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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 flight to an optimal control solver. Leveraging fast geometric planning 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

Simplex Control Methods for Robust Convergence of Small Unmanned Aircraft Flight Trajectories in the Constrained Urban Environment

Constrained optimal control problems for Small Unmanned Aircraft Systems (SUAS) have long suffered from excessive computation times caused by a combination of constraint modeling techniques, the quality of the initial path solution provided to the optimal control solver, and improperly defining the bounds on system state variables, ultimately preventing implementation into real-time, on-board systems. In this research, a new hybrid approach is examined for real-time path planning of SUAS. During autonomous flight, a SUAS is tasked to traverse from one target region to a second target region while avoiding hard constraints consisting of building structures of an urban environment. Feasible path solutions are determined through highly constrained spaces, investigating narrow corridors, visiting multiple waypoints, and minimizing incursions to keep-out regions. These issues are addressed herein with a new approach by triangulating the search space in two-dimensions, or using a tetrahedron discretization in three-dimensions to define a polygonal search corridor free of constraints while alleviating the dependency of problem specific parameters by translating the problem to barycentric coordinates. Within this connected simplex construct, trajectories are solved using direct orthogonal collocation methods while leveraging navigation mesh techniques developed for fast geometric path planning solutions. To illustrate two-dimensional flight trajectories, sample results are applied to flight through downtown Chicago at an altitude of 600 feet above ground level. The three-dimensional problem is examined for feasibility by applying the methodology to a small scale problem. Computation and objective times are reported to illustrate the design implications for real-time optimal control systems, with results showing 86% reduction in computation time over traditional methods