This paper proposes a transferable Map of Dynamics (MoD) framework that generalizes to unknown environments using only egocentric 3D LiDAR point clouds to overcome the long-standing limitation of traditional MoD methods. While MoDs are essential for encoding human motion characteristics to enable accurate pedestrian trajectory prediction or safe robot navigation, traditional approaches suffer from site-specificity, requiring exhaustive trajectory accumulation at every new location. Extending recent advances in neural implicit modeling, our framework trains a continuous, LiDAR-based MoD estimator across diverse environments. To mitigate the inherent sparsity and temporal bias of real-world trajectory data, we introduce a position-balanced sampling strategy and a multi-task learning architecture that jointly predicts motion distributions and a spatial frequency score map. The latter is further augmented by visibility-aware losses to compensate for incomplete observation data. Comprehensive experiments demonstrate that our method effectively reconstructs underlying motion maps even in unknown locations from a single instantaneous LiDAR scan, despite highly sparse training data. Finally, we show that our improvements enhance the reliability of downstream trajectory prediction.
Figures & tables
Figure 1: Concept of our framework compared to NeMo-map [ 34 ] . We train model across L multiple locations to build transferable map of dynamics.
Figure 2: Overview of transferable MoD framework EgoNeMo. A neural network with a BEV encoder and two task heads is trained to predict Semi-wrapped Gaussian Mixture Model (SWGMM) parameters and a frequency score from LiDAR input. SWGMM image is from paper [ 34 ]
Figure 3: Spatial sparsity of ATC, KTH and JRDB. Red color shows position counts from all trajectories in a sequence.
Model
JRDB-Known*
JRDB-Unknown
SiT
NeMo
12.0 (1.16)
N/A
N/A
BFF*
1.01 (0.06)
1.53 (0.05)
1.34 (0.12)
Ours
1.29 (0.16)
1.42 (0.05)
1.24 (0.11)
Table 1: NLL comparison with existing MoD methods. JRDB-Known* refer to three sequences with clear spatial overlaps with train sequences, gates-ai-lab-2019-04-17_0, huang-2-2019-01-25_1, and tressider-2019-03-16_2 from known location sequences.
JRDB-Known
JRDB-Unknown
SiT
Method
NLL
( 20∘ var)
NLL
( 20∘ var)
NLL
( 20∘ var)
Motion
1.22 (0.08)
4.12 (0.61)
1.79 (0.29)
4.66 (0.35)
1.63 (0.04)
4.68 (0.86)
Motion-Freq
1.14 (0.03)
3.68 (0.12)
1.67 (0.09)
4.03 (0.39)
1.45 (0.07)
3.82 (0.74)
Motion(GS)-Freq
1.14 (0.01)
2.82 (0.55)
1.47 (0.08)
3.34 (0.48)
1.22 (0.10)
2.80 (0.46)
Motion(GS)-FreqPU
0.95 (0.03)
3.08 (0.69)
1.33 (0.03)
3.88 (0.66)
1.22 (0.01)
3.43 (1.35)
Motion(GS)-FreqPNi
1.12 (0.07)
2.54 (0.27)
1.42 (0.05)
2.98 (0.51)
1.24 (0.11)
2.82 (0.74)
Table 2: NLL comparison in JRDB and SiT dataset. Motion corresponds to the baseline that simply extends NeMo-map [ 34 ] . Each value represents the mean of three trials, with the standard deviation shown in parentheses. The lowest mean value per column is in bold.
Figure 4: Outputs of Motion and Motion-Freq on JRDB unknown locations. In the motion maps, arrows visualize the velocity modes; opacity represents weight, arrow length represents speed, and hue represents direction using a cyclic color mapping. The same hue corresponds to the same direction across all maps. The reference column shows the sequence names and stitched images, horizontally compressed for visualization. The input column shows LiDAR data as BEV with height-based color from navy to yellow.
Figure 5: Frequency score and motion outputs of Motion(GS)-Freq , Motion(GS)-FreqPU , and Motion(GS)-FreqPNi . For each method, the left panel shows the predicted frequency score (brighter color means higher score), and the right panel shows the motion map. Samples and arrow encoding of motion maps are the top two rows of Fig. 4 , the rest are in the Appendix Fig. 4.
Fewer locations
Shorter durations
JRDB-Known
JRDB-Unknown
JRDB-Known
JRDB-Unknown
Method
NLL
( 20∘ var)
NLL
( 20∘ var)
NLL
( 20∘ var)
NLL
( 20∘ var)
M only
1.24 (0.08)
4.70 (0.54)
1.81 (0.09)
5.09 (0.16)
1.50 (0.14)
4.37 (0.58)
2.26 (0.54)
5.31 (0.74)
M-F
1.23 (0.06)
4.20 (0.48)
1.81 (0.03)
5.40 (0.54)
1.43 (0.10)
4.34 (0.23)
1.96 (0.05)
5.17 (0.43)
M(G)-F
1.51 (0.01)
3.40 (0.43)
1.87 (0.05)
4.11 (0.34)
1.30 (0.02)
2.89 (0.14)
1.75 (0.06)
3.78 (0.05)
M(G)-FPU
0.97 (0.04)
3.22 (0.45)
1.40 (0.02)
4.03 (0.64)
1.01 (0.03)
3.20 (0.35)
1.37 (0.06)
4.22 (0.76)
Table 3: NLL comparison in JRDB dataset for reduced train data. Each value represents the mean of three trials, with the standard deviation shown in parentheses. The lowest mean value in each column is highlighted in bold. The method column shows short-hand names (M, F, and G) instead of Motion, Freq, and GS, respectively.
T=12
T=18
T=24
Method
K
ADE
FDE
ADE
FDE
ADE
FDE
ST [ 24 ]
1
0.54
0.99
0.79
1.57
1.05
2.14
ViTE [ 14 ]
3
0.36
0.57
0.52
0.84
0.67
1.11
NeMo [ 34 ]
1
0.44
0.82
0.63
1.23
0.81
1.60
NeMo [ 34 ]
3
0.42
0.80
0.62
1.20
0.79
1.57
Ours-base
3
0.42
0.79
0.61
1.19
0.78
1.55
Table 4: Trajectory prediction errors on JRDB. K is the number of modes. NeMo uses CLiFF-LHMP algorithm [ 32 , 34 ] on the same MoD as Ours . All results are averaged over 3 training runs.
Parameter
Value
Time step size Δt
0.33 [s]
Kernel time scale σt
1.5 [s]
Mode weight threshold wth
0.05
Velocity blend parameter β
5.0 [ rad−2 ]
Prior speed variance σρ2
(0.01 [m/s])2
Prior angle variance σθ2
(0.4 [rad/s])2
Table S1 : Hyperparameter configurations utilized in the trajectory prediction evaluation.
JRDB-Known
JRDB-Unknown
Method
[0.0, 2.5]
[2.5, 5.0]
[5.0, 7.5]
[7.5, 10.0]
[0.0, 2.5]
[2.5, 5.0]
[5.0, 7.5]
[7.5, 10.0]
M only
1.16 (0.07)
1.19 (0.09)
1.53 (0.07)
1.68 (0.02)
1.71 (0.19)
1.76 (0.30)
1.98 (0.37)
1.92 (0.17)
M-F
1.11 (0.07)
1.11 (0.03)
1.44 (0.08)
1.54 (0.04)
1.61 (0.15)
1.67 (0.08)
1.83 (0.09)
1.87 (0.10)
M(G)-F
1.05 (0.04)
1.12 (0.05)
1.26 (0.03)
1.39 (0.06)
1.36 (0.04)
1.47 (0.09)
1.69 (0.13)
1.78 (0.19)
M(G)-FPU
0.87 (0.06)
0.95 (0.03)
1.08 (0.02)
1.20 (0.02)
1.28 (0.03)
1.32 (0.04)
1.47 (0.07)
1.62 (0.10)
M(G)-FPNi
1.06 (0.05)
1.07 (0.08)
1.29 (0.03)
1.44 (0.02)
1.43 (0.06)
1.40 (0.05)
1.61 (0.08)
1.70 (0.07)
Table S2 : Spatial range analysis across regions from center to boundary. Negative Log-Likelihood (NLL) is evaluated across non-overlapping region bins centered at the sensor origin. Ranges indicate the lower and upper bounding thresholds for both x and y absolute coordinates in meters. Each value represents the mean of three trials, with the standard deviation shown in parentheses. The lowest mean value in each column is highlighted in bold.
JRDB-Known
JRDB-Unknown
Method
[0.0, 2.5]
[2.5, 5.0]
[5.0, 7.5]
[7.5, 10.0]
[0.0, 2.5]
[2.5, 5.0]
[5.0, 7.5]
[7.5, 10.0]
M only
3.93 (1.04)
4.13 (0.57)
4.92 (0.60)
5.37 (0.51)
4.61 (0.90)
4.55 (0.32)
5.30 (0.30)
5.55 (0.67)
M-F
3.35 (0.55)
3.70 (0.10)
4.54 (0.50)
4.73 (0.52)
3.97 (0.25)
3.99 (0.32)
4.46 (0.53)
4.76 (0.24)
M(G)-F
2.32 (0.42)
2.87 (0.63)
3.21 (0.57)
3.53 (0.55)
2.73 (0.28)
3.43 (0.54)
4.03 (0.58)
4.25 (0.71)
M(G)-FPU
2.84 (1.20)
3.12 (0.66)
3.33 (0.21)
3.53 (0.15)
3.51 (1.03)
3.89 (0.61)
4.27 (0.71)
4.49 (0.40)
M(G)-FPNi
2.23 (0.35)
2.50 (0.28)
3.05 (0.16)
3.30 (0.03)
2.89 (0.55)
2.96 (0.51)
3.49 (0.63)
3.72 (0.27)
Table S3 : Spatial range analysis across regions from center to boundary. Negative Log-Likelihood (NLL) with a fixed angular variance 20∘ is evaluated across non-overlapping region bins centered at the sensor origin. Ranges indicate the lower and upper bounding thresholds for both x and y absolute coordinates in meters. Each value represents the mean of three trials, with the standard deviation shown in parentheses. The lowest mean value in each column is highlighted in bold.
Figure S1 : Occlusion sensitivity analysis. These plot show NLL for each frame in static-robot sequences from JRDB.
Figure S2 : Indoor vs outdoor performance. These plots show NLL for each frame in test sequences from JRDB.
JRDB-Known
JRDB-Unknown
SiT
Method
Input type
NLL
( 20∘ var)
NLL
( 20∘ var)
NLL
( 20∘ var)
BFF*
2D occ
1.17 (0.07)
4.80 (0.62)
1.53 (0.05)
4.82 (0.14)
1.34 (0.12)
4.07 (1.64)
Motion
3D pts
1.22 (0.08)
4.12 (0.62)
1.79 (0.29)
4.66 (0.35)
1.63 (0.04)
4.68 (0.86)
M(G)-FPNi
2D occ
1.05 (0.01)
2.58 (0.25)
1.43 (0.01)
3.60 (0.17)
1.35 (0.17)
3.21 (0.52)
M(G)-FPNi
3D pts
1.12 (0.07)
2.53 (0.27)
1.42 (0.05)
2.98 (0.51)
1.24 (0.11)
2.82 (0.74)
Table S4 : Input type comparison. 2D occ refers to models that take occupancy images as input following BFF [ 27 ] . Motion corresponds to the baseline that simply extends NeMo-map [ 34 ] . Each value represents the mean of three trials, with the standard deviation shown in parentheses. The lowest mean value per column is in bold.
Figure S3 : Known location evaluation for NeMo-map. Gray dots are LiDAR points that correspond to obstacle classes in panoptic segmentation labels.
gates-ai-lab-2019-04-17_0
huang-2-2019-01-25_1
tressider-2019-03-16_2
Model(/Train method)
Input
NLL
( 20∘ var)
NLL
( 20∘ var)
NLL
( 20∘ var)
NeMo-map
None
16.0 (0.91)
16.9 (0.90)
4.74 (0.92)
7.62 (0.14)
11.0 (1.65)
12.3 (1.22)
BFF*/Motion
2D occ
1.03 (0.08)
4.93 (1.08)
0.98 (0.04)
4.07 (1.23)
0.99 (0.04)
4.14 (1.62)
Ours-base/Motion
3D pts
1.18 (0.03)
3.86 (0.10)
0.83 (0.19)
2.94 (1.33)
1.06 (0.04)
2.81 (0.75)
BFF*/M(G)-FPNi
2D occ
1.05 (0.02)
2.81 (0.02)
0.75 (0.14)
1.64 (0.31)
0.85 (0.10)
2.49 (1.09)
Ours/M(G)-FPNi
3D pts
1.80 (0.10)
3.36 (0.26)
0.66 (0.21)
1.57 (0.77)
0.88 (0.19)
2.27 (1.20)
Table S5 : Comparison with NeMo-map [ 34 ] and extended BFF [ 27 ] on Known sequences in JRDB. 2D occ refers to models that take occupancy images as input following BFF [ 27 ] .
Figure S4 : Frequency score and motion outputs of Motion(GS)-Freq , Motion(GS)-FreqPU , and Motion(GS)-FreqPNi . For each method, the left panel shows the predicted frequency score, with brighter colors indicating higher scores, and the right panel shows the motion map. Arrow opacity, length, and hue represent mixture weight, speed, and heading direction, respectively.
T=12
T=18
T=24
T=48
T=96
Split
Method
ADE
FDE
ADE
FDE
ADE
FDE
ADE
FDE
ADE
FDE
JRDB-Known
ViTE
0.28
0.46
0.41
0.67
0.53
0.88
0.91
1.59
1.29
2.32
Ours
0.31
0.58
0.45
0.84
0.57
1.09
0.98
1.83
1.63
2.70
JRDB-Unknown
ViTE
0.42
0.65
0.61
0.98
0.79
1.30
1.47
2.64
2.46
4.56
Ours
0.47
0.89
0.69
1.35
0.89
1.77
1.53
3.10
2.36
4.52
Table S6 : Trajectory prediction errors on JRDB. All results are averaged over 3 training runs.
Pedestrian behavior modeling predicts and simulates how people move, interact, choose routes, and respond to vehicles, robots, hazards, and surroundings.
Efficient navigation in dynamic environments requires anticipating how motion patterns evolve beyond the robot's immediate perceptual range, enabling preemptive rather than purely reactive planning in crowded scenes. Maps of Dynamics (MoDs) offer a structured representation of motion tendencies in space useful for long-term global planning, but constructing them traditionally requires global environment observations over extended periods of time. We introduce EgoMoD, the first approach that learns to predict future MoDs directly from short egocentric video clips collected during robot operation. Our method learns to infer environment-wide motion tendencies from local dynamic cues using a video- and pose-conditioned architecture trained with MoDs computed from external observations as privileged supervision, allowing local observations to serve as predictive signals of global motion structure. Thanks to this, we offer the capacity to forecast future motion dynamics over the whole environment rather than merely extend past patterns in the robot's field of view. As a site-specific dynamic prior, EgoMoD replaces the external global sensing infrastructure required by prior MoD methods at inference time with standard onboard sensors. Experiments in large simulated environments show that EgoMoD predicts future MoDs under limited observability, while evaluation with real images showcases its zero-shot transferability to real systems.
Iacopo Catalano, David Morilla-Cabello, Jorge Pena-Queralta +1
I. Catalano is with the University of Turku, Finland. · E. Montijano and D. Morilla-Cabello are with the Instituto de Investigación en Ingeniería de Aragón, Universidad de Zaragoza, Spain. · J. Peña-Queralta is with the Centre for Artificial Intelligence, Zürich University of Applied Sciences, Winterthur, Switzerland.
Light detection and ranging (LiDAR) remains less explored than RGB-D sensing for perceptive legged locomotion, and existing LiDAR-based approaches often rely on explicit mapping. We present JEPLO (Joint-Embedding Predictive learning for legged LOcomotion), a single-stage learning framework for mapping-free, LiDAR-based perceptive locomotion for legged robots. We introduce a proprio-exteroceptive JEPA (PE-JEPA) world model to learn predictive egocentric terrain representations from onboard observations, including raw LiDAR scans. A concurrent JEPA-teacher-student (CJTS) pipeline is further proposed to train a locomotion policy informed by JEPA latent representations in simulation using deep reinforcement learning with a simple reward formulation. The framework achieves successful sim-to-real transfer, enabling omnidirectional traversal of diverse terrains, including long staircases and high boxes, with lightweight onboard computation. Evaluations demonstrate greater robustness than existing perceptive locomotion frameworks, particularly under degraded perception caused by occlusion, sparsity and noise. Further analysis validates JEPLO's ability to retain task-relevant information under these challenging conditions. We open-source our implementation, experimental datasets, and hardware setup designs https://github.com/ASIG-X/JEPLO.
Qihao Yuan, Yixuan Qiu, Ziyu Cao +2
Faculty of Science and Engineering, University of Groningen, The Netherlands · Department of Electrical Engineering, Linköping University, Sweden
Many pedestrian trajectory prediction algorithms have been proposed to improve the safety of navigation for mobile robots working in human-robot coexistence environments. Some pedestrian trajectory prediction algorithms extract information about obstacles near pedestrians from top-down view images to improve the accuracy of trajectory prediction. However, mobile robots typically create local occupancy maps using LiDAR, rather than top-down view images. Meanwhile, the vision sensors on board robots provide egocentric view images, which contain fine-grained behavioral information about the pedestrians near the robot. To better use the information collected by LiDAR and on-board vision sensors, we propose MamMA, a Mamba-based pedestrian trajectory prediction algorithm considering occupancy maps and pedestrian awareness states. MamMA divides the occupancy map by patches and extracts obstacle features from each patch to create map features. Pedestrian awareness states are divided and considered, as some studies show that awareness states affect the perception and speed of pedestrians. Furthermore, a Mamba-based model is proposed to predict the future trajectories of pedestrians based on different types of features. Experiments on the STCrowd, SiT, JRDB, ETH, and UCY datasets show that MamMA achieves better average displacement error and final displacement error than the state-of-the-art algorithms.
Juncen Long, Xiaofeng Jin, Gianluca Bardaro +2
Department of Electronics, Information and Bioengineering, Politecnico di Milano, Milan, Italy