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PITA: Physics-Informed Trajectory Autoencoder

Johannes Fischer, Kevin Rösch, Martin Lauer, Christoph Stiller

TL;DR

The novel Physics-Informed Trajectory Autoencoder (PITA) architecture is proposed, which incorporates a physical dynamics model into the loss function of the autoencoder, resulting in smooth trajectories that not only reconstruct the input trajectory but also adhere to the physical model.

Abstract

Validating robotic systems in safety-critical appli-cations requires testing in many scenarios including rare edgecases that are unlikely to occur, requiring to complement real-world testing with testing in simulation. Generative models canbe used to augment real-world datasets with generated data toproduce edge case scenarios by sampling in a learned latentspace. Autoencoders can learn said latent representation for aspecific domain by learning to reconstruct the input data froma lower-dimensional intermediate representation. However, theresulting trajectories are not necessarily physically plausible, butinstead typically contain noise that is not present in the inputtrajectory. To resolve this issue, we propose the novel Physics-Informed Trajectory Autoencoder (PITA) architecture, whichincorporates a physical dynamics model into the loss functionof the autoencoder. This results in smooth trajectories that notonly reconstruct the input trajectory but also adhere to thephysical model. We evaluate PITA on a real-world dataset ofvehicle trajectories and compare its performance to a normalautoencoder and a state-of-the-art action-space autoencoder.

PITA: Physics-Informed Trajectory Autoencoder

TL;DR

The novel Physics-Informed Trajectory Autoencoder (PITA) architecture is proposed, which incorporates a physical dynamics model into the loss function of the autoencoder, resulting in smooth trajectories that not only reconstruct the input trajectory but also adhere to the physical model.

Abstract

Validating robotic systems in safety-critical appli-cations requires testing in many scenarios including rare edgecases that are unlikely to occur, requiring to complement real-world testing with testing in simulation. Generative models canbe used to augment real-world datasets with generated data toproduce edge case scenarios by sampling in a learned latentspace. Autoencoders can learn said latent representation for aspecific domain by learning to reconstruct the input data froma lower-dimensional intermediate representation. However, theresulting trajectories are not necessarily physically plausible, butinstead typically contain noise that is not present in the inputtrajectory. To resolve this issue, we propose the novel Physics-Informed Trajectory Autoencoder (PITA) architecture, whichincorporates a physical dynamics model into the loss functionof the autoencoder. This results in smooth trajectories that notonly reconstruct the input trajectory but also adhere to thephysical model. We evaluate PITA on a real-world dataset ofvehicle trajectories and compare its performance to a normalautoencoder and a state-of-the-art action-space autoencoder.
Paper Structure (9 sections, 5 equations, 5 figures, 1 table)

This paper contains 9 sections, 5 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. Method
  4. Physical Model
  5. Loss definition
  6. Evaluation
  7. Experimental Setup
  8. Comparison to Baseline Models
  9. Conclusion

Figures (5)

  • Figure 1: Comparison of different trajectory reconstruction methods resulting in more or less smooth trajectories.
  • Figure 2: Physical loss weight scheduling scheme for different parameter values of $\gamma$.
  • Figure 3: Reconstruction root mean squared error on the validation dataset.
  • Figure 4: Boxplot of the model inputs necessary to follow the trajectories predicted by the different models wtih a KBM.
  • Figure 5: Boxplot of the distance of the predicted positions to the corresponding smoothed reference path.