With the increasing scale of space infrastructure such as large space telescopes, antenna arrays, and solar power stations, the payload fairing size of launch vehicles has become a critical bottleneck constraining their development. On-orbit autonomous assembly via deployable modules has emerged as an important technical approach to overcome this limitation. Deployable modules typically exhibit high packaging ratios; however, the geometric deviations caused by residual strain, assembly tolerances, and dynamic coupling effects after deployment can significantly affect docking accuracy and structural stability, and may even lead to assembly failure. Nevertheless, existing studies have mostly focused on post-deployment final configuration accuracy optimization, with insufficient attention paid to the cooperative strategies between real-time deformation control and motion control during the assembly process. Moreover, a dynamic modeling method capable of accurately describing the coupling between variable-length flexible components and rigid bodies is still lacking. Therefore, how to achieve active configuration correction and coordinated position–attitude control of deployable modules on orbit has become a key challenge in the autonomous assembly of large space structures.
In a recent study published in Space: Science & Technology, the team led by Hu Haiyan from the College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, designed a deployable assembly module consisting of three hexagonal mechanisms connected by thin-walled carbon-fiber shells, and proposed an assembly control strategy integrating deformation control and motion control. The study employs the natural coordinate method to describe rigid-body motion, and adopts the Arbitrary Lagrangian–Eulerian Absolute Nodal Coordinate Formulation (ALE-ANCF) to establish the dynamic model of variable-length thin-shell elements. By incorporating magnetic forces, thruster force allocation, and pulse constraints for topological changes, a complete set of rigid–flexible coupled multibody dynamic equations is constructed. On this basis, deformation controllers and motion controllers based on proportional–derivative (PD) control are designed to eliminate geometric deviations by adjusting the rotational speeds of motors to modify the three side lengths of the module, and to achieve synchronized planar position and attitude adjustments through cooperative pulse control of six nozzles. Numerical simulations demonstrate that the deformation controller can reduce geometric errors to below 0.013 mm. In ground-based air-floating experiments, deformation control reduces errors to below 1.5 mm; assembly experiments integrating deformation and motion control successfully achieve docking with a simulated assembly structure, whereas the absence of deformation control leads to docking failure. This research provides a solution integrating dynamic modeling and cooperative control for on-orbit autonomous assembly of deployable modules, offering significant theoretical support and engineering reference value for the on-orbit construction of large space structures.
First, this paper focuses on the core challenges of on-orbit autonomous assembly of large space structures and designs a planar deployable assembly module, along with establishing its rigid–flexible coupled dynamic model. As shown in Fig. 1, the module consists of three hexagonal mechanisms connected by thin-walled carbon-fiber shells, integrating motors, magnets, electromagnets, and thrusters, and is equipped with multiple functionalities including deployment actuation, configuration adjustment, docking guidance and latching, and planar motion control. After deployment, the module assumes a triangular configuration, with the three side lengths corresponding to the deployed lengths of the three carbon-fiber shell segments, which can be independently adjusted via motor drives to achieve variable-baseline configurations. Owing to the large overall motion and large deformation experienced by the carbon-fiber shells during deployment and deformation control, accompanied by continuous length variation over time, conventional fixed-length elements are inadequate for accurately describing their dynamic behavior. To address this, the study employs the Arbitrary Lagrangian–Eulerian Absolute Nodal Coordinate Formulation (ALE-ANCF) to establish the dynamic model of variable-length thin-shell elements, enabling accurate description of the additional inertial effects induced by material inflow and outflow, as well as geometric nonlinear deformations. Meanwhile, the natural coordinate method is adopted to describe the rigid-body motion of the hexagonal mechanisms, and the coupling between rigid bodies and flexible bodies is achieved through constraint equations. As shown in Fig. 2, this rigid–flexible coupled modeling framework also incorporates magnetic force models and thruster thrust models, with the velocity discontinuity arising from topological changes after docking handled through impulse constraints. This model provides an accurate mechanical foundation for the subsequent cooperative control of deformation and motion.
Second, this paper designs a PD control strategy integrating deformation control and motion control, achieving autonomous configuration correction and synchronized position–attitude adjustment of the module. As shown in Fig. 3, the objective of deformation control is to adjust the current triangular configuration of the module to the target triangular configuration. The system calculates the current three side lengths based on the center positions of the three hexagonal mechanisms, and compares them with the target side lengths measured from the assembly structure. The PD controller accordingly adjusts the rotational speeds of the three motors to retract or extend the three carbon-fiber shell segments, thereby accomplishing configuration correction. The geometric relationship between motor rotation angles and side-length variations provides the basis for accurate conversion of the actuation quantities. Motion control adopts a six-nozzle cooperative scheme, in which the controller computes the desired control force and torque based on the deviations between the module's current position and attitude and the target values, and then allocates the force and torque to the six nozzles through pulse-width modulation (PWM), enabling the module to achieve synchronized planar position and attitude control. Deformation control and motion control can be performed either independently or integrated in a temporal sequence: the module first performs deformation control according to the target configuration to eliminate geometric errors, then initiates motion control to approach the assembly structure, and finally completes docking and latching under magnetic guidance.
Finally, this paper systematically validates the effectiveness of the proposed control strategy through numerical simulations and ground-based air-floating experiments. Fig. 4 presents the geometric evolution process in the deformation control simulation, and Table 1 summarizes the geometric error convergence results under three sets of different target side-length conditions. The module error can be reduced to below 0.013 mm in all cases, with an accuracy improvement exceeding 99.98%, and the out-of-plane displacement and attitude variation are extremely small. Fig. 5 presents the assembly simulation results integrating deformation control and motion control, demonstrating that the module can accomplish docking regardless of whether the assembly structure is fixed or freely floating. In the ground-based air-floating experiments, Table 2 lists the error convergence results from three sets of deformation control experiments, where the geometric error is reduced to below 1.5 mm with an accuracy improvement exceeding 98%. The simulation and experimental error curves are generally consistent, with the deviations mainly attributed to friction disturbances from the air-floating platform and measurement fluctuations. Fig. 6 presents the integrated assembly experiment: the module first performs deformation control, followed by motion control initiation and successful docking. For comparison, Fig. 7 shows experimental photographs of docking failure due to excessive geometric deviation without deformation control, highlighting the necessity of deformation control. The simulations and experiments together demonstrate that the proposed control strategy can effectively eliminate the geometric errors of deployable modules, ensuring the successful completion of on-orbit autonomous assembly.
