External-Wrench Estimation for Aerial Robots Exploiting a Learned Model

TL;DR

The paper addresses external wrench estimation for multi-rotor aerial vehicles by augmenting a first-principles dynamics model with a Knowledge-based Neural ODE (KNODE) to learn residual dynamics. The resulting Neural Momentum-Based Observer (NeMO) integrates KNODE into a momentum-based wrench observer to separate external wrenches $w_e$ from unmodeled effects $φ$, improving estimation accuracy over a purely model-based approach. KNODE is trained offline on data with no external wrench, and its integration into MO via a neural correction yields more reliable wrench feedback for force-control tasks, as demonstrated in simulations across multiple residual-dynamics types and flight scenarios. The work contributes a practical, hybrid modeling framework for robust wrench estimation in MRAVs, with planned validation on physical platforms and a discussion of generalization to unseen disturbances.

Abstract

This paper presents an external wrench estimator that uses a hybrid dynamics model consisting of a first-principles model and a neural network. This framework addresses one of the limitations of the state-of-the-art model-based wrench observers: the wrench estimation of these observers comprises the external wrench (e.g. collision, physical interaction, wind); in addition to residual wrench (e.g. model parameters uncertainty or unmodeled dynamics). This is a problem if these wrench estimations are to be used as wrench feedback to a force controller, for example. In the proposed framework, a neural network is combined with a first-principles model to estimate the residual dynamics arising from unmodeled dynamics and parameters uncertainties, then, the hybrid trained model is used to estimate the external wrench, leading to a wrench estimation that has smaller contributions from the residual dynamics, and affected more by the external wrench. This method is validated with numerical simulations of an aerial robot in different flying scenarios and different types of residual dynamics, and the statistical analysis of the results shows that the wrench estimation error has improved significantly compared to a model-based wrench observer using only a first-principles model.

Figures (8)

• Figure 1: Block diagram explaining the difference between the proposed method and the model-based wrench observer. The estimated state is denoted as $\hat{\boldsymbol{x}}$, while $\hat{\boldsymbol{w}}_e$ denotes the estimated external wrench.
• Figure 2: Schematic representation of a fully-actuated MRAV with its reference frames.
• Figure 3: Block diagram of the KNODE Model and its training procedure. This example is for a prediction horizon $\alpha = 1$. The two models calculate the predicted dynamics of the system based on the initial condition of the states $\boldsymbol{x}(t)$ and the input $\boldsymbol{u}(t)$, then the predictions of the two models are combined and integrated using a numerical integrator (such as Runge-Kutta).
• Figure 4: A one dimensional example of the KNODE constrained optimization problem. The blue curve is the real time evolution of the system, while the blue dots are the observations, and the red curves are the predictions generated by $\hat{f}$ and the red dots are the samples at $t_s \in \mathbf{T}_s$. In this example $\alpha$ = 2, and therefore $\hat{f}$ generates predictions of two sampling time. The loss is then computed as the RMSE between the blue and red dots sampled at every time step in $\mathbf{T}_s$.
• Figure 5: External wrench estimation of a free-flight scenario following a 3D lemniscate with no external wrench applied to the system. The residual dynamics type is MG-1, and the model is trained with prediction horizon $\alpha = 1$. MO estimates have large errors due to the residual dynamics. On the other hand, NeMO estimates are better since it has learned the residual dynamics.