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This paper addresses the relative position and attitude tracking control in the framework of geometric mechanics for autonomous rendezvous and docking of two spacecraft where the relative motion of the leader and follower spacecraft tracks a desired time-varying trajectory. Using exponential coordinates on the Lie group SE ( 3 ) , which is the set of positions and orientations in three-dimensional Euclidean space, and the adjoint operator on the Lie algebra se ( 3 ) , the relative coupled translational and rotational dynamics is modeled. Based on the terminal sliding mode, a robust adaptive terminal sliding mode control scheme on SE ( 3 ) is proposed to ensure the finite-time convergence of the relative motion tracking errors using limited control inputs despite the presence of unknown disturbances and moment of inertia uncertainty. The control scheme is then applied to a situation where the follower spacecraft synchronizes its attitude motion with the leader, while maintaining a constant relative position with respect to the leader. The robustness of the controller is established using Lyapunov stability theory. Simulation results of close range rendezvous and docking verify that the proposed control scheme can achieve faster and more accurate tracking performance while consuming less control energy than the conventional terminal sliding mode control method.

With the continuous advancement and upgrading of human space exploration, the complexity and difficulty of space missions are increasing. Space manipulation, rendezvous and docking, and situation awareness of non cooperative targets have become important components of space missions. Relative position and attitude navigation system is an important part of space rendezvous and docking and space manipulation system. At present, the method of matching with cooperative target is mainly used for high-precision relative position and attitude measurement. This paper introduces a method of matching solid-state lidar with high-precision cooperative target for attitude determination. First, a design method of three-dimensional cooperative target is carried out, and then a mathematical model of target recognition is constructed. Three criteria for recognition and matching are proposed. In the third part of the article, the specific process of this method is introduced, and experimental verification is carried out. The experiment shows that the method can achieve the position measurement accuracy of 0.006m and the attitude measurement accuracy of 0.15 ° , and has important application value in various high-precision space missions.

This paper investigates a robust adaptive backstepping neural networks control for spacecraft rendezvous and docking with the coupled position and attitude dynamics. Backstepping technique is applied as the main control structure. The uncertainties of the relative dynamics are compensated by using radial basis function neural networks (RBFNNs). An adaptive switching controller is designed by combining a conventional adaptive neural networks controller and an extra robust controller. The conventional RBFNNs dominate in the neural active region, while the robust controller retrieves the transient outside the active region. The controllers work together not only improving the control accuracy, but also reducing real-time computing burden of the controller. Lyapunov theory is employed to prove that the states are globally uniformly ultimately bounded. Simulation example is given to illustrate the effectiveness of the proposed control strategy.

A robust nonlinear control strategy is presented for a cooperative spacecraft rendezvous and docking maneuver, where the pursuer spacecraft is subject to input saturation and actuator faults. The nonlinear coupled models for relative attitude and relative position dynamics are expressed in the pursuer body-fixed frame. A novel control strategy based on feedback linearization framework is developed, and a second-order disturbance observer is employed to estimate and compensate all uncertainties including parametric uncertainties, external disturbances, input saturation and actuator faults. It is proved that the closed-loop systems are uniformly ultimately bounded by using Lyapunov theory. Numerical simulations are given to illustrate effectiveness of the proposed control strategy.

This paper addresses the challenges of close proximity operations, such as rendezvous, docking, and fly-around maneuvers for micro/nano satellites, which require high control precision under the low power and limited computational capabilities of spacecraft. Firstly, a three-degree-of-freedom air float simulator platform is designed for ground-based experiments. Subsequently, model predictive controllers based on constraints aware of particle filtering (CAPF-NMPC) are developed for executing operations such as approach, fly-around, and docking maneuvers. The results validate the effectiveness of the experimental system, demonstrating position control accuracy less than 0.03 m and attitude control accuracy less than 3°, maintaining lower computational resource consumption. This study offers a practical solution for the onboard deployment of optimized control algorithms, highlighting significant value for further engineering applications.

Rendezvous and docking missions of small satellites are opening new scenarios to accomplish unprecedented in-obit operations. These missions impose to win the new technical challenges that enable the possibility to successfully perform complex and safety–critical manoeuvres. The disturbance forces and torques due to the hostile space environment, the uncertainties introduced by the onboard technologies and the safety constraints and reliability requirements lead to select advanced control systems. The paper proposes a control strategy based on Model Predictive Control for trajectory control and Sliding Mode Control for attitude control of the chaser in last meters before the docking. The control performances are verified in a dedicated simulation environment in which a non-linear six Degrees of Freedom and coupled dynamics, uncertainties on sensors and actuators responses are included. A set of 300 Monte Carlo Simulation with this Non-Linear system are carried out, demonstrating the capabilities of the proposed control system to achieve the final docking point with the required accuracy.

Background Manned spaceflight missions are characterized by significant operational risks, low fault tolerance, and high complexity, necessitating astronauts to achieve exceptional proficiency through training. This study employed a double-blind, randomized, placebo-controlled design to investigate the effects of transcranial direct current stimulation (tDCS) on astronauts’ acquisition of manual rendezvous and docking (RVD) skills. Additionally, electroencephalography (EEG) was utilized to analyze tDCS-induced cortical modulations during manual RVD training. Methods A total of 26 participants (tDCS group, n  = 14; sham group, n  = 12) completed the experiment. Each participant underwent eight blocks of manual RVD training, with EEG recordings throughout the training. A bilateral M1 montage (anode at C3, cathode at C4) was applied using 1.5 cm ring electrodes, with stimulation lasting 25 min over four training blocks. Learning outcomes for both groups were quantified using composite scores derived from endpoint accuracy parameters and performance metrics related to manual RVD training. Additionally, a skill retention test was administered three weeks after the completion of training. Results The tDCS group demonstrated superior performance in skill acquisition compared to the sham group. Significant group × time interactions were observed in both RVD attitude accuracy ( F  = 2.606, p  = 0.024, Cohen’s d = 0.367) and composite performance scores ( F  = 2.506, p  = 0.026, Cohen’s d = 0.646), with the tDCS group exhibiting an average performance improvement of 11% over the sham group. Furthermore, retention tests administered three weeks post-training revealed significantly higher scores in the tDCS group ( t  = 2.874, p  = 0.011, Cohen’s d = 1.189). EEG analysis indicated distinct θ band activity patterns in the right M1 region between the two groups during training [ F (1,50) = 5.910, p  = 0.025, η ² = 0.172], with the tDCS group showing characteristic neural modulation patterns that correlated with enhanced skill learning. Conclusion This study demonstrates that bilateral M1 tDCS enhances manual RVD skill acquisition in astronaut training. This technique shows promise for application in astronaut training, potentially improving the efficiency and retention of skill training for space missions.

This paper addresses the autonomous rendezvous and docking between a chaser spacecraft and a target spacecraft. An optimal control method is employed to plan the rendezvous and docking maneuver, considering various constraints, including force, velocity, field of view, and collision avoidance with a diamond-shaped obstacle. The optimal trajectories are derived using a symplectic algorithm, which ensures high accuracy and enhances computational efficiency. These trajectories serve as the reference for the maneuver. A PD-based tracking control method is proposed to enable real-time feedback control. An air-bearing experimental system, encompassing state measurement, data transmission, and processing, is established to conduct ground-based tracking experiments. Furthermore, specialized simulators for the chaser and target spacecraft, equipped with a docking mechanism, are designed. Experimental results validate both the feasibility of the reference trajectories and the effectiveness of the PD tracking control approach.

In spacecraft rendezvous and docking, traditional methods that rely on inertial navigation and sensor data face challenges due to sensor inaccuracies, noise, and a lack of multi-approach assurance. Focusing on exploring a new approach as assistance, this study marks the first application of deep learning-based image feature matching in spacecraft docking tasks, introducing the Class-Tuned Invariant Feature Transformer (CtIFT) algorithm. CtIFT incorporates an improved cross-attention mechanism and a custom-designed feature classification module. By using symmetric multi-layer cross-attention, it gradually strengthens inter-feature relationships perception. And, in the feature matcher, it employs feature classification to reduce computational load, thereby achieving high-precision matching. The model is trained on multi-source datasets to enhance its adaptability in complex environments. The method demonstrates outstanding performance across experiments on four spacecraft docking video scenes, with CtIFT being the only feasible solution compared to SIFT and eight state-of-the-art network methods: D2-Net, SuperPoint, SuperGlue, LightGlue, ALIKED, LoFTR, ASpanFormer, and TopicFM+. The number of successfully matched feature points per frame consistently reaches the hundreds, the successful rate remains 100%, and the average processing time is maintained below 0.18 s per frame, an overall performance which far exceeds other methods. The results indicate that this approach achieves strong matching accuracy and robustness in optical docking imaging, supports real-time processing, and provides new technical support for assistance of spacecraft rendezvous and docking tasks.

As interest in Moon exploration grows, and efforts to establish an orbiting outpost intensify, accurate modeling of spacecraft dynamics in cislunar space is becoming increasingly important. Contrary to satellites in Low Earth Orbit (LEO), where it takes around 5 ms to communicate back and forth with a ground station, it can take up to 2.4 s to communicate with satellites near the Moon. This delay in communication can make the difference between a successful docking and a catastrophic collision for a remotely controlled satellite. Moreover, due to the unstable nature of trajectories in cislunar space, it is necessary to design spacecraft that can autonomously make frequent maneuvers to stay on track with a reference orbit. The communication delay and unstable trajectories are exactly why autonomous navigation is critical for proximity operations and rendezvous and docking missions in cislunar space. Because spacecraft computational hardware is limited, reducing the computational complexity of navigational algorithms is both desirable and often necessary. By the introduction of a linear system approach to the deputy spacecraft motion, this research avoids the computational burden of integrating the deputy relative equations of motion. In this research, the relative CR3BP equations of motion are derived and linearized using a matrix exponential approximation. This research continues the development of the matrix exponential linearized relative circular restricted three-body problem (CR3BP) equations by applying the dynamics model to estimation and control applications. A simulation is performed to compare state estimation results obtained from using the linearized equations of motion utilizing a Kalman filter and for state estimation utilizing an unscented Kalman filter with the full nonlinear equations of motion. The linearized exponential model is shown to be sufficient for state estimation in the presence of noisy measurements for an example scenario. Additionally, a linear quadratic regulator (LQR) controller was added to optimally control a deputy spacecraft to rendezvous with a chief spacecraft in cislunar space. The contribution of this work is twofold: to provide a proof of concept that the matrix exponential solution for the linearized relative CR3BP equations can be used as the dynamics model for state estimation, as well as to simulate an optimal rendezvous maneuver in the presence of measurement noise.