Simplex Solutions for Optimal Control Flight Paths in Urban Environments

This paper identifies feasible fight paths for Small Unmanned Aircraft Systems in a highly constrained environment. Optimal control software has long been used for vehicle path planning and has proven most successful when an adequate initial guess is presented to an optimal control solver. Leveraging computer animation techniques, a large search space is discretized into a set of simplexes where a Dubins path solution is generated and contained in a polygonal search corridor free of path constraints. Direct optimal control methods are then used to determine the optimal flight path through the newly defined search corridor. Two scenarios are evaluated. The first is limited to heading rate control only, requiring the air vehicle to maintain constant speed. The second allows for velocity control which permits slower speeds, reducing the vehicles minimum turn radius and increasing the search domain. Results illustrate the benefits gained when including speed control to path planning algorithms by comparing trajectory and convergence times, resulting in a reliable, hybrid solution method to the SUAS constrained optimal control problem.