340 research outputs found

    Underactuated Spacecraft Switching Law for Two Reaction Wheels and Constant Angular Momentum

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    Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/140660/1/1.g001680.pd

    Model Predictive Control of an Underactuated Spacecraft with Two Reaction Wheels

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    Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143105/1/1.G000320.pd

    Practical Implementation of Attitude-Control Algorithms for an Underactuated Satellite

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    The challenging problem of controlling the attitude of satellites subject to actuator failures has been the subject of increased attention in recent years. The problem of controlling the attitude of a satellite on all three axes with two reaction wheels is addressed in this paper. This system is controllable in a zero-momentum mode. Three-axis attitude stability is proven by imposing a singular quaternion feedback law to the angular velocity trajectories.Two approaches are proposed and compared to achieve three-axis control: The first one does not require angular velocity measurements and is based on the assumption of a perfect zero momentum, while the second approach consists of tracking the desired angular velocity trajectories. The full-state feedback is a nonlinear singular controller. In-orbit tests of the first approach provide an unprecedented practical proof of three-axis stability with two control torques. The angular velocity tracking approach is shown to be less efficient using the nonlinear singular controller. However, when inverse optimization theory is applied to enhance the nonlinear singular controller, the angular velocity tracking approach is shown to be the most efficient. The resulting switched inverse optimal controller allows for a significant enhancement of settling time, for a prescribed level of the integrated torque

    Advances in Underactuated Spacecraft Control

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    This dissertation addresses the control of a spacecraft which either becomes underactuated due to onboard failures or is made underactuated by design. Successfully controlling an underactuated spacecraft can extend spacecraft operational life in orbit and improve the robustness of space missions. The novel contributions of the dissertation include the following. Firstly, switching feedback controllers are developed for the attitude control of an underactuated spacecraft equipped with two pairs of thrusters, or two reaction wheels (RWs), or two control moment gyros (CMGs). The problem is challenging; e.g., even in the zero total angular momentum case, no smooth or even continuous time-invariant feedback law for stabilizing a desired orientation exists. The method exploits the separation of the system into inner-loop base variables and outer-loop fiber variables. The base variables track periodic reference trajectories, the amplitude of which is governed by parameters that are adjusted to induce an appropriate change in the fiber variables towards the desired pointing configuration. Secondly, nonlinear Model Predictive Control (MPC) is applied to the attitude dynamics of an underactuated spacecraft with two RWs and zero angular momentum. MPC has the remarkable ability to generate control laws that are discontinuous in the state. By utilizing nonlinear MPC, the obstruction to stabilizability is overcome and attitude maneuvers can be performed while enforcing constraints. Thirdly, an unconventional pathway is discussed for recovering the linear controllability of an underactuated spacecraft with two RWs by accounting for the effects of solar radiation pressure (SRP) in the spacecraft attitude model. Necessary and sufficient conditions for recovering linear controllability are given, and with linear controllability restored, conventional controllers can be designed for underactuated spacecraft. Lastly, two sets of coupled translational and rotational equations of motion for a spacecraft in a central gravity field are derived. The spacecraft is assumed to have only internal attitude actuators and the equations of motion are relative with respect to an equilibrium orbit. Under reasonable assumptions on the spacecraft configuration and equilibrium orbit, the coupled dynamics are small-time locally controllable (STLC), which opens a path to utilizing conventional control techniques to move translationally in space by employing attitude control only.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133430/1/cdpete_1.pd

    Feedback Synthesis for Controllable Underactuated Systems using Sequential Second Order Actions

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    This paper derives nonlinear feedback control synthesis for general control affine systems using second-order actions---the needle variations of optimal control---as the basis for choosing each control response to the current state. A second result of the paper is that the method provably exploits the nonlinear controllability of a system by virtue of an explicit dependence of the second-order needle variation on the Lie bracket between vector fields. As a result, each control decision necessarily decreases the objective when the system is nonlinearly controllable using first-order Lie brackets. Simulation results using a differential drive cart, an underactuated kinematic vehicle in three dimensions, and an underactuated dynamic model of an underwater vehicle demonstrate that the method finds control solutions when the first-order analysis is singular. Moreover, the simulated examples demonstrate superior convergence when compared to synthesis based on first-order needle variations. Lastly, the underactuated dynamic underwater vehicle model demonstrates the convergence even in the presence of a velocity field.Comment: 9 page

    Recovering Linear Controllability of an Underactuated Spacecraft by Exploiting Solar Radiation Pressure

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    Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/140657/1/1.G001446.pd

    Dynamics and Control of Higher-order Nonholonomic Systems

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    A theoretical framework is established for the control of higher-order nonholonomic systems, defined as systems that satisfy higher-order nonintegrable constraints. A model for such systems is developed in terms of differential-algebraic equations defined on a higher-order tangent bundle. A number of control-theoretic properties such as nonintegrability, controllability, and stabilizability are presented. Higher-order nonholonomic systems are shown to be strongly accessible and, under certain conditions, small time locally controllable at any equilibrium. There are important examples of higher-order nonholonomic systems that are asymptotically stabilizable via smooth feedback, including space vehicles with multiple slosh modes and Prismatic-Prismatic-Revolute (PPR) robots moving open liquid containers, as well as an interesting class of systems that do not admit asymptotically stabilizing continuous static or dynamic state feedback. Specific assumptions are introduced to define this class, which includes important examples of robotic systems. A discontinuous nonlinear feedback control algorithm is developed to steer any initial state to the equilibrium at the origin. The applicability of the theoretical development is illustrated through two examples: control of a planar PPR robot manipulator subject to a jerk constraint and control of a point mass moving on a constant torsion curve in a three dimensional space

    Online Estimation of Unknown Parameters for Flexible Spacecraft

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    Attitude controls methods of highly flexible spacecraft have seen increased interest over the last decades thanks to the technological development of flexible solar panels and deploy-ables, which improves the capabilities of small satellites. However, a high-fidelity model of the flexible mode dynamics is hard to obtain in on-ground testing because not all modes of frequencies can be observed, complicating the controller design. Furthermore, plastic deformations due to long periods of storage of stowed flexible components could result in exciting frequencies outside of the designed controller’s bandwidth, leading to an uncontrollable system. This thesis proposes a method to develop a high-fidelity model of a spacecraft with a flexible appendage subject to large deformations by modeling it as a finite series of rigid links connected by torsional springs and dampers. To overcome the uncertainties in the flexible dynamics, an onboard estimation through an adaptive controller is performed for these un- knowns while the spacecraft is maneuvered. The controller uses integral concurrent learning (ICL), an adaptive scheme that records inputs and outputs provided by sensors mounted on the flexible body. The novelty of this investigation is the development of self-adapting control gains for both the tracking error and the learning matrix obtained from ICL. After tuning the controller for the system’s initial conditions, it achieves the objective of tracking a desired trajectory while accurately learning the unknown physical parameters of the flexible appendage by only using the recorded measurements. It was observed that for a finer discretization of the flexible appendage and therefore a higher fidelity model of the flexible dynamics, the estimation algorithm is able to observe all the frequencies necessaries to learn the unknown mechanical properties of the flexible body
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