Abstract
Various missions carried out by Unmanned Aerial Vehicles (UAVs) are concerned with permanent monitoring of a predefined set of ground targets under relative deadline constraints, which means that there is an upper bound on the time between two consecutive scans of that target. The targets have to be revisited ‘indefinitely’ while satisfying these constraints. Our goal is to minimize the number of UAVs required for satisfying the timing constraints. The solution to this problem is given in the form of cyclic (synchronized) routes that jointly satisfy the timing constraints. We develop lower- and upper-bounds on the number of required UAVs, show a reduction of the problem to a Boolean combination of ‘difference constraints’ (constraints of the form \(x - y \ge c\) where \(x,y \in \mathcal {R}\) and c is a constant), and present numerical results based on our experiments with several hundred randomly generated problems.
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Notes
- 1.
The problem was given to us by an industrial partner that develops software for the UAV industry. It has not yet materialized into a product.
- 2.
This matrix is typically symmetric, but we do not pose this as an assumption since our suggested solutions do not rely on this fact.
- 3.
Note that T is a cycle of the whole system, not just of one of the UAVs. In other words, the time it takes the system to return to the same state, where a state includes the location of the UAVs, the remaining time at the vertices until the relative deadlines expire, and finally the current target of each of the UAVs.
- 4.
- 5.
This implies that there can be non-integral and even irrational figures. We rounded in such cases the figures according to the overapproximation strategy explained above, with \(\gamma = 1\).
- 6.
A counterexample to their theorem is given in the appendix of http://arxiv.org/abs/1411.2874.
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Drucker, N., Penn, M., Strichman, O. (2016). Cyclic Routing of Unmanned Aerial Vehicles. In: Quimper, CG. (eds) Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2016. Lecture Notes in Computer Science(), vol 9676. Springer, Cham. https://doi.org/10.1007/978-3-319-33954-2_10
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