some additional experiments or analyses needed.", "clarity_of_presentation": "Good: Minor revision needed to improve organization or clarity.", "potential_impact": "", "robotics_focus": "Sufficient demonstration on hardware", "quality_of_limitations": "Limitations are addressed clearly", "questions_for_rebuttal": "- In SOGMP, wouldn't it be equal to SOGMP++ with dynamic objects having a velocity of zero? The reason of the performance difference in between these two should be stated more clearly.\n- The details of the training is not clear to me. In auto-regressive mechanism, do you use the ground truth for each step (t+1, t+2, t+3, ..., t+n) and find the loss at each time step, or do you make the estimations for all n steps (t+n), and compute the loss at the end of n steps only?\n- For high velocity models (robots or autonomous vehicles), wouldn't a constant velocity motion model assumption fail frequently? Can you analyse your results for a platform for varying speeds?\n- Would it be possible to give the times/fps rates for the computation power?", "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": "I think that only ego-centric approaches are considered, however, allo-centric occupancy grids also improve the prediction performance, as shown in [1].\n\nI don't agree with the assumption that Eqn.2 does not represent the kinematics and dynamics of the scene. Indeed, this function assumes that the kinematics of the environment can be learned stochastically from sufficient large samples.\n\nIn SOGMP, wouldn't it be equal to SOGMP++ with dynamic objects having a velocity of zero? The reason of the performance difference in between these two should be stated more clearly.\n\nThe details of the training is not clear to me. In auto-regressive mechanism, do you use the ground truth for each step (t+1, t+2, t+3, ..., t+n) and find the loss at each time step, or do you make the estimations for all n steps (t+n), and compute the loss at the end of n steps only?\n\nFor high velocity models (robots or autonomous vehicles), wouldn't a constant velocity motion model assumption fail frequently? Can you analyse your results for a platform for varying speeds?\n\nWould it be possible to give the times/fps rates for the computation power?\n\nFor the simulation, usage of the pedestrians does not make any difference, since there are no other types of obstacles. Simple cylinders should also be used, which would accelerate the simulation speed.\n\n[1] Asghar, R., Rummelhard, L., Spalanzani, A., & Laugier, C. (2022, December). Allo-centric Occupancy Grid Prediction for Urban Traffic Scene Using Video Prediction Networks. In 2022 17th International Conference on Control, Automation, Robotics and Vision (ICARCV) (pp. 255-260). IEEE.", "extra_scores": {"impact": "3: The work is incremental and unlikely to have much impact, even though it may be technically correct and well executed."}, "extra_text": {}}]

Author rebuttal:

Meta-review: The paper presents an approach to occupancy grid map (OGM) prediction that generates stochastic predictions using a VAE and by compensating for ego robot motion. Reviews all agreed that the problem formulation was interesting and principled, with clear results, both in simulation and in extensive real world experiments using a turtlebot/jackal/Spot robot. The primary reviewer concerns were around a lack of modern neural network baselines for occupancy grid prediction and the simple dynamics model used (constant velocity).

The authors responded well, addressing a number of concerns, but did not directly address issues around baselines, instead arguing that modern baselines were infeasible for use here given computational and training requirements. They also argued that an improved dynamics model could be used if desired. Despite these weaknesses, I think the simplicity of the proposed approach and extensive experimental results marginally outweigh these concerns, and recommend acceptance. I encourage the reviewers to address remaining reviewer concerns and incorporate rebuttal clarifications in the final version of the paper.
Decision: Accept (Poster)