Prediction with Approximated Gaussian Process Dynamical Models
This work addresses a bottleneck in control theory for complex systems like soft robotics, though it is incremental by focusing on approximation rather than a new paradigm.
The authors tackled the challenge of analyzing and controlling Gaussian process dynamical models (GPDMs) by developing approximated GPDMs that are Markov, enabling theoretical analysis and bounded trajectory conditions, with results showing significantly reduced computational time in numerical examples.
The modeling and simulation of dynamical systems is a necessary step for many control approaches. Using classical, parameter-based techniques for modeling of modern systems, e.g., soft robotics or human-robot interaction, is often challenging or even infeasible due to the complexity of the system dynamics. In contrast, data-driven approaches need only a minimum of prior knowledge and scale with the complexity of the system. In particular, Gaussian process dynamical models (GPDMs) provide very promising results for the modeling of complex dynamics. However, the control properties of these GP models are just sparsely researched, which leads to a "blackbox" treatment in modeling and control scenarios. In addition, the sampling of GPDMs for prediction purpose respecting their non-parametric nature results in non-Markovian dynamics making the theoretical analysis challenging. In this article, we present approximated GPDMs which are Markov and analyze their control theoretical properties. Among others, the approximated error is analyzed and conditions for boundedness of the trajectories are provided. The outcomes are illustrated with numerical examples that show the power of the approximated models while the the computational time is significantly reduced.