摘要
随着空间交会对接和编队飞行技术的发展与应用,航天器近距离相对运动成为当前航天领域的研究热点与前沿。预计今后航天器近距离相对飞行将成为空间活动的日常形式。论文以航天器近距离相对运动的轨迹规划与控制为中心,系统研究了自然周期相对轨迹设计、相对状态转移轨迹规划和相对运动控制等问题,并将其应用于航天器近距离观测和空间机器人抓捕两类典型任务。
首先,论文以二体条件下三种常见相对运动模型(C-W方程、T-H方程和几何法相对运动模型)的一阶解析解为基础,研究了自然周期相对轨迹的设计问题,建立了设计参数与相对轨迹形状大小的直观对应关系,给出了平根数空间下J2不变周期相对轨迹的设计方法。通过仿真自然周期相对轨迹的漂移,分析了不同模型的误差,给出了模型的适用度准则。
其次,针对不同的推力模式,系统研究了脉冲推力、继电型推力和连续常值小推力作用下相对状态转移的轨迹规划问题。在二脉冲机动模型基础上,针对近圆参考轨道,给出了基于导航点的多脉冲固定时间转移轨迹生成模型;研究了适用于任意偏心率轨道的基于随机优化的多脉冲自由时间转移轨迹生成策略。对继电型推力模式,利用离散化动力学模型,考虑线性化状态约束、控制约束和安全性约束,建立了线性规划或混合整数线性规划形式的轨迹规划模型。对连续常值小推力模式,推导了常值控制下的状态解析表达,应用极小值原理,分别解决了近圆参考轨道和椭圆参考轨道相对状态转移的最小时间轨迹和最小能量轨迹生成问题。仿真算例验证了以上模型与算法的有效性。
第三,研究了航天器近距离相对运动的控制策略和控制器设计问题,给出了相应的仿真结果。描述了相对运动控制的仿真框架,通过引入误差盒提出了三种控制策略。基于完全非线性相对动力学模型推导了滑模变结构反馈控制律,该控制律鲁棒性强,适用于任意偏心率参考轨道,具有偏差渐近收敛、控制参数便于调节等优点。通过引入集合理论,采用鲁棒可变时域模型预测控制和混合整数线性规划,有效解决了航天器近距离相对运动状态转移的鲁棒控制问题,可以确保鲁棒可行和鲁棒完成。
第四,针对近圆轨道目标,从动力学出发,研究了航天器近距离观测的任务轨迹设计与控制问题。通过分析C-W方程特性提出了椭圆型、振荡型、跳跃型和飞跃型四种基本的相对运动类型。考虑碰撞避免,提出了自然椭圆绕飞、自然螺旋绕飞、单脉冲“水滴”形绕飞、多脉冲圆形绕飞和多脉冲“田径场”形绕飞五种绕飞观测轨迹模式,以及自然椭圆V-bar方位观测、单脉冲受限R-bar方位观测和多脉冲受限任意方位观测三种局部观测轨迹模式,给出了相应的仿真算例。利用修正罗德里格斯参数建立了六自由度动力学模型,假设仅使用推力器控制,推导了考虑航天器形状和推力器配置的六自由度滑模控制律,有效解决了六自由度耦合推力控制问题。
最后,针对空间机器人抓捕的机动逼近问题,分别研究了三轴稳定卫星和无控旋转卫星的机动逼近策略。前者属于三自由度问题,采用直线逼近策略,给出了多脉冲直线逼近模型,提出了一种基于切向脉冲与径向连续推力组合机动的V-bar逼近策略。后者属于六自由度问题,建立了飞越逼近和同步控制逼近模型,利用自适应输出反馈控制,分别推导了轨道同步和姿态同步跟踪控制律,仿真算例验证了模型与算法的有效性。
总之,论文系统研究了航天器近距离相对运动轨迹规划与控制的理论方法、模型与算法,并针对航天器近距离观测任务和空间机器人抓捕任务进行了应用设计与分析。研究工作对航天器相对运动任务规划进行了有益探索,为进一步深入研究奠定了坚实基础。
With the development and application of space rendezvous and docking and formation flying technology, spacecraft proximity relative motion has been a key concern in space domain. In the future, spacecraft proximity operations will be routine in space activities. The paper aims at investigating trajectory planning and control for spacecraft proximity relative motion. The natural periodic relative trajectory design, relative state transition trajectory planning and relative motion control are discussed and applied in the spacecraft proximity inspection and space robot capture missions.
Firstly, under the general two-body problem, the natural periodic relative trajectory design is solved one by one for three different linearized relative motion models. As a result, the simple and obvious relations between the design parameters and the relative trajectory shape are established. Considering the notable influence of the J2 perturbation, J2 invariant relative orbits are presented in the mean orbital element space. And the choice guidelines of relative motion models are summarized by errors analysis with numerical simulations.
Secondly, the trajectory planning models and algorithms are examined in depth based on three different thrust modes named impulse thrust, Bang-Bang thrust and continuous constant low thrust. For impulse thrust mode, on the basis of the two-impulse maneuver models, a new trajectory generation strategy is put forward to solve finite-time relative state transition in circular reference orbits. Moreover, according to randomized tree-based A* network search algorithm, the constrained multi-impulse transition trajectory is fast generated and sub-optimized, which is valid for arbitrary elliptical orbits. For Bang-Bang thrust mode, the LP or MILP trajectory planning model is established and simulated by applying discrete dynamics model and a great variety of linear constraints, including state constraints, control constraints and security constraints. For continuous constant low thrust, with the derived state analytic solutions under constant control and Minimum Theory, the minimum-time maneuver and minimum-fuel maneuver is solved for relative state transition in circular and elliptical reference orbits respectively. The simulations validate the effectiveness of models and algorithms.
Thirdly, the control strategies and controller design for spacecraft relative motion are studied and the simulation results are also provided. The general simulation framework and three control strategies are presented by bringing in an error box. The robust sliding mode feedback control law, whose control parameters are easy to adjust, is derived from the fully nonlinear dynamics model and sliding mode control theory. It is valid for arbitrary elliptical orbits. And the derivations converge asymptotically. The robust control problem of spacecraft proximity relative motion, considering control constraints, state constraints, unknown bounded disturbance, control error and navigation error, is solved by set theory, mixed-integer linear programming and variable horizon model predictive control, which guarantees robust feasibility and finite-time entry of the target set.
Fourthly, for the target in a circular orbit, the trajectory design and control are investigated for spacecraft proximity inspection mission. Four elementary relative trajectories, i.e. the elliptic, oscillating, hop and overflying trajectories, are proposed by analyzing C-W equations. In consideration of collision avoidance, the flyaround inspection and local inspection missions are studied respectively. For flyaround inspection, five mission patterns, i.e. natural elliptical flyaround inspection, natural spiral flyaround inspection, single-impulse tear-drop flyaround inspection, multi-impulse circular flyaround inspection and multi-impulse gymkhana flyaround inspection, are proposed. For local inspection, three mission patterns, i.e. natural elliptical V-bar inspection, single-impulse R-bar inspection and multi-impulse arbitrary inspection are presented. For each mission pattern, the simulation is given. Moreover, a coupled 6-DOF dynamics model is derived from the fully nonlinear relative dynamics equations and attitude kinematics equations described by Modified Rodrigues Parameters. Given the size and thruster layout of the spacecraft, a globally stable sliding mode robust control law is derived to solve 6-DOF coupled thrust control problem.
Finally, for space robots capture mission, the approach process is studied respectively for three-axis control satellites and uncontrolled rotating satellites. The former belongs to 3-DOF problem and adopts the straight line approach strategy, whose general model is given. And a new strategy for V-bar approach is presented based on the combination of a tangential impulse maneuver and a constant continuous radial thrust maneuver. The latter belongs to 6-DOF problem and the models of fly-by approach and synchronization control approach are formulated. The control laws for translational and rotational synchronization are derived respectively by adaptive output feedback control. The simulations validate the effectiveness.
To sum up, by modeling and simulating, the paper systematically studies the methods, models and algorithms of trajectory planning and control for spacecraft proximity relative motion, which are applied in the trajectory design and control for the spacecraft proximity inspection and space robots capture missions. All of these provide a good foundation to further research in spacecraft relative motion mission planning.
引文
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