Human-like motion generation for robots often draws inspiration from biomechanical studies, which often categorize complex human motions into hierarchical taxonomies. While these taxonomies provide rich structural information about how movements relate to one another, this information is frequently overlooked in motion generation models, leading to a disconnect between the generated motions and their underlying hierarchical structure. This paper introduces the \ac{gphdm}, a novel approach that learns latent representations preserving both the hierarchical structure of motions and their temporal dynamics to ensure physical consistency. Our model achieves this by extending the dynamics prior of the Gaussian Process Dynamical Model (GPDM) to the hyperbolic manifold and integrating it with taxonomy-aware inductive biases. Building on this geometry- and taxonomy-aware frameworks, we propose three novel mechanisms for generating motions that are both taxonomically-structured and physically-consistent: two probabilistic recursive approaches and a method based on pullback-metric geodesics. Experiments on generating realistic motion sequences on the hand grasping taxonomy show that the proposed GPHDM faithfully encodes the underlying taxonomy and temporal dynamics, and generates novel physically-consistent trajectories.

Predicting the end-of-life or remaining useful life of batteries in electric vehicles is a critical and challenging problem, predominantly approached in recent years using machine learning to predict the evolution of the state-of-health during repeated cycling. To improve the accuracy of predictive estimates, especially early in the battery lifetime, a number of algorithms have incorporated features that are available from data collected by battery management systems. Unless multiple battery data sets are used for a direct prediction of the end-of-life, which is useful for ball-park estimates, such an approach is infeasible since the features are not known for future cycles. In this paper, we develop a highly-accurate method that can overcome this limitation, by using a modified Gaussian process dynamical model (GPDM). We introduce a kernelised version of GPDM for a more expressive covariance structure between both the observable and latent coordinates. We combine the approach with transfer learning to track the future state-of-health up to end-of-life. The method can incorporate features as different physical observables, without requiring their values beyond the time up to which data is available. Transfer learning is used to improve learning of the hyperparameters using data from similar batteries. The accuracy and superiority of the approach over modern benchmarks algorithms including a Gaussian process model and deep convolutional and recurrent networks are demonstrated on three data sets, particularly at the early stages of the battery lifetime.

This paper introduces Gaussian Process Dynamical Models (GPDM) for nonlinear time series analysis. A GPDM comprises a low-dimensional latent space with associated dynamics, and a map from the latent space to an observation space. We demonstrate the approach on human motion capture data in which each pose is 62-dimensional. Despite the use of small data sets, the GPDM learns an effective representation of the nonlinear dynamics in these spaces.

The recently proposed Gaussian process dynamical models (GPDMs) have been successfully applied to time series modeling. There are four learning algorithms for GPDMs: maximizing a posterior (MAP), fixing the kernel hyperparameters α_ (Fix.α_),

The recently proposed Gaussian process dynamical models (GPDMs) have been successfully applied to time series modeling. There are four learning algorithms for GPDMs: maximizing a posterior (MAP), fixing the kernel hyperparameters α _ (Fix.α _ ), balanced GPDM (B-GPDM) and two-stage MAP (T.MAP), which are designed for model training with complete data. When data are incomplete, GPDMs reconstruct the missing data using a function of the latent variables before parameter updates, which, however, may cause cumulative errors. In this paper, we present four new algorithms (MAP+, Fix.α + , B-GPDM+ and T.MAP+) for learning GPDMs with incomplete training data and a new conditional model (CM+) for recovering incomplete test data. Our methods adopt the Bayesian framework and can fully and properly use the partially observed data. We conduct experiments on incomplete motion capture data (walk, run, swing and multiple-walker) and make comparisons with the existing four algorithms as well as k-NN, spline interpolation and VGPDS. Our methods perform much better on both training with incomplete data and recovering incomplete test data.

This paper introduces Gaussian Process Dynamical Models (GPDM) for nonlinear time series analysis. A GPDM comprises a low-dimensional latent space with associated dynamics, and a map from the latent space to an observation space.

This paper introduces Gaussian Process Dynamical Models (GPDM) for nonlinear time series analysis. A GPDM comprises a low-dimensional latent space with associated dynamics, and a map from the latent space to an observation space.

Two main themes are the use of switching linear models (e.g.,