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Generating Reliable and Efficient Predictions of Human Motion: A Promising Encounter between Physics and Neural Networks

Alessandro Antonucci, Gastone Pietro Rosati Papini, Luigi Palopoli, Daniele Fontanelli

arXiv:2006.08429v1cs.RO

TL;DR

Robot planners need accurate short-horizon predictions of pedestrian motion, but Social Force Model parameters are difficult to estimate. The paper embeds that model in a neural network to learn its unknown parameters and forces. The authors report consistent predictions in a novel environment, while noting that pedestrian interaction forces are not included.

  • Problem

    Estimating the Social Force Model’s many parameters, especially attractive and repulsive force intensities and directions, is difficult, and heuristic choices work only in specific conditions.

    Source: §I · p. 1

  • Method

    The network embeds Social Force Model dynamics and concentrates learning on unknown model parameters and forces.

    Source: §I · p. 2

  • Results

    Net2 predictions remained consistent in a novel environment despite slight underestimation of forces during horizontal wall collisions.

    Source: §IV · p. 6

  • Takeaways & Limitations

    The embedded model keeps the network simpler and its predictions physically interpretable, and the authors report accurate predictions with relatively few synthetic samples across different scenarios.

    Source: §I · p. 2

    The model neglects pedestrian interaction forces, which the authors identify as future work.

    Source: B. Social force model · p. 3

Abstract

from arXiv · show

Generating accurate and efficient predictions for the motion of the humans present in the scene is key to the development of effective motion planning algorithms for robots moving in promiscuous areas, where wrong planning decisions could generate safety hazard or simply make the presence of the robot "socially" unacceptable. Our approach to predict human motion is based on a neural network of a peculiar kind. Contrary to conventional deep neural networks, our network embeds in its structure the popular Social Force Model, a dynamic equation describing the motion in physical terms. This choice allows us to concentrate the learning phase in the aspects, which are really unknown (i.e., the model's parameters) and to keep the structure of the network simple and manageable. As a result, we are able to obtain a good prediction accuracy with a small synthetically generated training set, and the accuracy remains acceptable even when the network is applied in scenarios quite different from those for which it was trained. Finally, the choices of the network are "explainable", as they can be interpreted in physical terms. Comparative and experimental results prove the effectiveness of the proposed approach.

I. INTRODUCTION

Human-motion prediction matters for robot planning around pedestrians, but estimating Social Force Model parameters is difficult and conventional neural networks raise concerns about complexity and explainability. The paper embeds the Social Force Model in a neural network, while related work explores physics-based and learning-based alternatives.

I. INTRODUCTION

  • The Social Force Model’s many parameters, especially attractive and repulsive force intensities and directions, are difficult to estimate; heuristic choices work only in specific conditions.The cited example is interaction between a robot and a human in free space.Source: §I · p. 1
  • A conventional deep neural network may require many layers, neurons, and training samples, while its lack of a prior model makes its decisions difficult to explain.Explainability matters for understanding autonomous-system decisions, debugging, and assigning legal responsibility.Source: §I · p. 2
  • The proposed network embeds Social Force Model dynamics and learns unknown parameters and forces, reducing network size and supporting accurate predictions from small synthetic datasets.The authors estimate one or two orders of magnitude fewer neurons and report acceptable accuracy in scenarios different from training.Source: §I · p. 2

A. Related Work

  • Physics-based methods are easy to implement and often faster, but describe local dynamics better than medium- or long-term intent, whose walking targets remain difficult to estimate online.Prior approaches estimate virtual goals from constant-velocity motion or trajectory sub-goals in structured environments.Source: A. Related Work · p. 2
  • Prior work has combined Social Force Models with learned parameters or direction predictors, while neural models can overfit or depend on training information and may lose to constant velocity on linear trajectories.The cited related works include gradient descent, predictor comparisons, and evolutionary parameter optimization.Source: A. Related Work · p. 3
  • A related vehicle-dynamics network embeds physical structure to guide learning, reduce trainable parameters, avoid overfitting, and reduce required training examples.The paper describes pre-wiring a network with human-motion physics as relatively new.Source: A. Related Work · p. 3

B. Social force model

The Social Force Model represents pedestrian motion as a second-order dynamic driven by goal-directed attraction and environmental forces. The paper describes static-obstacle forces as repulsion, compression, and sliding friction, while omitting pedestrian interaction forces.

B. Social force model

  • A pedestrian moves toward a target under a second-order dynamic, with total force equal to attractive force plus environmental force.The model describes the pedestrian as a particle with mass and radius, affected by obstacles and other agents.Source: B. Social force model · p. 3
  • The attractive force uses a characteristic time parameter that determines the rate of velocity change and a unit vector pointing toward the goal.The prose identifies the velocity as the derivative of position.Source: B. Social force model · p. 3
  • Static-obstacle force combines repulsion, compression, and sliding friction; compression and friction apply only when the pedestrian touches the obstacle.The model parameters include A, B, k1, and k2; pedestrian interaction forces are neglected as future work.Source: B. Social force model · p. 3

III. NEURAL NETWORK MODEL

The structured network mirrors Social Force Model force computation, using separate branches for attractive and repulsive effects before summing them into a resulting force.

III. NEURAL NETWORK MODEL

  • Separate network branches estimate attractive and repulsive Social Force Model effects, which are summed to produce the resulting force.The no-obstacle scenario uses only the attractive-force branch; the obstacle scenario also models static-object repulsion.Source: §III · p. 4

A. Open environment

For open-environment motion, Net1 uses recent pedestrian positions to estimate the attractive Social Force Model components. Its estimates combine learned velocity, goal direction, and desired speed with model parameters.

A. Open environment

  • Net1 predicts the two components of the attractive force from a window of past pedestrian positions, normalized relative to the first sample to avoid spatial biases.The window includes positions up to the current time.Source: A. Open environment · p. 4
  • Two hidden-layer branches estimate instantaneous velocity on the two axes, while the most recent relative motion estimates the normalized goal-directed unit vector.A sigmoid-based estimate supplies desired speed, and the estimates are combined and weighted according to the model parameters.Source: A. Open environment · p. 4
  • Net1 has 123 learnable parameters, 100 of which are devoted to desired-velocity estimates.The structured formulation uses a sigmoid activation to keep the desired-speed estimate positive.Source: A. Open environment · p. 4

B. Structured environment

Net2 models motion in environments with obstacles using separate branches for attractive and repulsive forces. Its obstacle branch uses pedestrian-to-obstacle distance and direction as inputs, while the goal is supplied directly to the attractive-force branch.

B. Structured environment

  • Net2 has two parallel branches that estimate the x and y components of force in environments with obstacles.The supplied passage cuts off after introducing this design.Source: B. Structured environment · p. 4
  • The attractive-force branch receives the goal direction directly because observed motion alone cannot distinguish goal attraction from obstacle effects.The strategy for choosing the goal position is described in Section III-C.Source: B. Structured environment · pp. 4–5
  • The obstacle-force branch uses current obstacle distance and unit-vector components, with two learnable weights representing the SFM parameters A and B.The obstacle force is combined in exponential form; compression and sliding friction are omitted from both the simulations and the network.Source: B. Structured environment · p. 5

C. Multi-goal prediction

The multi-goal method generates trajectories for candidate exits, then selects the most likely one using pseudo-Kalman filtering and likelihood analysis. It assumes pedestrians do not stop in corridor interiors, while allowing sudden stops to be modeled.

C. Multi-goal prediction

  • The method assumes pedestrians aim for one of the scenario's exits rather than stopping in the middle of a corridor.Walls are treated as obstacles, not points of interest; corridor sudden stops can also be modeled.Source: C. Multi-goal prediction · p. 5
  • It generates goal hypotheses from the initial measured position and uses Net2 to produce a trajectory for each candidate goal.Source: C. Multi-goal prediction · p. 5
  • A first-order generalized pseudo-Bayesian estimator applies the Multiple Model Approach to select the trajectory with the highest likelihood given the observations.The Multiple Model Approach is cited as.Source: C. Multi-goal prediction · p. 5

IV. EXPERIMENTS

The experiments train Net1 and Net2 on synthetic Social Force Model trajectories, then assess force and trajectory predictions. Results include validation in a novel environment and comparisons of real-world prediction accuracy with other methods.

IV. EXPERIMENTS

  • Net1 and Net2 were trained on synthetic trajectories from open and structured environments, respectively, using Adam with a 0.005 learning rate, batch size 128, and 300 epochs.The structured environment comprised two intersecting corridors.Source: §IV · p. 5
  • The synthetic training sets used 800 open-environment simulations and 1,200 corridor simulations; 70% of each set was used for training and the rest for validation.The motion observation window was empirically set to 10 samples as a trade-off between learning speed and prediction accuracy.Source: §IV · pp. 5–6
  • Figure 1 depicts an agent moving from the uppermost area toward the right-side exit and reports probabilities for three waypoints.Source: Figure 1 · p. 6, §IV · p. 6
  • Training showed no overfitting, with mean squared errors of 8.98 · 10^-5 N for Net1 and 1.20 · 10^-3 N for Net2.Source: §IV · p. 6
  • Net2 predictions remain consistent in a novel environment despite slight force underestimation during horizontal wall collisions; reported open-loop trajectories are fairly well replicated.For open-loop prediction, force inputs depend on positions predicted in the preceding 10-step window.Source: §IV · p. 6

A. Net1 experimental validation

Net1 is evaluated on real pedestrian trajectories from ETH and UCY using a 1-second observation window and a 4.8-second prediction horizon. The reported average MDE is about 40 cm except in ETH, and performance is similar to or sometimes better than the compared methods despite the shorter observation window.

A. Net1 experimental validation

  • The real-world evaluation uses ETH and UCY pedestrian trajectory datasets, with five scenes across the two datasets.The scenarios are open, with static-obstacle influence described as mostly negligible.Source: A. Net1 experimental validation · pp. 7–8
  • Net1 achieves an average MDE of about 40 cm across the datasets except ETH, with performance similar to and sometimes better than the compared methods.The comparison includes Constant Velocity, Constant Accelerated, Feed Forward, and LSTM models; final displacement errors worsen, which the authors mainly attribute to nonlinear real-world trajectories that are difficult to follow in open loop.Source: A. Net1 experimental validation · p. 9
  • Net1 observes 1 second of real-world motion and predicts the next 4.8 seconds, compared with an 8-timestep observation window in other works.Errors are measured using MDE, the average pointwise Euclidean distance, and FDE, the final-position distance.Source: A. Net1 experimental validation · pp. 8–9

B. Multi-goal prediction on synthetic trajectories

Net2 evaluates multiple waypoint hypotheses for the intersecting-corridors scenario. It identifies the correct goal after about two seconds, with confidence in the simulated trajectory increasing afterward.

B. Multi-goal prediction on synthetic trajectories

C. Net2 validation

In a hallway experiment, Net2 uses one second of observed motion and three possible destinations to forecast trajectories in open loop. It discards the incorrect left exit after about four seconds and identifies the correct goal after about six seconds.

C. Net2 validation

  • After about 6 seconds, Net2 identifies the correct goal, having discarded the left exit after about 4 seconds.Confidence in the two remaining waypoint hypotheses stays almost equal until the correct goal is found.Source: C. Net2 validation · p. 10
  • The open-loop forecasts use just 1 second of observed pedestrian motion and knowledge of three possible waypoints.The hallway data were collected with a 360° LIDAR at 20 frames per second.Source: C. Net2 validation · p. 10
  • Figure 5 shows the collected hallway trajectories, with bold lines marking those used for classifier evaluation.The experimental setup depicts paths from the starting position toward each destination.Source: Figure 5 · p. 11, C. Net2 validation · p. 11

V. CONCLUSION

The paper combines a neural network with the Social Force Model (SFM) to predict human motion, using the model to structure learning. The authors report reduced network complexity and training-sample needs alongside physically interpretable predictions, and identify further comparisons and extensions as future work.

V. CONCLUSION

  • Embedding the SFM structures the neural network, reducing its complexity and the number of training samples needed.The network learns the SFM parameter set, which is difficult to estimate conventionally because of the model's strong nonlinearities.Source: §V · p. 11
  • The neural network's predictions are explainable and physically interpretable.The SFM supplies structure while the network supplies flexibility to learn the model's complex parameters.Source: §V · p. 11
  • Figure 6 compares trajectory predictions with ground truth and shows probabilities for the trajectory predictions.The accompanying result describes the pedestrian moving toward the blue goal.Source: Figure 6 · p. 12, §V · p. 12
  • The authors identify a full comparison with a standard DNN across realistic use cases as future work.They also propose embedding potentially more realistic models and developing motion-planning algorithms that use learned predictions.Source: §V · p. 12
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