Safe Iterative Learning for Attitude Tracking of Rigid Bodies Under Nonconvex Constraints

This article is aimed at developing novel safe iterative learning methods to deal with the high-precision attitude tracking problems of rigid bodies subjected to both nonconvex orientation constraints and iteration-dependent uncertainties. A 'reactive exploration' strategy involving a dual-component mechanism is posed to realize safe iterative learning. The first component, named the learning mechanism, adeptly adjusts the learning intervals' lengths and learns the information about the unmodeled dynamics and external disturbances. The second component, named the safety mechanism, handles the problem of multiple nonconvex orientation constraints. The two mechanisms operate independently, avoiding any potential coupling problems between them. Moreover, thanks to constructing two energy functions based on the auxiliary error information, the orientation constraint satisfaction and perfect tracking can be rigorously verified, regardless of the iteration-dependent learning intervals and the absence of the persistent full-learning assumption. In particular, the nonconvex orientation constraints can be time-iteration-dependent. Two simulation tests are provided to validate the effectiveness of the proposed safe iterative learning method for rigid spacecraft in a Sun-synchronous orbit. Note to Practitioners - Attitude tracking of rigid spacecraft or unmanned aerial/surface vehicles generally requires both safe operation and high precision for some specific periodical tasks, such as the repetitive sensing mission of satellites equipped with star sensors which are prevented from pointing to some undesired directions. With iterative learning control (ILC), it becomes possible to extract the useful information from previous operations and achieve perfect attitude tracking. However, conventional ILC is difficult to apply to the repetitive attitude tracking tasks when nonconvex orientation constraints exist. This work provides new insights into the 'repetitive property,' leading to the development of safe ILC based on the 'reactive exploration' strategy. This strategy resolves the coupling issue between the learning mechanism and the safety mechanism, which simplifies the controller design for practitioners. Moreover, perfect attitude tracking can be achieved despite the presence of time-iteration-dependent nonconvex constraints and iteration-dependent learning intervals. A novel composite energy function-based analytical method and numerical simulations are introduced to demonstrate the effectiveness of the proposed safe ILC method.