Physics-Informed Neural Network for Multirotor Slung Load Systems Modeling

TL;DR

This work addresses the challenge of accurately modeling a quadrotor carrying a slung payload, where purely classical models struggle to capture nonlinear, coupled dynamics over long horizons. It introduces a physics-informed neural network built as an encoder–decoder LSTM with Bahdanau attention, trained with a four-term loss that blends data fit, a discretized first-principles dynamics term, projection to unit-quaternion orientation, and slack variables to accommodate unmodeled effects. Real-world flight data is used to train and evaluate the model, showing that the proposed approach outperforms both a pure physics-based predictor and a baseline neural network lacking physics regularization, particularly on longer prediction horizons, while maintaining feasible inference times. The results demonstrate the method’s potential for enhancing model-based control and long-horizon prediction in aerial payload transport applications, with avenues for extending to other platforms and integration with controllers such as model-predictive control.

Abstract

Recent advances in aerial robotics have enabled the use of multirotor vehicles for autonomous payload transportation. Resorting only to classical methods to reliably model a quadrotor carrying a cable-slung load poses significant challenges. On the other hand, purely data-driven learning methods do not comply by design with the problem's physical constraints, especially in states that are not densely represented in training data. In this work, we explore the use of physics informed neural networks to learn an end-to-end model of the multirotor-slung-load system and, at a given time, estimate a sequence of the future system states. An LSTM encoder decoder with an attention mechanism is used to capture the dynamics of the system. To guarantee the cohesiveness between the multiple predicted states of the system, we propose the use of a physics-based term in the loss function, which includes a discretized physical model derived from first principles together with slack variables that allow for a small mismatch between expected and predicted values. To train the model, a dataset using a real-world quadrotor carrying a slung load was curated and is made available. Prediction results are presented and corroborate the feasibility of the approach. The proposed method outperforms both the first principles physical model and a comparable neural network model trained without the physics regularization proposed.

Figures (6)

• Figure 1: Intel Aero quadrotor carrying a cube-shaped slung load attached by a string in a dedicated motion capture arena.
• Figure 2: Proposed encoder-decoder architecture with an attention mechanism. The network encoder receives a temporal history of $\mathrm{M}$ system states and control inputs. The decoder receives the hidden state and output of the encoder, the last measured state of the system $\mathbf{x}_{\mathrm{M-1}}$, and the previous input of the system $\mathbf{u}_{\mathrm{M-1}}$, which are combined in an attention module to produce a prediction of the next system state $\mathbf{\hat{x}}_{\mathrm{M}}$ and the corresponding slack variables $\mathbf{s}_{\mathrm{M}}$. Each prediction of the decoder module is concatenated with an input control signal to generate multi-step predictions of the system state in the following iterations.
• Figure 3: Subset of the trajectories executed by the quadrotor carrying a slung load during data acquisition.
• Figure 4: Comparison between the evolution of the MAE and standard deviation of the prediction error of the proposed model and the physics-based state predictor, evaluated on the test set. The vertical dashed line denotes the prediction horizon of $\mathrm{N}=25$ time steps ($750\ms$) used during training.
• Figure 5: Prediction of the vehicle position, linear velocity, orientation, and the position of the slung load as a function of time for a single sequence of the test set. The time series predicted by the network are depicted in dashed lines over the expected values in solid lines. The time series predicted by the discretized dynamics model are depicted in dotted lines for comparison. The vertical dashed lines denote the prediction horizon of $750\ms$ used during training.