A model predictive convex programming (MPCP) on SE (3) parametrized by trigonometric series control is proposed in this paper, to solve the optimal control problem of spacecraft attitude orbit integration. Firstly, the geometric modeling of the spacecraft with six degrees of freedom for the attitude orbit integration is performed by the differential manifold SE (3), which can effectively avoid the problems of ambiguity, receding winding, and singularity that occurs in the conventional methods for rigid body attitude description. Then, based on differential geometric theories, such as the variational principle, the left-invariant principle of Lie group, and the topology of Lie algebraic space, MPCP is applied to SE (3). It can solve a class of optimization problems with process constraints and control input constraints during spacecraft flight. Furthermore, a control framework of trigonometric series is constructed, which is seamlessly integrated into MPCP to achieve smoother trajectory optimization control. Finally, the practicality and effectiveness of the proposed method are verified by numerical simulation.

A linear time-varying model predictive control (LTV-MPC) method based on SE (3) is proposed, to solve the problem of the control accuracy and energy consumption of spacecraft. First, left-invariant principle of Lie group, Lie algebra SO (3), and other differential geometry theories are applied to extend LTV-MPC to SE (3). Then, considering the obstacle avoidance problem of the spacecraft in space, a suitable optimization function is selected to ensure smooth tracking of the desired working trajectory. By controlling the incremental output with the fastest convergence rate, the controller enables effective trajectory tracking. Finally, the effectiveness and applicability of the controller are verified by simulation experiments. These simulations validate the controller’s ability to achieve constraint satisfaction, optimize transient processes, and enhance control accuracy. The results provide compelling evidence of the controller’s potential for real-world spacecraft control applications.

In-depth research on the rehabilitation mechanism and motion characteristics of a rehabilitation training robot based on 4-UPUS parallel mechanism. The overall design and the working principle of each key component are explained, and the robot rehabilitation scheme is described. The static analysis and modal analysis of the robot bearing structure are carried out to verify whether the static mechanical characteristics of the mechanism meet the application requirements under working conditions.A simplified mathematical model of the six-bar linkage mechanism is established, and the kinematics of the mechanism is solved by the geometric analysis method. The motion characteristic diagram of each key point is obtained through simulation calculation. Establish the motion model of the parallel mechanism, and discuss the working space and motion performance analysis of the mechanism. The forward solution analysis of the mechanism position is carried out by using the numerical analysis method, and the three-dimensional graphics of the attitude angle and linear displacement of the reachable working space are obtained.Taking the UPUS single branch chain as the analysis object, the single open chain analysis method is used to solve the kinematics image of the corresponding surface in the working space of the mechanism, which verifies the correctness of the kinematics theoretical solution and the feasibility of simulation.The research results show that the 4-UPUS parallel mechanism rehabilitation training robot can cooperate with the ankle joint for rehabilitation training. It makes up for the single movement of the current lower limb rehabilitation robot and the unsatisfactory rehabilitation effect, and provides a reference for the practical application of the subsequent ankle joint rehabilitation robot system.

In the complex process of assembling biomass heating systems, traditional paper documents and construction process card management methods have weak information correlation and take a long time for information retrieval, which seriously restricts the assembly efficiency and quality. Moreover, the assembly process involves numerous components and complex processes, making it difficult for traditional management methods to cope with. To address this issue, a knowledge graph-based assembly information integration method is proposed to integrate scattered assembly information into a graph database, providing pathways for accessing assembly information and assisting on-site management. The biomass heating system assembly knowledge graph (BAKG) adopts the top-down method construction. After the construction of the upper schema layer, the 3DXML file was parsed, the XML.dom parser in Python3.7.16 was used to extract the equipment structure information, and the RoBERTa-BiLSTM-CRF model was applied to the named entity recognition of the assembly document, which improved the accuracy of entity recognition. The experimental results show that the F1 score of the RoBERTa-BiLSTM-CRF model in entity recognition during the assembly process reaches 92.19%, which is 3.1% higher than that of the traditional BERT-BiLSTM-CRF model. Moreover, the knowledge graph structure generated by the equipment structure data based on 3DXML file is similar to the equipment structure tree, but is more clear and intuitive. Finally, taking the second-phase construction process records of a company as an example, BAKG was constructed and assembly information was stored in the Neo4j graph database in the form of graphs, which verified the effectiveness of the method.