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The usage of commercial Micro Aerial Vehicles (MAVs) has increased drastically during the last decade. While the added value of MAVs to society is apparent, their growing use is also coming with increasing risks like violating public airspace at airports or committing privacy violations. To mitigate these issues it is becoming critical to develop solutions that incorporate the detection and tracking of MAVs with autonomous systems. This work presents a method for the detection and tracking of MAVs using a novel, low-cost rosette scanning LiDAR on a pan-tilt turret. Once the static background is captured, a particle filter is utilized to detect a possible target and track its position with a physical, programmable pan-tilt system. The tracking makes it possible to keep the MAV in the center, maximizing the density of 3D points measured on the target by the LiDAR sensor. The developed algorithm was evaluated within the indoor MIcro aerial vehicle and MOtion capture (MIMO) arena and has state-of-the-art tracking accuracy, stability, and fast re-detection time in case of tracking loss. Based on the outdoor tests, it was possible to significantly increase the detection distance and number of returned points compared to other similar methods using LiDAR.

We consider edge decompositions of $K_v^{(3)}-I$, the complete 3-uniform hypergraph of order $v$ minus a 1-factor (parallel class, packing of $v/3$ disjoint edges). We prove that a decomposition into tight 6-cycles exists if and only if $v\equiv 0,3,6$ (mod 12) and $v\geq 6$; and a decomposition into tight 9-cycles exists for all $v\geq 9$ divisible by 3. These results are complementary to the theorems of Akin et al. [Discrete Math. 345 (2022)] and Bunge et al. [Australas. J. Combin. 80 (2021)]., Comment: 45 pages