FLD: Fourier Latent Dynamics for Structured Motion Representation and Learning

Abstract: Motion trajectories offer reliable references for physics-based motion learning but suffer from sparsity, particularly in regions that lack sufficient data coverage. To address this challenge, we introduce a self-supervised, structured representation and generation method that extracts spatial-temporal relationships in periodic or quasi-periodic motions. The motion dynamics in a continuously parameterized latent space enable our method to enhance the interpolation and generalization capabilities of motion learning algorithms. The motion learning controller, informed by the motion parameterization, operates online tracking of a wide range of motions, including targets unseen during training. With a fallback mechanism, the controller dynamically adapts its tracking strategy and automatically resorts to safe action execution when a potentially risky target is proposed. By leveraging the identified spatial-temporal structure, our work opens new possibilities for future advancements in general motion representation and learning algorithms.

• The paper introduces FLD as a novel framework that leverages Fourier-transformed latent dynamics to significantly reduce reconstruction and prediction errors over extended horizons.
• It enhances traditional periodic autoencoders by incorporating a continuously parameterized latent space that captures critical trajectory parameters like frequency, amplitude, and offset.
• FLD demonstrates robust performance in robotics and animation by effectively generalizing to unseen motions and yielding structured latent manifolds with regular temporal consistency.

A Self-Supervised Structured Representation for Motion Learning via Fourier Latent Dynamics

The paper presents a novel framework termed Fourier Latent Dynamics (FLD) to address the challenges of motion interpolation and generalization in physics-based motion learning using sparse motion trajectories. The core aim is to develop a method that effectively captures the spatial-temporal relationships inherent in periodic or quasi-periodic motions for robust motion learning applications.

Overview of the Methodology

At the heart of the proposed approach is the enhancement of traditional autoencoders with a structured learning paradigm that emphasizes a continuously parameterized latent space. By employing a periodic autoencoder (PAE) as the baseline, FLD extends its capabilities by introducing predictive knowledge within the Fourier-transformed latent space. The learning formulation utilizes latent dynamics to maintain and predict trajectory parameters—namely frequency, amplitude, and offset—across an extended horizon, relying on a quasi-constant parameterization assumption over periodic-like motions. This assumption permits the approximation of latent trajectories with bounded error over time, significantly reducing the required dimensions for accurate and generalizable representation.

Numerical Evaluation and Results

The experimental evaluation demonstrates the advantages of FLD in both reconstruction and prediction tasks, exhibiting reduced mean squared errors over longer prediction horizons compared to traditional models such as feed-forward networks and base PAEs. The model's robustness is particularly noted in its ability to generalize to unseen motions, validated through the diagonal run motion example where FLD consistently predicts future states with smaller errors relative to alternative modeling approaches.

Moreover, the paper highlights FLD's proficiency in manifesting structured latent manifolds, which assert intrinsic motion similarities by clustering latent features in a meaningful way. Compared to a Variational Autoencoder (VAE) and raw input states, FLD's enforcement of latent structure yields significantly enhanced temporal regularity and consistency in the learned manifold.

Practical Implications and Future Directions

The potential implications of this work span both theoretical advancements and practical applications. Practically, the ability to interpolate and generate realistic motion sequences with fewer data points makes FLD particularly valuable for robotic systems and virtual character animations, where data scarcity often limits performance. The proposed fallback mechanism serves as a safety net for such systems, dynamically shifting strategies to avoid dangerous states and ensuring reliable motion execution even in unanticipated conditions.

Theoretically, FLD invites further exploration into enhancing self-supervised learning architectures for complex temporal tasks, potentially expanding the framework to accommodate broader non-periodic or transient actions through adaptive structure modifications. Future works could explore the integration of this methodology with reinforcement learning to dynamically adapt agents' strategies in complex environments. Moreover, addressing limitations such as quasi-constant parameter assumptions for mixed motion phases could lead to further refinements and broader applicability of the framework in diverse settings.

In conclusion, FLD offers an innovative pathway to reconcile motion learning with the need for compact and effective representation, fostering enhanced interpolation and generalization capabilities that hold promise across a range of computational and robotic applications.