Guidance and Control of Autonomous Unmanned Aerial Systems for Maritime Operations

In this dissertation, guidance and control of autonomous unmanned aerial systems (UAS) are explored. Specifically, we investigate model reference adaptive control (MRAC) based systems for tailsitter UAS, and guidance and control of multi-rotor UAS for tactical maneuvering and coverage. Applications, both current and potential, are investigated and gaps in existing technologies are identified.

To address the controls problem of a particular class of tailsitter UAS, that is, quadrotor-biplanes, subject to modeling uncertainties, unmodeled payloads, wind gusts, and actuator faults and failures, two approaches are developed. In the first approach, the longitudinal dynamics of a tailsitter UAS are regulated using an MRAC law for prescribed performance and output tracking in a novel control architecture. The MRAC law for prescribed performance and output tracking incorporates a Linear Quadratic Regulator (LQR) baseline controller using integral-feedback interconnections. Constraints on the trajectory tracking error are enforced using barrier Lyapunov functions, and a user-defined rate of convergence of the trajectory tracking error is guaranteed by employing a reference model for the trajectory tracking error's transient dynamics. In this control system, the translational and rotational dynamics are split into an outer loop and an inner loop, respectively, to account for the underactuation of the quadrotor-biplane. In the outer loop, estimates of the aerodynamic forces and MRAC laws are used to stabilize the translational dynamics. Furthermore, the reference pitch angle is deduced such that the vehicle's total thrust never points towards the Earth for safety, and discontinuities inherent to the signed arctangent function commonly used for determining orientations are avoided. In the inner loop, estimates of the aerodynamic moment and an MRAC law are used to stabilize the rotational dynamics. A law for determining the desired total thrust is proposed, which ensures that if the vehicle's orientation is close enough to the desired orientation, then the proper thrust force is applied. A control allocation scheme is presented to ensure that the desired moment of the thrust force is always realized, and constraints on the non-negativity of the thrust force produced by the actuators are satisfied. The proposed control architecture employing MRAC for prescribed performance and output signal tracking is validated in simulation, and the MRAC law for prescribed performance is compared to the classical MRAC law.

In the second approach, a unified control architecture based on MRAC is presented which does not separate the longitudinal and lateral-directional dynamics. The translational and rotational dynamics are separated into outer and inner loops, respectively, to address the underactuation of the tailsitter UAS. Since it is expected that the vehicle will undergo large rotations, the tailsitter's orientation is captured using quaternions, which are singularity-free. Furthermore, the windup phenomenon is addressed by employing barrier Lyapunov functions to ensure that the first component of the tracking error quaternion is positive, and thus, the shortest rotation is followed to drive the vehicle's current orientation to the reference orientation. In the outer loop, the desired thrust force is determined using estimates of the aerodynamic forces and an MRAC law. The reference orientation is determined as a solution of the orthogonal Procrustes' problem, which finds the smallest rotation from the current orientation of the thrust force, to the orientation of th desired thrust force. The angular velocity and acceleration cannot be deduced by taking the time derivative of the solution of the orthogonal Procrustes' problem due to the discontinuous nature of the singular value decomposition. Therefore, the twice continuously differentiable function, spherical linear interpolation, is used to find a geodesic joining the unit quaternion capturing the vehicle's current orientation, and the unit quaternion capturing the reference orientation. An interesting result is that the angular velocity and acceleration depend only on the first and second derivatives of the scalar-valued function which parameterizes the spherical linear interpolation function; the actual function is immaterial. However, determining the shape of this function is nontrivial, and hence, an approach inspired by model predictive control is used. In the inner loop, estimates of the aerodynamic moment and an MRAC law are used to stabilize the rotational dynamics, and the thrust force is allocated to the individual propellers. The validity of the proposed control scheme is presented in simulation.

An integrated guidance and control system for autonomous UAS is proposed to maneuver in an unknown, dynamic, and potentially hostile environment in a reckless or tactical manner as prescribed by the user. Tactical maneuvering in this guidance and control system is enabled through exploitation of obstacles in the environment for shelter as the vehicle approaches its goal. Reckless maneuvering is enabled by ignoring the presence of nearby obstacles while proceeding towards the goal, while remaining collision-free. The demarcation of reckless and tactical behaviors are bio-inspired, since these tactics are used by animals or ground-based troops. The guidance system fuses a path planner, collision-avoidance algorithm, vision-based navigation system, and a trajectory planner. The path planner is based on the A* search algorithm, and a custom tunable cost-to-come and heuristic function are proposed to enable the exploitation of the obstacles' set for shelter by decreasing the weight of edges in the underlying graph that capture nodes close to the obstacles' set. The consistency of the heuristic is established, and hence, the search algorithm will return an optimal solution, and not expand nodes multiple times. In realistic scenarios, fast replanning is necessary to ensure that the system realizes the desired behavior, and does not collide with obstacles. The trajectory planner is based on fast model predictive control (fMPC), and thus, can be executed in real time. A custom tunable cost function, which weighs the importance of proximity to the obstacles' set and proximity to the goal, is employed to provide another mechanism for enabling tactical behaviors. The novel collision avoidance algorithm is based on the solution of a particular class of semidefinite programming problems, that is, quadratic discrimination. The collision avoidance algorithm produces convex sets of free space near the UAS by finding ellipsoids that separate the UAS from the obstacles' set. The convex sets are used in the fMPC framework as inequality constraints.
The collision avoidance algorithm's computational burden is determined empirically, and is shown to be faster than two similar algorithms in the literature. The modules above are integrated into a single guidance system, which supplies reference trajectories to an arbitrary control system, and the validity of the proposed approach is exhibited in several simulations and flight tests. Furthermore, a taxonomy of flight behaviors is presented to understand how the tunable parameters affect the recklessness or stealthiness of the resulting trajectory.

Lastly, an integrated guidance and control system for autonomous UAS performing tactical coverage in an unknown, dynamic, and potentially hostile environment in a reckless or tactical manner as prescribed by the user is presented. The guidance problem for coverage concerns strategies and route planning for gathering information about an environment. The aim of gathering information about an unknown environment is to aid in situational awareness and planning for service organizations and first-responders. To address this problem, goal selection, path planning, collision avoidance, and trajectory planning are integrated. A novel goal selection algorithm based on the Octree data structure is proposed to autonomously determine goal points for the path planner. In this algorithm, voxel maps deduced by a navigation system, which capture the occupancy and exploration status of areas of the environment, are segmented into partitions that capture large unexplored areas, and large explored areas. Large unexplored areas are used as candidates for goal points. The feasibility of goal points is determined by employing a greedy $A\ast$ technique. The algorithm boasts tunable parameters that allow the user to specify a greedy or systematic behavior when determining a sequence of goal points. The computational burden of this technique is determined empirically, and is shown to be useful for real-time use in realistic scenarios. The path planner is based on the Lifelong Planning $A\ast$ ($LPA\ast$) search algorithm which is shown to have advantages over the $A\ast$ technique. A custom tunable cost-to-come and heuristic function are proposed to enable tactical or reckless path planning. A novel collision avoidance algorithm is proposed as an improved version of the aforementioned collision avoidance algorithm, where the volume of the resulting constraint sets are improved, and thus, more of the free space is captured by the convex set, and hence, the trajectory planner can exploit more of the environment for tactical maneuvering. This algorithm is based on semidefinite programming and a fast approximate convex hull algorithm. The trajectory planner is based on fMPC, employs a custom cost function to enable tactical maneuvering by coasting the surface of obstacles and regulation of the desired acceleration as a function of proximity to shelter, employs barrier functions to constrain the attitude of the vehicle and ensure thrust positivity, and employs a quadrotor UAS' output feedback linearized equations of motion as differential constraints to enable aggressive maneuvering. The efficacy of the proposed system is validated using a custom-made C++ simulator.