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

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

Determining Follower Aircraft's Optimal Trajectory in Relation to a Dynamic Formation Ring

The specific objective of this paper is to develop a tool that calculates the optimal trajectory of the follower aircraft as it completes a formation rejoin, and then maintains the formation position, defined as a ring of points, until a fixed final time. The tool is designed to produce optimal trajectories for a variety of initial conditions and leader trajectories. Triple integrator dynamics are used to model the follower aircraft in three dimensions. Control is applied directly to the rate of acceleration. Both the follower's and leader's velocities and accelerations are bounded, as dictated by the aircraft's performance envelope. Lastly, a path constraint is used to ensure the follower avoids the leader's jet wash region. This optimal control problem is solved through numerical analysis using the direct orthogonal collocation solver GPOPS-II. Two leader trajectories are investigated, including a descending spiral and continuous vertical loops. Additionally, a study of the effect of various initial guesses is performed. All trajectories displayed a direct capture of the formation position, however changes in solver initial conditions demonstrate various behaviors in how the follower maintains the formation position. The developed tool has proven adequate to support future research in crafting real-time controllers capable of determining near-optimal trajectories.Comment: 11 pages, 20 figures, 2 table

Optimal Wind Corrected Flight Path Planning for Autonomous Micro Air Vehicles

This research effort focuses on determining the optimal flight path required to put a micro air vehicle\u27s (MAVs) fixed sensor on a target in the presence of a constant wind. Autonomous flight is quickly becoming the future of air power and over the past several years, the size and weight of autonomous vehicles has decreased dramatically. As these vehicles were implemented into the field, it was quickly discovered that their flight paths are severely altered by wind. However, since the size of the vehicle does not allow for a gimbaled camera, only a slight perturbation to the attitude of the vehicle will cause the sensor footprint to be displaced dramatically. Therefore, the goal of this research was to use dynamic optimization techniques to determine the optimal flight path to place a MAV\u27s sensor footprint on a target when operating in wind for three different scenarios. The first scenario considered the minimum time path given an initial position and heading and a final position and heading. The second scenario minimized the error between the MAV\u27s ground track and a straight line to the target in order to force a desired path on the vehicle. The final scenario utilized both a forward mounted sensor as well as a side mounted sensor to optimize the time the target is continually in view of the sensor footprint. Each of these scenarios has been captured in simulated plots that depict varying wind angles, wind speeds, and initial and final heading angles. These optimal flight paths provide a benchmark that will validate the quality of future closed-loop wind compensation control systems