Foundations of the Geometric Mechanics Udwadia-Kalaba Framework for Rigid Body Constrained Motion Analysis

Presented herein are multiple tools for constrained motion analysis extended to different dynamical frameworks. The Udwadia-Kalaba (UK) formalism for the constrained motion analysis of a point mass is a well-documented and applied methodology. Here, UK formulation is generalized to the dynamics of rigid bodies on nonlinear manifolds in the geometric mechanics framework. This approach simultaneously treats rotational and translational motion in a unified method without encountering singularites or non-uniqueness, issues that would arise were attitude parameterization sets used. The viability of this geometric mechanics UK formalism is demonstrated for the cases of fully and underconstrained systems. The nominal UK formalism requires the complete knowledge of the system dynamics. In the presence of unmodeled dynamics or uncertainties in the system, the stability of the system cannot be assessed using the nominal UK formulation. Therefore, a controller is presented that stabilizes the system under unmodeled dynamics and external perturbations. In addition, the UK formulation has been historically applied to systems with equality constraints. However, it has not been formulated for usage with inequality constraints. Here, the implementation of slack and excess variables to treat this class of constraints is presented for usage within the UK formulation for the point mass constrained motion with inequality constraints. Also contained within is an extension of pre-existing work which models the gravitational force acting on a rigid body from a nonuniform gravitational field that holds for any degree and order of spherical harmonics

Dynamics Of Reconfigurable Multibody Space Systems Connected By Magnetic Flux Pinning

Many future space systems, from solar power collection satellites to sparseaperture telescopes, will involve large-scale space structures which must be launched in a modular fashion. Currently, assembling modular structures in orbit is a challenging problem in multi-vehicle control or human-vehicle interaction. Some novel approaches to assembling modular space structures or formation-flying space systems involve augmenting the system dynamics with non-contacting force fields such as electromagnetic interactions. However, familiar divergenceless forces are subject to Earnshaw's Theorem and require active control in 6 DOF for stability. This study proposes an approach to modular spacecraft assembly based on the passively stable physics of magnetic flux pinning, an interaction between superconductors and magnetic fields which is not limited by Earnshaw's Theorem. Spacecraft modules linked by flux pinning passively fall into stable, many-degree-of-freedom basins of attraction in which flux pinning holds the modules together with stiffness and damping but no mechanical contact. This dissertation reports several system identification experiments that characterize the physical properties of flux pinning for spacecraft applications and identify avenues for design of flux-pinning space hardware. Once assembled in orbit, altering a spacecraft to effect repairs or adapt to new missions presents significant control challenges as well. Flux-pinning technology also offers exciting possibilities for new spacecraft-reconfiguration techniques, in which a spacecraft changes structure and function at the system level. Flux-pinned modular spacecraft can reconfigure in such a way that the passive physics of flux pinning and the space environment govern the low-level dynamics of a reconfiguration maneuver, instead of full-state feedback control. These reconfiguration maneuvers take the form of sequences of passively stable evolutions to equilibrium states, with joint kinematics between modules preventing collisions. This dissertation develops a theory for multibody spacecraft reconfiguration controllers that take a high-level, hybrid-systems approach in which a pre-computed graph structure stores all the reachable configurations that meet certain design-specified criteria. Edges of the graph carry mission-related weights so that a space system can optimize power consumption, robustness measures, or other performance metrics during a maneuver. These technologies and control strategies may provide opportunities for versatile space systems that can accomplish a wide variety of future missions

Close-range rendezvous with a moving target spacecraft using udwadia-kalaba equation

This paper presents an analytical dynamics based formulation for close-range planar rendezvous of two chaser spacecraft onto an uncontrolled target spacecraft. The control requirements on the chaser system is formulated based on displacement constraints with respect to target. Exact control forces are then generated based on the acceleration constraint equation, which is derived from the displacement constraint, and substituted into the Udwadia-Kalaba equation. As the major contribution, a new formulation is developed for both a single and dual-chaser close-range rendezvous. The simulation results highlight the simultaneous angular velocity synchronization and stand-off distance maintenance with respect to the target

Automatic Flight Control Systems

The history of flight control is inseparably linked to the history of aviation itself. Since the early days, the concept of automatic flight control systems has evolved from mechanical control systems to highly advanced automatic fly-by-wire flight control systems which can be found nowadays in military jets and civil airliners. Even today, many research efforts are made for the further development of these flight control systems in various aspects. Recent new developments in this field focus on a wealth of different aspects. This book focuses on a selection of key research areas, such as inertial navigation, control of unmanned aircraft and helicopters, trajectory control of an unmanned space re-entry vehicle, aeroservoelastic control, adaptive flight control, and fault tolerant flight control. This book consists of two major sections. The first section focuses on a literature review and some recent theoretical developments in flight control systems. The second section discusses some concepts of adaptive and fault-tolerant flight control systems. Each technique discussed in this book is illustrated by a relevant example