Routing and Control of Unmanned Aerial Vehicles for Performing Contact-Based Tasks

In this dissertation, two main topics are explored, the vehicle routing problem (VRP) and model reference adaptive control (MRAC) for unknown nonlinear systems. The VRP and its extension, the split delivery VRP (SVRP), are analyzed to determine the effects of using two different objective functions, the total cost objective, and the last delivery objective. A worst-case analysis suggests that using the SVRP can improve total costs by as much as a factor of 2 and the last delivery by a factor that scales with the number of vehicles over the classical VRP. To test the theoretical worst-cases against the solutions of benchmark datasets, a heuristic is developed based on embedding a random variable neighborhood search within an iterative local search heuristic. Results suggest that the split deliveries do in fact improve total cost and last delivery times over the classical formulation.

The SVRP has been developed classically for use with vehicles such as trucks which have large payload capacities and typically long ranges for deliveries, but are limited to traversing on roads. Unmanned aerial vehicles (UAVs) are useful for their high maneuverability, but suffer from limited capacity for payloads and short ranges. The classical SVRP formulation is extended to one more suitable for UAVs by accounting for limited range, limited payloads, and the ability to swap batteries at known locations. Instead of Euclidean distances, path plans which are adjusted for a known, constant wind underlie the cost matrix of the optimization problem. The effects of payload on the vehicle's range are developed using propeller momentum theory, and simulations verify that the proposed approach could be used in a realistic scenario.

Two novel MRAC laws are then developed. The first, MRAC laws for prescribed performance, exploits barrier Lyapunov functions and a 2-Layer approach to guarantee user-defined performance. This control law allows unknown nonlinear systems to verify a user-defined rate of convergence of the tracking error while verifying apriori control and tracking error constraints. Numerical simulations are performed on the roll dynamics of a delta-wing aircraft. The second novel MRAC law is MRAC for switched dynamical systems which is proven in two different mathematical frameworks. Applying the Caratheodory framework, it is proven that if the switching signal has an arbitrarily small, but non-zero, dwell-time, then solutions of both the trajectory tracking error's and the adaptive gains' dynamics exist, are unique, and are defined almost everywhere, and the trajectory tracking error converges asymptotically to zero. Employing the Filippov framework, it is proven that if the switching signal is Lebesgue integrable and has countably many points of discontinuity, then maximal solutions of both the trajectory tracking error and the adaptive gains dynamics exist and are defined almost everywhere, and the trajectory tracking error converges to zero asymptotically. The proposed MRAC law is experimentally verified in the case where a UAV with tilting propellers is tasked with mounting an unknown camera onto a wall.

The previous results are then combined into a novel application in construction. A method for using a UAV to measure autonomously the moisture of an exterior precast concrete envelope is developed which can provide data feedback through contact-based measurements to improve safety and real-time data acquisition through the integration with the Building Information Model (BIM). To plan the path of the vehicle, the path planning and SVRP for UAV approaches developed in previous chapters are utilized. To enable the UAS to contact surfaces, a switched MRAC law is employed to control the vehicle throughout and guarantee successful measurements. A full physics-based simulation environment is developed, and the proposed framework is used to simulate taking multiple measurements.