Speaker
Description
Traditionally, building an inverse dynamics model to control a multibody system (MBS) involves deriving it from first principles. Such physics-based representations lead to ordinary differential or differential-algebraic formulations, which extrapolate well by design and are usually preferred in model-based control strategies. Nevertheless, it is often that parameters of the model remain unknown, models of the phenomena governing the physics introduce too much simplification, or it is not known at the moment of the design which of them would impact the system behavior significantly.
With recent advancements, data-driven techniques to identify dynamics directly from data are quickly growing. The emerging method, dynamic mode decomposition (DMD), seems to be a highly versatile and powerful approach to discovering dynamics from time-series recordings or numerical simulations.
We propose using DMD to directly derive the inverse dynamics model, which is subsequently employed for control. The model is updated online as new measurements are acquired. We refer to this approach as data-driven inverse dynamics (DID), a method we introduced in our recent work to assist feedback and feedforward controllers based on physics-informed neural networks by modeling their error. In this study, however, we focus on an inverse controller that operates either alongside a simple PID controller or independently. The DID model is trained to capture the complete dynamics of the multibody system under control. The PID controller is used for the starting phase, in which DID is initialized and, as DMD generally linearizes the problem, a preliminary tracking of the desired trajectory is needed.
We evaluate the proposed method in a simulation of a five-bar linkage mechanism, where motors attached to the outer links are controlled, and the positions and velocities of these links are measured. The online updates of the DID model employ a moving window over the collected data, with older measurements being weighted or decayed. The results demonstrate that the DID controller significantly reduces the signal magnitudes produced by the PID controller and achieves satisfactory trajectory tracking independently. This includes tracking complex paths, such as Lissajous curves and trajectories with sharp, non-differentiable turns.
Although the tested system is relatively low-dimensional, the flexibility of DMD extensions allows us to adjust model dimensionality through embeddings or mode reductions. This capability enables the proposed updating method to be applied to more complex systems. We are also conducting real-world experiments to validate these findings.
