Satellite clusters, as a distributed spacecraft system architecture, exhibit considerable application potential in domains such as space-based synthetic aperture radar interferometry, sparse aperture optical imaging, Earth remote sensing, astronomical observation, and deep space exploration, owing to their collaborative and distributed characteristics. The safe, efficient, and energy-conserving motion paths are generated by trajectory planning methods from the current position to the target position for each satellite in the cluster. It serves as a crucial link for converting configuration control objectives into actual spatial movement and a prerequisite for the execution of in-orbit missions by satellite clusters. The trajectory planning problem for satellite clusters is a non-deterministic polynomial-time problem that is challenging to tackle directly. It encounters several challenges, including computational efficiency, trajectory optimality, constraint handling, and initial sensitivity. Consequently, investigating the trajectory planning issue of satellite clusters possesses both theoretical research value and practical engineering significance.

Based on the quantity of satellite clusters, the conceptions and projects for satellite clusters are delineated in two classifications: small to medium-sized clusters and large-scale clusters. Small and medium-sized projects, exemplified by distributed clusters and contact clusters, have emerged as the primary drivers of technical verification, whereas most large-scale cluster projects remain in the conceptual research phase, with their application potential being profoundly transformative. The primary challenges encountered by satellite clusters include high-precision relative state maintenance, inter-satellite communication, and autonomous collaborative control.

Trajectory planning approaches can be categorized into Euclidean space and manifold space based on various definitions of coordinate systems. The trajectory planning method for satellite clusters in Euclidean space involves the computational approach and strategy for designing the optimal or feasible motion paths for satellite clusters that comply with specific constraints within three-dimensional Euclidean space. Generally, it can be categorized into two types: direct method and indirect method. The direct method can be subdivided into the shooting method, collocation method, convex optimization, parameterized approximation method, graph search method, intelligent optimization algorithm, random sampling method, and so on. To address the issues of singularity and suboptimal solutions arising from the disregard of the non-Euclidean geometric and topological properties of the system's configuration space within Euclidean space, more research has focused on trajectory planning methods in manifold space. The methods in manifold space can be categorized into four elements according to the principles: Lie group-based method, vector field-based method, sampling-based method, and invariant manifold-based method. Considering the current research status both domestically and internationally, an overview of the fundamental concepts, benefits, and drawbacks of diverse methodologies is provided. The existing methods primarily encounter the challenges of matching constraint scale and processing capacity and achieving both solution accuracy and computational efficiency.

The rapid advancement of artificial intelligence technology has promoted the development of new trajectory planning paradigms for satellite clusters. Researchers have combined deep learning with conventional optimization methods to improve the solving speed while ensuring computation accuracy. Moreover, reinforcement learning has demonstrated significant robustness in addressing multi-agent trajectory planning problems. The principles and challenges are examined from three perspectives: centralized learning, decentralized learning, and centralized training with decentralized execution. The existing methodologies mostly encounter difficulties of requiring plenty of training datasets for deep learning and long training duration for reinforcement learning. The surge in large language model technology research has promoted innovation in orbit control technologies for satellite clusters.

The design methodology for satellite cluster trajectory planning algorithms is transitioning from conventional Euclidean space to manifold space and from classic optimization theory to intelligent fusion approaches. In the future, it will facilitate the profound integration of conventional optimization techniques with machine learning, artificial intelligence, and large language models to systematically elevate the intelligence and operational efficiency of algorithms.