The ability to collect and assess different types of data from Unmanned Aerial Systems in real-time or near real-time is still a difficult challenge. Issues faced can include significant computation times, signal strength and wireless transmission delays or limitations, open source software versus proprietary data, etc. To attempt to remedy such issues, we aim for achieving on-board capabilities for automatic object detection, image analysis, and adaptable situational assessment. The result is real-time comparison between flights as well as preliminary data assessment using techniques from topological data analysis.

The objective of swarms is to enable multiple agents to collaborate toward a common goal, as one would find in a remote sensing setting. In this paper we focus on swarms of unmanned aerial vehicles (UAVs), which for instance have an objective to optimize the survey of a prescribed area and/or the detection of a specific object. Instructing each individual agent from a central command control quickly becomes inefficient, even for small groups of agents. Agreement protocol is done locally by the multi-agents without external user input. Because of the wide variety of conditions UAVs can face, the algorithm needs to be robust despite external disturbances.

We present new results for three problems dealing with a set $\mathcal{P}$ of n convex constant-complexity fat polyhedra in 3-space. (i) We describe a data structure for vertical ray shooting in $\mathcal{P}$ that has $O(\log^2 n)$ query time and uses $O(n\log^2 n)$ storage. (ii) We give an algorithm to compute in $O(n\log^3 n)$ time a depth order on $\mathcal{P}$ if it exists. (iii) We give an algorithm to verify in $O(n\log^3 n)$ time whether a given order on $\mathcal{P}$ is a valid depth order. All three results improve on previous results.

We present a data structure for ray-shooting queries in a set of convex fat polyhedra of total complexity n in R3. The data structure uses O(n2+ε) storage and preprocessing time, and queries can be answered in O(log2 n) time. A trade-off between storage and query time is also possible: for any m with n < m < n2, we can construct a structure that uses O(m1+ε) storage and preprocessing time such that queries take O((n/√m)log2 n) time.We also describe a data structure for simplex intersection queries in a set of n convex fat constant-complexity polyhedra in R3. For any m with n < m < n3, we can construct a structure that uses O(m1+ε) storage and preprocessing time such that all polyhedra intersecting a query simplex can be reported in O((n/m1/3)log n+k) time, where k is the number of answers.