  This work develops feasible path trajectories for a coordinated strike with
multiple aircraft in a constrained environment. Using direct orthogonal
collocation methods, the two-point boundary value optimal control problem is
transcribed into a nonlinear programming problem. A coordinate transformation
is performed on the state variables to leverage the benefits of a simplex
discretization of the search domain. Applying these techniques allows each path
constraint to be removed from the feasible search space, eliminating
computationally expensive, nonlinear constraint equations and problem specific
parameters from the optimal control formulation. Heuristic search techniques
are used to determine a Dubins path solution through the space to seed the
optimal control solver. In the scenario, three aircraft are initiated in
separate directions and are required to avoid all constrained regions while
simultaneously arriving at the target location, each with a different viewing
angle. A focus of this work is to reduce computation times for optimal control
solvers such that real-time solutions can be implemented onboard small unmanned
aircraft systems. Analysis of the problem examines optimal flight paths through
simplex corridors, velocity and heading vectors, control vectors of
acceleration and heading rate, and objective times for minimum time flight.

Optimization and Control