Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1992. / Vita. Abstract. Includes bibliographical references (leaves 113-118). Also available via the Internet.

An innovative dynamics and control algorithm is developed for a dual-nanosatellite formation flying mission. The principal function of this algorithm is to use regular GPS state measurements to determine the controlled satellite's tracking error from a set of reference trajectories in the local-vertical/local-horizontal reference frame. A linear state-feedback control law--designed using a linear quadratic regulator method--calculates the optimal thrusts necessary to correct this error and communicates the thrust directions to the attitude control system and the thrust durations to the propulsion system. The control system is developed to minimize the conflicting metrics of tracking error and ΔV requirements. To reconfigure the formation, an optimization algorithm is designed using the analytical solution to the state-space equation and the Hill-Clohessy-Wiltshire state transition matrix to solve for dual-thrust reconfiguration maneuvers. The resulting trajectories require low ΔV, use finite-time thrusts and are accurate in a fully nonlinear orbital environment. This algorithm will be used to control the CanX-4&5 formation flying demonstration mission. In addition, an iterative method which numerically generates quasi periodic trajectories for a satellite formation is presented. This novel technique utilizes a shooting approach to the Newton method to close the relative deputy trajectory over a specific number of orbits, then fits the actual perturbed motion of the deputy with a Fourier series to enforce periodicity. This process is applied to two well-known satellite formations: a projected circular orbit and a J2-invariant formation. Compared to conventional formations, these resulting quasi-periodic trajectories require a dramatically lower control effort to maintain and could therefore be used to extend ΔV-limited formation flying missions. Finally, an analytical study of the stability of the formation flying algorithm is conducted. To facilitate the proof, the control algorithm is converted into a discrete-time linear time-varying system. Stability of the system is determined via discrete Floquet theory. This analysis is applied to the CanX-4&5 control laws for tracking along-track orbits, projected circular orbits, and quasi J2-invariant formations.

An innovative dynamics and control algorithm is developed for a dual-nanosatellite formation flying mission. The principal function of this algorithm is to use regular GPS state measurements to determine the controlled satellite's tracking error from a set of reference trajectories in the local-vertical/local-horizontal reference frame. A linear state-feedback control law--designed using a linear quadratic regulator method--calculates the optimal thrusts necessary to correct this error and communicates the thrust directions to the attitude control system and the thrust durations to the propulsion system. The control system is developed to minimize the conflicting metrics of tracking error and ΔV requirements. To reconfigure the formation, an optimization algorithm is designed using the analytical solution to the state-space equation and the Hill-Clohessy-Wiltshire state transition matrix to solve for dual-thrust reconfiguration maneuvers. The resulting trajectories require low ΔV, use finite-time thrusts and are accurate in a fully nonlinear orbital environment. This algorithm will be used to control the CanX-4&5 formation flying demonstration mission. In addition, an iterative method which numerically generates quasi periodic trajectories for a satellite formation is presented. This novel technique utilizes a shooting approach to the Newton method to close the relative deputy trajectory over a specific number of orbits, then fits the actual perturbed motion of the deputy with a Fourier series to enforce periodicity. This process is applied to two well-known satellite formations: a projected circular orbit and a J2-invariant formation. Compared to conventional formations, these resulting quasi-periodic trajectories require a dramatically lower control effort to maintain and could therefore be used to extend ΔV-limited formation flying missions. Finally, an analytical study of the stability of the formation flying algorithm is conducted. To facilitate the proof, the control algorithm is converted into a discrete-time linear time-varying system. Stability of the system is determined via discrete Floquet theory. This analysis is applied to the CanX-4&5 control laws for tracking along-track orbits, projected circular orbits, and quasi J2-invariant formations.

This dissertation addresses the generalization of rigid-body attitude kinematics, dynamics, and control to higher dimensions. A new result is developed that demonstrates the kinematic relationship between the angular velocity in N-dimensions and the derivative of the principal-rotation parameters. A new minimum-parameter description of N-dimensional orientation is directly related to the principal-rotation parameters. The mapping of arbitrary dynamical systems into N-dimensional rotations and the merits of new quasi velocities associated with the rotational motion are studied. A Lagrangian viewpoint is used to investigate the rotational dynamics of N-dimensional rigid bodies through Poincar??e??s equations. The N-dimensional, orthogonal angularvelocity components are considered as quasi velocities, creating the Hamel coefficients. Introducing a new numerical relative tensor provides a new expression for these coefficients. This allows the development of a new vector form of the generalized Euler rotational equations. An N-dimensional rigid body is defined as a system whose configuration can be completely described by an N??N proper orthogonal matrix. This matrix can be related to an N??N skew-symmetric orientation matrix. These Cayley orientation variables and the angular-velocity matrix in N-dimensions provide a new connectionbetween general mechanical-system motion and abstract higher-dimensional rigidbody rotation. The resulting representation is named the Cayley form. Several applications of this form are presented, including relating the combined attitude and orbital motion of a spacecraft to a four-dimensional rotational motion. A second example involves the attitude motion of a satellite containing three momentum wheels, which is also related to the rotation of a four-dimensional body. The control of systems using the Cayley form is also covered. The wealth of work on three-dimensional attitude control and the ability to apply the Cayley form motivates the idea of generalizing some of the three-dimensional results to Ndimensions. Some investigations for extending Lyapunov and optimal control results to N-dimensional rotations are presented, and the application of these results to dynamical systems is discussed. Finally, the nonlinearity of the Cayley form is investigated through computing the nonlinearity index for an elastic spherical pendulum. It is shown that whereas the Cayley form is mildly nonlinear, it is much less nonlinear than traditional spherical coordinates.

Thesis (M.E.)--University of Canterbury, 2007. / Typescript (photocopy). Includes bibliographical references (leaves 105-106). Also available via the World Wide Web.

The work undertaken in this research aims to develop a mathematical model which can replicate the behaviour of a racing driver controlling a vehicle at its handling limit. Most of the models proposed in the literature assume a perfect driver. A formulation taking human limitations into account would serve as a design and simulation tool for the automotive sector. A nonlinear vehicle model with five degrees of freedom under the action of external disturbances controlled by a Linear Quadratic Regulator (LQR) is first proposed to assess the validity of state variances as stability metrics. Comparison to existing stability and controllability criteria indicates that this novel metric can provide meaningful insights into vehicle performance. The LQR however, fails to stabilise the vehicle as tyres saturate. The formulation is extended to improve its robustness. Full nonlinear optimisation with direct transcription is used to derive a controller that can stabilise a vehicle at the handling limit under the action of disturbances. The careful choice of discretisation method and track description allow for reduced computing times. The performance of the controller is assessed using two vehicle configurations, Understeered and Oversteered, in scenarios characterised by increasing levels of non- linearity and geometrical complexity. All tests confirm that vehicles can be stabilised at the handling limit. Parameter studies are also carried out to reveal key aspects of the driving strategy. The driver model is validated against Driver In The Loop simulations for simple and complex manoeuvres. The analysis of experimental data led to the proposal of a novel driving strategy. Driver randomness is modelled as an external disturbance in the driver Neuromuscular System. The statistics of states and controls are found to be in good agreement. The prediction capabilities of the controller can be considered satisfactory.

The challenge of sensing relative motion between vehicles is an important subject in the engineering field in recent years. The associated applications range from spacecraft rendezvous and docking to autonomous ground vehicle operations. The focus of this thesis is to develop the simulation tools to examine this problem in the laboratory environment. More specifically, the goal is to create a virtual unmanned ground vehicle that operates in the same manner as an actual vehicle. This simulated vehicle allows for safely testing other software or hardware components before application to the actual vehicle. In addition, the simulated vehicle, in contrast to the real vehicle, is able to operate on different surfaces or even different planets, with different gravitational accelerations. To accomplish this goal, the equations of motion of a two-wheel driven unmanned vehicle are developed analytically. To study the spacecraft application, the equations of motion for a spacecraft cluster are also developed. These two simulations are implemented in a modular form using the UMBRA framework. In addition, an interface between these two simulations is created for the unmanned vehicle to mimic the translational motion of a spacecraft's relative orbit. Finally, some of the limitations and future improvements of the existing simulations are presented. / Master of Science

Multiple robot manipulators cooperating in a common manipulation task can accomplish complex tasks that a single manipulator would be unable to complete. To achieve physical cooperation with multiple manipulators working on a common object, interaction forces need to be controlled throughout the motion. The aim of this research is to develop an inverse dynamics model-based cooperative force and position control scheme for multiple robot manipulators. An extended definition of motion is proposed to include force demands based on a constrained Lagrangian dynamics and Lagrangian multipliers formulation. This allows the direct calculation of the inverse dynamics with both motion and force demands. A feedforward controller based on the proposed method is built to realise the cooperative control of two robots sharing a common load, with both motion and force demands. Furthermore, this thesis develops a method to design an optimal excitation trajectory for robot dynamic parameter estimation utilising the Schroeder Phased Harmonic Sequence. This method yields more precise and accurate inverse dynamics models, which result in better control. The proposed controller is then tested in an experimental set-up consisting of two robot manipulators and a common load. Results show that in general the proposed controller performs noticeably better position and force tracking, especially for higher speed motions, when compared to traditional hybrid position/force controllers.

For precise robot control, endpoint compliance strategies utilize feedback from a force sensor located near the tool/workpiece interface. Such endpoint force control systems have been observed in the laboratory to be limited to unsatisfactory closed-loop performance. This paper discusses the particular dynamic properties of robot systems which can lead to instability and limit performance. A series of lumped-parameter models is developed in an effort to predict the closed-loop dynamics of a force-controlled single axis arm. The models include some effects of robot structural dynamics, sensor compliance, and workpiece dynamics. The qualitative analysis shows that the robot dynamics contribute to force-controlled instability. Recommendations are made for models to be used in control system design.

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