The Research On The Calculation Method Of Four-axis Gimbal Frame Angles Based On Constrained Optimization Theory

At present, three-axis gimbal flight motion simulator is generally applied to emulate the attitude of the flight in hardware-in-the-loop simulation system of aircraft motion. However,considering the limitation of mechanical structure of three-axis turntable, it cannot simulate some attitude conditions because of unavoidable kinematic singularity, which restricts the test ability of the simulating environment. This project, on the background of vertical-launched cruise missile, introduces a kind of four-axis gimbal flight motion simulator(four-axis turntable for short), which can avoid the kinematic singularity and accurately simulate missile’s attitude taking advantage of redundant system’s peculiarity. Taking four-axis gimbal as research object, the paper mainly discusses the following content:First of all, some common frame of reference and the transform of them are introduced, and define the missile attitude angle and the attitude matrix. Around the center of mass of the missile motion equation is deduced, the kinematic singularity is discussed. Propose the basic principle for simulating missile’s attitude motion of horizontal and vertical three-axis turntable and analyze kinematic singularity, and point out the limitation of the three-axis gimbal to simulate the whole flying trajectory attitude motion of vertical-launched cruise missile.Secondly, considering the unavoidable kinematic singularity of three-axis gimbal set, we propose the four-axis gimbal set model to solve the problem, and establish the gimbal coordinate system and the load coordinate system and derive the differential equations of the velocity of the four gimbals around the center and discuss the basic principle of the whole ballistic attitude motion of the four-axis turntable. Through theoretical analysis, it is proved that the four-axis turntable can simulate the attitude motion of the whole trajectory and the large angle maneuver condition as avoiding the singularity.Once again, four-axis turntable frame angle solution method based on the constrained optimization theory is proposed. Giving three attitude angles and attitude angle velocities, four gimbal angles can be solved by this method, driving the rotation of the four gimbals to creating movement of the load, and reproduce the attitude motion to be simulated.. The feasibility and correctness of this method are verified by MATLAB simulation.Finally, the algorithm is designed and realized by C program language, and then the algorithm program is embedded into the program of four-axis turntable. Through the experiment, the actual project feasibility of this solution method is verified.