摘要
旋转双棱镜用于目标跟踪时,在其观测场中心区存在控制奇异性问题。当系统出射光束或视轴跟踪目标至系统旋转轴附近时,要求棱镜高速大角度旋转,这为棱镜驱动控制带来挑战。本文基于两步法解算的反向解析解,计算了棱镜转速与光束转向率之比;分别分析了连续时间域及离散时间域下,系统跟踪观测场中心区目标时控制奇异性问题的特点及根源;揭示了最优解跟踪方法缓解奇异性控制问题的原理依据;估算了中心区目标跟踪对棱镜旋转驱动控制的要求以及中心区跟踪盲区的角度范围。结果表明:中心区目标跟踪的奇异性问题源自于目标切向移动导致的目标方位角大幅度改变。目标越靠近观察区中心,控制奇异性问题越突出。最优解跟踪方法能缓解跨中心点运动目标方位角跃变带来的棱镜旋转驱动控制困难,但跟踪中心点附近一定角度范围内的目标仍要求较强的棱镜驱动控制能力。对于确定的旋转双棱镜系统和跟踪应用,观测场中心区存在一定角度范围的跟踪盲区。本文提出的分析方法和结果能为棱镜驱动控制方案设计以及系统跟踪性能评估提供评判依据。
Objective Risley prisms encounter a control singularity in the center region of the field of regard(FOR) during target tracking.When the emerging beam or the line of sight(LOS) of the system tracks a target near the system rotation axis,the prisms need to rotate at an extremely high speed and even make an instantaneous 180° flip.Due to the limited maximum speeds of driving motors,the control singularity problem challenges the drive and control of the prisms when tracking a continuous and smooth path close to or passing through the system rotation axis,restricting the system,s real-time target tracking capability.Although three-element Risley prisms can eliminate these singularities,adding a third prism not only enlarges the size and increases the cost but also demands complex control algorithms.To maintain simplicity,two prisms seem a reasonable choice.However,to relieve control difficulties,it is beneficial to discuss the characteristics and sources of the control singularity problem,which can assist in guiding the control system design and exploring solutions to the singularity problem.In our current study,based on our previous research on the nonlinearity problem in Risley-prism-based target tracking,we aim to analyze the inverse solutions of prism orientations for targets in the center region of the FOR.Then,the characteristics and root causes of the control singularity problem are disclosed in continuous and discrete time domains.Moreover,the internal mechanism and implementation effect of the optimal-solution method for resolving the singularity problem are further investigated.Methods Focusing on the center of the FOR,the inverse solutions of prism orientations are obtained using the two-step method,and their singularities are then analyzed.For the targets passing through the center or moving near the center [Fig.2(a)],the ratios of the rotational speed of the prisms to the slewing rate of the beams,denoted as the M values,are calculated in continuous time domains.By analyzing the M value,the origin of the singularity is uncovered,and the performance characteristics of the singularity are discussed.For target tracking in the discrete time domain(Fig.3),the required rotation angles of the prisms for tracking the target from one point to other points in the center zone are calculated(Fig.4) and the average M values are derived(Fig.5).Based on these results,the characteristics and root causes of the singularity in discrete time domains are studied(Figs.6 and 7).The principle basis is revealed to explain why the optimalsolution method can mitigate the control singularity problem.The requirements of target tracking for driving and controlling prism rotation and the angular region of tracking blind zone in the center region are estimated(Figs.6 and 8).Results and Discussions For the center of the FOR,the singularity of the inverse solutions of prism orientations results from the uncertainty of the azimuth angle.For the targets moving near the center [Fig.2(a)],the tangential movement leads to large variation in azimuth,yielding the maximum M value,denoted as Mm [Fig.2(b)].As the altitude angle approaches zero,Mm increases sharply and becomes infinite [Fig.2(c)].For the targets passing through the center,the optimal-solution method can solve the singularity problem.In the discrete time domain(Fig.3),if the same set of solutions is used to track a target when the target moves from one side of the center to the other side,the average M value increases significantly(Fig.5).This singularity problem can be alleviated by switching the solutions,that is,adopting the optimalsolution method(Fig.6).However,a strong control ability to drive prism rotation is still necessary for tracking the target within a certain angle range near the center.For a given rotational double prism system and tracking application,a tracking blind zone with a certain angle range exists in the center region of the FOR(Fig.8).Conclusions Based on the inverse solutions of prism orientations obtained using the two-step method,the ratios of the rotational speed of the prisms to the slewing rate for the beams are calculated.The characteristics and root causes of the control singularity problem are analyzed when the system tracks a target in the center region of the FOR in continuous-time and discrete-time domains respectively.It is discovered that for target tracking in the center region,the control singularity problem stems from the large variation in target azimuth,caused by the tangential movement of the target.The closer the target is to the center of the FOR,the more prominent the control singularity problem is.The optimal-solution method can relieve the control difficulties of prism rotation resulting from the azimuth jump of the target crossing the center.There is still a tracking blind zone in the center region of the FOR,and its angle range is determined by the driving and control ability of the system to prism rotation and the target tracking requirements.The proposed analysis methods and results can provide a foundation for the design of the prism drive control scheme and the evaluation of the system tracking performance.
作者
周远
陈英
孙利平
邹子星
邹莹畅
陈喜桥
范世珣
范大鹏
Zhou Yuan;Chen Ying;Sun Liping;Zou Zixin;Zou Yingchang;Chen Xiqiao;Fan Shixun;Fan Dapeng(College of Electronic Communication and Electrical Engineering,Changsha University,Changsha 410022,Hunan,China;College of Intelligence Science and Technology,National University of Defense Technology,Changsha 410073,Hunan,China)
出处
《光学学报》
北大核心
2025年第3期125-135,共11页
Acta Optica Sinica
基金
国家自然科学基金(52402171,62101073,62301084)
长沙市技术创新中心平台项目(2024-170)。
关键词
光学设备
旋转双棱镜
目标跟踪
奇异性问题
两步法
反向解析解
optical device
rotational double prism
target tracking
singularity problem
two-step method
analytic inverse solution
作者简介
通信作者:陈英,yingchenccsu@163.com。
