Nonlinear Control for Dual Quaternion Systems

The motion of rigid bodies includes three degrees of freedom (DOF) for rotation, generally referred to as roll, pitch and yaw, and 3 DOF for translation, generally described as motion along the x, y and z axis, for a total of 6 DOF. Many complex mechanical systems exhibit this type of motion, with constraints, such as complex humanoid robotic systems, multiple ground vehicles, unmanned aerial vehicles (UAVs), multiple spacecraft vehicles, and even quantum mechanical systems. These motions historically have been analyzed independently, with separate control algorithms being developed for rotation and translation. The goal of this research is to study the full 6 DOF of rigid body motion together, developing control algorithms that will affect both rotation and translation simultaneously. This will prove especially beneficial in complex systems in the aerospace and robotics area where translational motion and rotational motion are highly coupled, such as when spacecraft have body fixed thrusters. A novel mathematical system known as dual quaternions provide an efficient method for mathematically modeling rigid body transformations, expressing both rotation and translation. Dual quaternions can be viewed as a representation of the special Euclidean group SE (3). An eight dimensional representation of screw theory (combining dual numbers with traditional quaternions), dual quaternions allow for the development of control techniques for 6 DOF motion simultaneously. In this work variable structure nonlinear control methods are developed for dual quaternion systems. These techniques include use of sliding mode control. In particular, sliding mode methods are developed for use in dual quaternion systems with unknown control direction. This method, referred to as self-reconfigurable control, is based on the creation of multiple equilibrium surfaces for the system in the extended state space. Also in this work, the control problem for a class of driftless nonlinear systems is addressed via coordinate transformation. It is shown that driftless nonlinear systems that do not meet Brockett\u27s conditions for coordinate transformation can be augmented such that they can be transformed into the Brockett\u27s canonical form, which is nonholonomic. It is also shown that the kinematics for quaternion systems can be represented by a nonholonomic integrator. Then, a discontinuous controller designed for nonholonomic systems is applied. Examples of various applications for dual quaternion systems are given including spacecraft attitude and position control and robotics

Fuzzy-Model-Based (FMB) Control of a Spacecraft with Fuel Sloshing Dynamics

During the upper-stage separation and orbit injection, orbital control, and attitude maneuver, propellant slosh in partially-filled fuel tanks can cause dynamical instability or pointing errors. The spacecraft dynamics combined with propellant sloshing results in a highly nonlinear and coupled dynamic system that requires a complicated control law. This problem has been a long-standing concern for space missions. The purpose of this research is two fold. The first part is to investigate and develop nonlinear Takagi-Sugeno (T-S) fuzzy model-based controllers for a spacecraft with fuel sloshing considering the input constraints on the actuators. It includes i) a fuzzy controller/observer with a minimum upper-bound control input based on the parallel-distributed compensation (PDC) technique, ii) a fuzzy controller/observer based on the linear quadratic regulator (LQR) that uses the premises of the T-S model, and iii) a robust-optimal fuzzy-model-based controller/observer. The designed controllers are globally asymptotically stable and have a satisfactory performance and robustness. The second part of the research is to develop a mathematical model of a spinning spacecraft with fuel sloshing during high-g maneuvers. The equations of motion of a spacecraft with partially-filled multiple-tanks are derived using the Kane’s method. To do this, two spherical pendulums as an equivalent mechanical model of the fuel sloshing are adopted. The effect of the slosh model parameters on the spacecraft nutation angle is studied. The developed model is validated via several numerical simulations

Retrospective Cost-based Adaptive Spacecraft Attitude Control.

Fixed gain attitude control laws are sensitive to modeling errors and actuator nonlinearities. Adaptive control can solve many of these challenges. We present a retrospective cost-based adaptive spacecraft attitude controller designed using the system's impulse response as modeling information. The performance metric is based on rotation matrices and thus, the controller does not suffer from singularities or discontinuities present in vector attitude representations. We demonstrate robustness to inertia and actuator scaling as well as actuator misalignment and nonlinearities, unknown disturbances, sensor noise and bias for thrusters and reaction wheels through numerical simulations. We implement an averaged Markov parameter and decentralized control to address the problem of the singular input matrix of magnetic torquers. For control moment gyros, we develop a hybrid linearization and impulse response-based Markov parameter and present new guidelines to evaluate the feasibility of desired rest-to-rest maneuvers. Finally, we address the problem of angular velocity-free attitude control of a flexible spacecraft with noncollocated sensors and actuators. We present a new approach to controlling harmonic nonminimum-phase systems using the step and impulse response of the linearized system. We demonstrate robustness to model uncertainty through system analysis and numerical simulations.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/111607/1/gecruz_1.pd

Advances in Spacecraft Systems and Orbit Determination

"Advances in Spacecraft Systems and Orbit Determinations", discusses the development of new technologies and the limitations of the present technology, used for interplanetary missions. Various experts have contributed to develop the bridge between present limitations and technology growth to overcome the limitations. Key features of this book inform us about the orbit determination techniques based on a smooth research based on astrophysics. The book also provides a detailed overview on Spacecraft Systems including reliability of low-cost AOCS, sliding mode controlling and a new view on attitude controller design based on sliding mode, with thrusters. It also provides a technological roadmap for HVAC optimization. The book also gives an excellent overview of resolving the difficulties for interplanetary missions with the comparison of present technologies and new advancements. Overall, this will be very much interesting book to explore the roadmap of technological growth in spacecraft systems

Optimization-Based Control Methodologies with Applications to Autonomous Vehicle

This thesis includes two main parts. In the first part, the main contribution is to develop nonsingular rigid-body attitude control laws using a convex formulation, and implement them in an experimental set up. The attitude recovery problem is first parameterized in terms of quaternions, and then two polynomial controllers using an SoS Lyapunov function and an SoS density function are developed. A quaternion-based polynomial controller using backstepping is also designed to make the closed-loop system asymptotically stable. Moreover, the proposed quaternion-based controllers are implemented in a Quanser helicopter, and compared to the polynomial controllers and a PID controller experimentally. The main contribution of the second part of this thesis is to analytically solve the Hamilton-Jacobi-Bellman equation for a class of third order nonlinear optimal control problems for which the dynamics are affine and the cost is quadratic in the input. One special advantage of this work is that the solution is directly obtained for the control input without the computation of a value function first. The value function can however also be obtained based on the control input. Furthermore, a Lyapunov function can be constructed for a subclass of optimal control problems, yielding a proof certificate for stability. Using the proposed methodology, experimental results of a path following problem implemented in a Wheeled Mobile Robot (WMR) are then presented to verify the effectiveness of the proposed methodology

Design of Attitude Control Actuators for a Simulated Spacecraft

The Air Force Institute of Technology\u27s attitude dynamics simulator, SimSat, is used for hardware-in-the-loop validation of new satellite control algorithms. To provide the capability to test algorithms for control moment gyroscopes, SimSat needed a control moment gyroscope array. The goal of this research was to design, construct, test, and validate a control moment gyroscope array for SimSat. The array was required to interface with SimSat\u27s existing structure, power supply, and electronics. The array was also required to meet maneuver specifications and disturbance rejection specifications. First, the array was designed with initial sizing estimates based on requirements and vehicle size. Next, the vehicle and control dynamics were modeled to determine control moment gyroscope requirements and provide a baseline for validation. Control moment gyroscopes were then built, calibrated, and installed on the vehicle. The actuators were then validated against the dynamics model. Testing shows minor deviation from the expected behavior as a result of small misalignments from the theoretical design. Once validation was complete, the array was tested against the performance specifications. The performance tests indicated that the control moment gyroscope array is capable of meeting specification

Control Laws for a Dual-Spin Stabilized Platform

This paper describes two attitude control laws suitable for atmospheric flight vehicles with a steady angular momentum bias in the vehicle yaw axis. This bias is assumed to be provided by an internal flywheel, and is introduced to enhance roll and pitch stiffness. The first control law is based on Lyapunov stability theory, and stability proofs are given. The second control law, which assumes that the angular momentum bias is large, is based on a classical PID control. It is shown that the large yaw-axis bias requires that the PI feedback component on the roll and pitch angle errors be cross-fed. Both control laws are applied to a vehicle simulation in the presence of disturbances for several values of yaw-axis angular momentum bias. It is seen that both control laws provide a significant improvement in attitude performance when the bias is sufficiently large, but the nonlinear control law is also able to provide improved performance for a small value of bias. This is important because the smaller bias corresponds to a smaller requirement for mass to be dedicated to the flywheel

Modeling and System Identification of an Ornithopter Flight Dynamics Model

Ornithopters are robotic flight vehicles that employ flapping wings to generate lift and thrust forces in a manner that mimics avian flyers. At the small scales and Reynolds numbers currently under investigation for miniature aircraft, where viscous effects deteriorate the performance of conventional aircraft, ornithopters achieve efficient flight by exploiting unsteady aerodynamic flow fields, making them well-suited for a variety of unmanned vehicle applications. Parsimonous dynamic models of these systems are requisite to augment stability and design autopilots for autonomous operation; however, flapping flight is fundamentally different than other means of engineered flight and requires a new standard model for describing the flight dynamics. This dissertation presents an investigation into the flight mechanics of an ornithopter and develops a dynamical model suitable for autopilot design for this class of system. A 1.22 m wing span ornithopter test vehicle was used to experimentally investigate flapping wing flight. Flight data, recorded in trimmed straight and level mean flight using a custom avionics package, reported pitch rates and heave accelerations up to 5.62 rad/s and 46.1 m/s^2 in amplitude. Computer modeling of the vehicle geometry revealed a 0.03 m shift in the center of mass, up to a 53.6% change in the moments of inertia, and the generation of significant inertial forces. These findings justified a nonlinear multibody model of the vehicle dynamics, which was derived using the Boltzmann-Hamel equations. Models for the actuator dynamics, tail aerodynamics, and wing aerodynamics, difficult to obtain from first principles, were determined using system identification techniques with experimental data. A full nonlinear flight dynamics model was developed and coded in both MATLAB and FORTRAN programming languages. An optimization technique is introduced to find trim solutions, which are defined as limit cycle oscillations in the state space. Numerical linearization about straight and level mean flight resulted in both a canonical time-invariant model and a time-periodic model. The time-invariant model exhibited an unstable spiral mode, stable roll mode, stable dutch roll mode, a stable short period mode, and an unstable short period mode. Floquet analysis on the identified time-periodic model resulted in an equivalent time-invariant model having an unstable second order and two stable first order modes, in both the longitudinal and lateral dynamics