--We investigate the performance of a lightweight tracking controller, based on a flow version of the Newton-Raphson method, applied to a miniature blimp and a mid-size quadrotor . This tracking technique has been shown to enjoy theoretical guarantees of performance and has been applied with success in simulation studies and on mobile robots with simple motion models. This paper investigates the technique through real-world flight experiments on aerial hardware platforms subject to realistic deployment and onboard computational constraints. The technique's performance is assessed in comparison with the established control frameworks of feedback linearization for the blimp, and nonlinear model predictive control for both quadrotor and blimp. The performance metrics under consideration are (i) root mean square error of flight trajectories with respect to target trajectories, (ii) algorithms' computation times, and (iii) CPU energy consumption associated with the control algorithms. The experimental findings show that the Newton-Raphson flow-based tracking controller achieves comparable or superior tracking performance to the baseline methods with substantially reduced computation time and energy expenditure. HE past two decades have seen a significant shift in the nature of hardware research for trajectory control of aerial platforms like quadrotors. First, testing and verification of novel techniques relied heavily on numerical simulators, later transitioning to real-world deployments that depended on ground station computers and simplified models (e.g. Today, powerful single-board computers (SBCs) have enabled research to shift toward onboard execution even for computationally intensive control methods [2]-[4].

In this paper, we present a new strategy to prove the convergence of deep learning architectures to a zero training (or even testing) loss by gradient flow. Our analysis is centered on the notion of Rayleigh quotients in order to prove Kurdyka-Łojasiewicz inequalities for a broader set of neural network architectures and loss functions.

In this paper, we present a new strategy to prove the convergence of deep learning architectures to a zero training (or even testing) loss by gradient flow. Our analysis is centered on the notion of Rayleigh quotients in order to prove Kurdyka-{\L}ojasiewicz inequalities for a broader set of neural network architectures and loss functions. We show that Rayleigh quotients provide a unified view for several convergence analysis techniques in the literature. Our strategy produces a proof of convergence for various examples of parametric learning. In particular, our analysis does not require the number of parameters to tend to infinity, nor the number of samples to be finite, thus extending to test loss minimization and beyond the over-parameterized regime.

The work presented in this paper demonstrates our approach to intercepting a faster intruder UAV, inspired by the MBZIRC2020 Challenge 1. By leveraging the knowledge of the shape of the intruder's trajectory we are able to calculate the interception point. Target tracking is based on image processing by a YOLOv3 Tiny convolutional neural network, combined with depth calculation using a gimbal-mounted ZED Mini stereo camera. We use RGB and depth data from ZED Mini to extract the 3D position of the target, for which we devise a histogram-of-depth based processing to reduce noise. Obtained 3D measurements of target's position are used to calculate the position, the orientation and the size of a figure-eight shaped trajectory, which we approximate using lemniscate of Bernoulli. Once the approximation is deemed sufficiently precise, measured by Hausdorff distance between measurements and the approximation, an interception point is calculated to position the intercepting UAV right on the path of the target. The proposed method, which has been significantly improved based on the experience gathered during the MBZIRC competition, has been validated in simulation and through field experiments. The results confirmed that an efficient visual perception module which extracts information related to the motion of the target UAV as a basis for the interception, has been developed. The system is able to track and intercept the target which is 30% faster than the interceptor in majority of simulation experiments. Tests in the unstructured environment yielded 9 out of 12 successful results.