  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.
