Task 4

Preliminary Mission Strategy

Michael Vegh

The initial mission plan is to have the aircraft climb to 50 ft. near the boundary of Lag Lagunita, at the section of the Lake 90ᵒ from the wind direction, facing the wing (as shown below, assuming wind direction is known a priori). The exact starting position will change based on the field of view function (such that the field of view will be adjacent to the boundary) at the initial mission height of 50 ft.

The exact size and shape of the spiral in the plane of the aircraft, in addition to the initial orientation of the aircraft, will be altered based on the results of subsequent optimization, which will be used to determine a more effective search algorithm, but for now, this algorithm seems appropriate as a starting initial guess. For reference, this trajectory takes approximately 105.5 seconds to fly, assuming an average airspeed of 10 m/s, which, from what is known of the fire propogation algorithm, will result in a spread of 7 cells before the entire field is search. With the field of view function known, an altered search pattern will be used which should cover the field more efficiently.

When one or more potential fires are identified, a stochastic approach will be used to determine the best course of action; depending on the aircraft orientation, distance from the potential fire(s), as well as wind direction, the aircraft will turn and close in on the object of interest, and either put out the fire or drop water on nearby cells to prevent further spread. The decision will be based on a random number generator between 0 and 1, with weights for the different decisions used as inputs into an optimization problem which will be run a number of times to determine the best course of action in the general case. Constraints based on aircraft performance dynamics will be added and iterated upon as development of the project unfolds. Exact parameters of the optimization problem will be decided upon receipt of the fire propagation scripts, after some familiarity with their tendency as well as the effect of wind is determined. Vehicle configuration will also be partly determined based on optimization sweeps of the a.i., depending on vehicle top flight speed, turning radius, as well as number of potential water drops; the best course of action in certain scenarios may be to allow certain sections of the lake to burn, while only dousing a few cells to mitigate the spread.

In the event that the problem can be formulated as a convex optimization problem, the aircraft should be able to process the problem using cvx in-flight, which will yield the optimum flight path to put out a given fire. This is, however, a stretch goal, and may very well be beyond the computing power of the system. Additionally, this problem as a convex optimization problem may oversimplify many of the parameters, although it may be very enlightening as an "initial guess."