Immersion and invariance orbital stabilization of underactuated mechanical systems with collocated pre-feedback

In this note we study the generation of attractive oscillations of a class of mechanical systems with underactuation one. The proposed design consists of two terms, i.e., a partial linearizing state feedback, and an immersion and invariance orbital stabilization controller. The first step is adopted to simplify analysis and design, however, bringing an additional difficulty that the model loses its Euler-Lagrange structure after the collocated pre-feedback. To address this, we propose a constructive solution to the orbital stabilization problem via a smooth controller in an analytic form, and the model class identified in the paper is characterized via some easily apriori verifiable assumptions on the inertia matrix and the potential energy function

Optimal Stabilization of Periodic Orbits

In this contribution the optimal stabilization problem of periodic orbits is studied in a symplectic geometry setting. For this, the stable manifold theory for the point stabilization case is generalized to the case of periodic orbit stabilization. Sufficient conditions for the existence of a \gls{nhim} of the Hamiltonian system are derived. It is shown that the optimal control problem has a solution if the related periodic Riccati equation has a unique periodic solution. For the analysis of the stable and unstable manifold a coordinate transformation is used which is moving along the orbit. As an example, an optimal control problem is considered for a spring mass oscillator system, which should be stabilized at a certain energy level.Comment: Submitted for IFAC World Congress 202

Adaptive Reduced-Attitude Control for Spacecraft Boresight Alignment with Safety Constraints and Accuracy Requirements

This paper investigates the boresight alignment control problem under safety constraints and performance requirements, involving pointing-forbidden constraint, attitude angular velocity limitation, and pointing accuracy requirement. Meanwhile, the parameter uncertainty issue is taken into account simultaneously. To address this problem, we propose a modified composite framework integrating the Artificial Potential Field (APF) methodology and the Prescribed Performance Control (PPC) scheme. The APF scheme ensures safety, while the PPC scheme is employed to realize an accuracy-guaranteed control. A Switched Prescribed Performance Function (SPPF) is proposed to facilitate the integration, which monitors various constraints and further establishes compatibility between safety and performance concerns by leveraging a special PPC freezing mechanism. To further address the parameter uncertainty, we introduce the Immersion-and-Invariance (I\&I) adaptive control technique to derive an adaptive APF-PPC composite controller, further guaranteeing the closed-loop system's asymptotic convergence. Finally, numerical simulations are carried out to validate the effectiveness of the proposed scheme.Comment: Submitted to T-AE

Energy-Based Control for the Cart-Pole System in Implicit Port-Hamiltonian Representation

This master thesis is devoted to the design, analysis, and experimental validation of an energy-based control strategy for the well-known benchmark cart-pole system in implicit Port-Hamiltonian (PH) representation. The control scheme performs two tasks: swingup and (local) stabilization. The swing-up controller is carried out on the basis of a generalized energy function and consists of bringing the pendulum trajectories from the lower (stable) position to a limit cycle (homoclinic orbit), which passes by the upright (unstable) position, as well as the cart trajectories to the desired point. The (local) stabilizing controller is designed under a novel algebraic Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) technique and ensures the upright (asymptotic) stabilization of the pendulum as well as the cart at a desired position. To illustrate the effectiveness of the proposed control scheme, this work presents simulations and real-time experiments considering physical damping, i.e., viscous friction. The results are additionally contrasted with another energy-based control strategy for the cart-pole system in explicit Euler-Lagrange (EL) representation.Diese Masterarbeit widmet sich dem Entwurf, der Analyse und der experimentellen Validierung einer energiebasierten Regelstrategie für das bekannte Benchmarksystem des inversen Pendels auf einem Wagen in impliziter Port-Hamiltonscher (PH) Darstellung. Das Regelungssystem erfüllt zwei Aufgaben: das Aufschwingen und (lokale) Stabilisierung. Das Aufschwingen erfolgt auf Grundlage der generalisierten Energiefunktion und besteht darin, sowohl die Trajektorien des Pendels von der unteren (stabilen) Position in einen Grenzzyklus (homokliner Orbit) zu bringen, wobei die (instabile) aufrechte Lage passiert wird, als auch den Wagen in einer gewünschten Position einzustellen. Die (lokale) Regelung zur Stabilisierung ist nach einer neuartigen algebraischen Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) Methode konzipiert und gewährleistet die aufrechte (asymptotische) Stabilisierung des Pendels sowie die Positionierung des Wagens an einem gewünschten Referenzpunkt. Um die Funktionalität des entworfenen Regelungssystems zu veranschaulichen, werden in dieser Masterarbeit Simulationen und Echtzeit-Experimente unter Berücksichtigung der physikalischen Dämpfung, d.h. der viskosen Reibung, vorgestellt. Die Ergebnisse werden zusätzlich mit einem weiteren energiebasierten Regelungsansatz für das System des inversen Pendels auf einem Wagen in expliziter Euler-Lagrange (EL) Darstellung verglichen.Tesi

Autonomous formation flying: unified control and collision avoidance methods for close manoeuvring spacecraft

The idea of spacecraft formations, flying in tight configurations with maximum baselines of a few hundred meters in low-Earth orbits, has generated widespread interest over the last several years. Nevertheless, controlling the movement of spacecraft in formation poses difficulties, such as in-orbit high-computing demand and collision avoidance capabilities, which escalate as the number of units in the formation is increased and complicated nonlinear effects are imposed to the dynamics, together with uncertainty which may arise from the lack of knowledge of system parameters. These requirements have led to the need of reliable linear and nonlinear controllers in terms of relative and absolute dynamics. The objective of this thesis is, therefore, to introduce new control methods to allow spacecraft in formation, with circular/elliptical reference orbits, to efficiently execute safe autonomous manoeuvres. These controllers distinguish from the bulk of literature in that they merge guidance laws never applied before to spacecraft formation flying and collision avoidance capacities into a single control strategy. For this purpose, three control schemes are presented: linear optimal regulation, linear optimal estimation and adaptive nonlinear control. In general terms, the proposed control approaches command the dynamical performance of one or several followers with respect to a leader to asymptotically track a time-varying nominal trajectory (TVNT), while the threat of collision between the followers is reduced by repelling accelerations obtained from the collision avoidance scheme during the periods of closest proximity. Linear optimal regulation is achieved through a Riccati-based tracking controller. Within this control strategy, the controller provides guidance and tracking toward a desired TVNT, optimizing fuel consumption by Riccati procedure using a non-infinite cost function defined in terms of the desired TVNT, while repelling accelerations generated from the CAS will ensure evasive actions between the elements of the formation. The relative dynamics model, suitable for circular and eccentric low-Earth reference orbits, is based on the Tschauner and Hempel equations, and includes a control input and a nonlinear term corresponding to the CAS repelling accelerations. Linear optimal estimation is built on the forward-in-time separation principle. This controller encompasses two stages: regulation and estimation. The first stage requires the design of a full state feedback controller using the state vector reconstructed by means of the estimator. The second stage requires the design of an additional dynamical system, the estimator, to obtain the states which cannot be measured in order to approximately reconstruct the full state vector. Then, the separation principle states that an observer built for a known input can also be used to estimate the state of the system and to generate the control input. This allows the design of the observer and the feedback independently, by exploiting the advantages of linear quadratic regulator theory, in order to estimate the states of a dynamical system with model and sensor uncertainty. The relative dynamics is described with the linear system used in the previous controller, with a control input and nonlinearities entering via the repelling accelerations from the CAS during collision avoidance events. Moreover, sensor uncertainty is added to the control process by considering carrier-phase differential GPS (CDGPS) velocity measurement error. An adaptive control law capable of delivering superior closed-loop performance when compared to the certainty-equivalence (CE) adaptive controllers is finally presented. A novel noncertainty-equivalence controller based on the Immersion and Invariance paradigm for close-manoeuvring spacecraft formation flying in both circular and elliptical low-Earth reference orbits is introduced. The proposed control scheme achieves stabilization by immersing the plant dynamics into a target dynamical system (or manifold) that captures the desired dynamical behaviour. They key feature of this methodology is the addition of a new term to the classical certainty-equivalence control approach that, in conjunction with the parameter update law, is designed to achieve adaptive stabilization. This parameter has the ultimate task of shaping the manifold into which the adaptive system is immersed. The performance of the controller is proven stable via a Lyapunov-based analysis and Barbalat’s lemma. In order to evaluate the design of the controllers, test cases based on the physical and orbital features of the Prototype Research Instruments and Space Mission Technology Advancement (PRISMA) are implemented, extending the number of elements in the formation into scenarios with reconfigurations and on-orbit position switching in elliptical low-Earth reference orbits. An extensive analysis and comparison of the performance of the controllers in terms of total Δv and fuel consumption, with and without the effects of the CAS, is presented. These results show that the three proposed controllers allow the followers to asymptotically track the desired nominal trajectory and, additionally, those simulations including CAS show an effective decrease of collision risk during the performance of the manoeuvre

A cumulative index to the 1977 issues of a continuing bibliography on aerospace medicine and biology

This publication is a cumulative index to the abstracts contained in the Supplements 164 through 175 of Aerospace Medicine and Biology: A Continuing Bibliography. It includes three indexes-- subject, personal author, and corporate source

Novel uses of spatial light modulators in optical tweezers

In recent years spatial light modulators (SLMs) have become an integral part of many optical trapping experiments. Yet their usefulness, which stems from their flexibility, is often under exploited. In this thesis I seek to demonstrate how it is possible to expand the range of optical trapping applications that may benefit from the use of spatial light modulators. From exploring the benefits of increased resolution to demonstrating novel applications like position clamping and polarization control, I show how SLMs are a resource which can benefit optical trapping in new and unconventional ways. The optical properties of liquid crystals have long been known however it is only recently that they have been applied to optical tweezers. The physics and operation of spatial light modulators are discussed in chapter 1, with specific attention paid to those aspects of operation which are of pertinent practical use to optical trapping. In chapter 2 it is shown how phase only modulation can be used to create effective holographic optical tweezers systems which are capable of manipulating micron scale particles and measuring pico-Newton forces. Chapter 3 charts the development and characterization of a 4 Mega-pixel spatial light modulator which was created as an improvement on current SLM technology. The role of SLMs in utilising lights angular momentum as a tool for creating rotational torque is discussed in chapter 4. In chapter 5 describes how SLMs can be used to create torques based the application of spin angular momentum to birefringent particles. We show, in chapter 6 how with suitable software engineering it is possible to both move optical traps and track particles in real time. Since the use of SLMs has been previously been limited by their bandwidth constraints we discuss in chapter 7 the use spatial light modulators in closed loop systems. We finish with a discussion of the use of SLMs in a new technique that may be applied to microrheology

Aerospace Medicine and Biology. A continuing bibliography with indexes (supplement 225)

This bibliography lists 140 reports, articles, and other documents introduced into the NASA scientific and technical information system in October 1981