Abstract
The spacecraft attitude control problem has long been a research topic of considerable attraction due to its wide application in on-orbit communication and observation missions. A fundamental objective in solving this problem is to direct the onboard payload such as photoelectric sensors and antenna along a desired direction. Such a goal can be achieved by stabilizing a three-axis attitude (full attitude) or reduced attitude system. However, this type of maneuvering usually encounters complex pointing constraints during its motion. For example, some equipped sensitive payloads such as optoelectronic sensors are required to avoid direct exposure to external celestial objects or bright sources of energy. Therefore, achieving the desired attitude while avoiding pointing toward the forbidden orientations is of paramount importance. The topology of the configuration manifold for attitude (both full and reduced attitude) systems of rigid spacecraft is fundamentally challenging from a control perspective. This is because the attitude dynamics evolves on the compact Riemannian manifold that does not admit a globally continuous feedback control law. Such problems become even more challenging in the case of pointing constraints as removing the pointing constraints from the compact Riemannian manifolds results in a non-convex region. Most existing works utilize navigation function- and optimal control-based methods to handle conventional motion-constrained control problems. However, on the one hand, the exact form of the navigation functions on the Riemannian manifold is yet to be explored. On the other hand, the non-linearity of the attitude dynamics and the nonconvexity of pointing constraints make it difficult to solve the optimal control problem.This thesis aims to develop constrained attitude control strategies for rigid spacecraft attitude systems under some forms of practical constraints. Both motion-constrai-ned control problems in reduced and full attitude systems are considered. The main results of this thesis consist of two parts. The first part addresses the constrained reduced attitude control problem with parameter uncertainties. The main results of this part are summarized as follows.
The reduced attitude control problem for rigid spacecraft subject to both parameter uncertainties and elliptical pointing constraints is considered. A novel diffeomorphic projection is proposed to map the constraints from 2-sphere to elliptical 2-sphere while preserving the pointing direction. Then, the constrained reduced attitude control problem is transformed into a conventional obstacle avoidance problem on the 2-dimensional (2-D) Euclidean space via the elliptical stereographic projection. Benefiting from properties of the diffeomorphism and Kodischek-Rimon navigation functions, a sufficient condition to exclude local minima is obtained. A constrained adaptive reduced attitude controller is further developed and it is shown that almost asymptotical stability of the resulting closed-loop system can be ensured in the sense of a measure zero set.
The second part of this thesis addresses the constrained full attitude control problems of rigid spacecraft while some important practical issues are considered, including input saturation and fuel optimization. The main results of this part are summarized as follows.
1) A novel scalar map on 3-sphere with boundary Hopf fibration is constructed, which is proved to be a valid navigation function under mild conditions. Moreover, it is shown that the gradient of the proposed navigation function can be utilized to solve the constrained attitude control problem of rigid spacecraft.
2) The full attitude control problem for rigid spacecraft with input saturation and pointing constraints is considered. A novel vector field on 3-sphere with boundary Hopf fibration is exploited in the controller design to improved the convergence performance of the navigation function. Benefiting from the bounded property of the gradient of the proposed navigation function, the control capability under any given control limit can be estimated and adjusted by changing feedback gains. The almost asymptotical stability of the closed-loop system is proved by using the Lyapunov and the dual Lyapunov theorems.
3) The fuel-optimal attitude control problem for rigid spacecraft with input and pointing constraints is considered. The relaxation/convexification of control constraints is proposed that is proven to be losslessÍž i.e., the relaxed optimal control problem is equivalent to the original one. By discretization and successive linearization, the relaxed optimal control problem is transformed to a sequence of second order cone programming (SOCP) subproblems. The convergence of the algorithm is proved based on the recursive feasibility of the sequential SOCP.
| Date of Award | 6 Nov 2023 |
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| Original language | English |
| Awarding Institution |
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| Supervisor | Qinglei HU (External Supervisor), Gang Gary FENG (Supervisor) & Lu LIU (Co-supervisor) |