【作者】 张鹏；

【导师】 李元春；

【作者基本信息】 吉林大学 ， 控制理论与控制工程， 2016， 博士

【摘要】 小天体是太阳系内环绕太阳运动,但体积和质量远小于行星的岩石或金属天体。探测小天体有助于防御近地小天体撞击、了解太阳系和生命的起源、开发太空资源、试验新型技术等研究,具有十分重要的科学价值和现实意义。小天体探测器所需的导航、制导和控制(GNC)技术与传统大天体的探测器有很大区别。由于目标天体距离地球遥远,基于深空网的传统GNC技术难以为小天体探测器提供足够的支持和保障。由于小天体引力场弱且不规则,在其附近的探测器运动呈现出显著的非线性特征,还会受到太阳光压、其他天体引力等外界扰动的影响。此外,小天体的形状、质量、密度、自转状态等物理参数难以通过地面观测精确测定,导致探测器的动力学模型存在较大的不确定性。上述特性对小天体探测器的GNC技术提出了自主性、最优性和鲁棒性的要求。本文在973项目“行星表面精确着陆导航与制导控制问题研究”的支持下,采用直接法和间接法优化算法、神经网络技术、滑模控制算法等研究了探测器软着陆小天体的最优轨迹设计方法、自主最优制导方法、鲁棒轨迹追踪控制方法和探测器主动盘旋Tumbling小天体的轨道、姿态控制方法。论文的主要内容如下:首先,针对探测器软着陆小天体的最优轨迹设计问题,分别采用基于伪谱法与序列二次规划(SQP)的直接法优化算法、基于同伦法与初值猜测技术的间接法优化算法进行了研究。建立了着陆轨迹优化问题的数学描述,采用伪谱法将其离散化为一类参数优化的非线性规划问题(NLP),应用SQP求解该NLP得到了软着陆的能量最优轨迹。所设计的着陆轨迹在满足两端约束的同时,相比传统多项式轨迹燃耗较少。基于极大值原理将着陆轨迹优化问题转化为一个两点边值问题(TPBVP),采用打靶法对该TPBVP进行了求解;针对求解燃料最优轨迹的初值敏感困难,采用同伦法扩大打靶方程的收敛域,并应用初值猜测技术确保同伦法的成功初始化,从而获得了满足两端约束的燃料最优着陆轨迹,进一步节省了燃料。然后,基于神经网络技术对探测器软着陆小天体的自主最优制导方法进行了研究。在间接法优化算法的基础上提出了一类自主最优制导方法:通过采用广义径向基神经网络(GRBFNN)逼近探测器初始状态到最优协态变量初值的映射,避免了打靶方程求解过程带来的巨大计算量,提高了优化算法的实时性,从而实现了最优着陆轨迹的在线设计。通过仿真分析发现,增加GRBFNN的神经元数量和训练样本的规模能有效提高该方法制导下的探测器着陆精度。基于双向极限学习机(B-ELM)改进了所提出的自主最优制导方法,在获得足够着陆精度的同时大幅减少神经网络的训练时间和隐层神经元数量,降低了该方法离线训练和在线应用的计算成本。随后,考虑小天体引力场模型不确定性和外界扰动的影响,基于滑模控制算法对探测器软着陆小天体轨迹追踪的鲁棒控制方法进行了研究。假设控制推力不可调,构建一类滑模双阈值触发器设计了探测器轨迹追踪的常推力控制方法,确保追踪误差一致有界;通过在软着陆不同阶段切换阈值参数,保证了着陆精度,同时有效降低了控制推力的抖振频率。假设控制推力可调,针对传统滑模控制的抖振问题,基于自适应超螺旋算法设计了探测器的轨迹追踪控制方法;该方法保持了精度高、鲁棒性强、结构简单、收敛速度快等优点,不需要扰动和不确定性的任何信息;同时采用连续补偿项保证控制器的鲁棒性,有效抑制了控制信号的抖振。最后,对Tumbling小天体附近探测器主动盘旋的轨道/姿态控制方法进行了研究。考虑小天体自转和引力场模型的不确定性、其他天体引力和太阳光压等外界扰动的影响,建立了探测器的轨道动力学模型;基于自适应反馈线性化提出了探测器轨道的鲁棒LQR控制方法,确保了主动盘旋的稳定性;采用滑模制导来规划过渡过程,避免了初始误差造成的执行器饱和问题。考虑多种不确定性(包括小天体自转、引力场、探测器转动惯量)和外界扰动的影响,基于误差四元数建立了探测器的姿态动力学模型;基于非奇异终端滑模和自适应超螺旋算法提出了探测器姿态的连续有限时间控制方法;该方法可保证探测器盘旋姿态的有限时间稳定性,无需不确定性和外界扰动的任何信息,非奇异且无抖振,与传统滑模控制方法相比收敛速度更快。更多还原

【Abstract】 Small body is the rock and metal celestial body which is much smaller than planets and orbits the sun in the solar system. The exploration of small bodies promotes the earth defense, the understanding of the origin of the solar system and life, the utilization of space resource and novel technologies, it has significant scientific and practical values. The technical requirements of small body probe’s navigation, guidance and control(GNC) system are different from the planet probe’s. Far away from the earth, the small body probe cannot be supported enough by the GNC from the Deep Space Network. The irregular gravity of small bodies and the external disturbances, such as the solar radiation pressure and the gravity of other celestial bodies, make the motion of small body probe significant nonlinear. Since the parameters of small body are hardly determined on earth, such as shape, quality, density and spin state, the dynamic model of small body probe has large uncertainties. Due to the above characteristics, the autonomy, optimality and robustness of small body probe’s GNC system become very important.Supporting by the 973 program ‘Research on navigation, guidance and control for spacecraft precise landing on the surface of the planet’, the thesis investigates the optimal trajectory design, autonomous optimal guidance, robust trajectory track control for soft landing on small bodies, and the orbital/attitude control for hovering tumbling small bodies. These works are carried out based on the trajectory optimization algorithms, the neural network technologies and the sliding mode control scheme. The main contents of the thesis are as follows:Firstly, the optimal trajectory of probe soft landing on small bodies is investigated, with the application of the direct optimization, which is based on the pseudo-spectral method and the sequential quadratic programming(SQP), and the indirect optimization, which is based on the homotopic approach and the initial variable guess, respectively. The mathematical description of the optimal landing problem is established. The pseudo-spectral method is applied to disperse the optimization problem into a nonlinear programming(NLP), and then an SQP method is adopted to solve the NLP and obtain the energy-optimal trajectory. The designed trajectory meets the constraints at each end of the soft landing and consumes less fuel than the traditional polynomial trajectory. The optimization problem of soft landing trajectory is converted to a two-point boundary value problem(TPBVP) by the Pontryagin Principle, and then solved by the shooting method. In order to mitigate the initial sensitive problem, a homotopic approach is employed to expand the convergence domain of relative shooting equations. A guess technology is used to generate reasonable iterative initial values and ensures the solution of shooting equations. By doing this, the fuel-optimal trajectory, which meets the constraints of the soft landing and consumes less fuel than the energy-optimal trajectory, can be obtained.Secondly, the autonomous optimal guidance for soft landing on small bodies is investigated based on the neural network technologies. An autonomous optimal guidance scheme is proposed on the basis of the structure of indirect optimization. A generalized radial basis function neural network(GRBFNN) is used to achieve the map between the initial states of probe and the optimal initial co-states which determine the soft landing trajectory. By doing so, the guidance scheme does not need to solve the relative shoot equations, and reduces its computational complexity to design the optimal soft landing trajectory online. Through the simulations and analysis, it is found that the accuracy of the guidance improves with the increasing of GRBFNN’s nodes and training samples. A novel learning algorithm, which is so-called bidirectional extreme learning machine(B-ELM), is employed to obtain a low-cost autonomous optimal guidance scheme. The B-ELM trained neural network can get sufficient precision of soft landing with less network node and shorter training time, which leads to a lower cost of the online application and offline training.Then, considering the effect of the uncertainty of gravity field model and external disturbances, the robust tracking control scheme of probe soft landing on small bodies is investigated based on the sliding mode control algorithm. Assuming that the control thrust is constant, a double threshold trigger based sliding mode algorithm is proposed and the tracking control scheme is designed, which guarantees the tracking error of soft landing uniformly bounded. By changing the trigger threshold in different stages of soft landing, the proposed control scheme ensures the landing precision and reduces the switching frequency of thrust. Assuming that the control thrust is variable, a robust tracking control scheme based on the adaptive gain super-twisting algorithm is proposed to mitigate the chattering problem of traditional sliding mode control. The proposed scheme retains the advantages of conventional sliding mode control, which including the high precision, strong robustness, simple structure and quick convergence. Also, it does not require any knowledge on the uncertainties and disturbances. A continuous compensation term is applied to ensure the robustness of proposed scheme, which effectively alleviates the control output chattering.Finally, the orbit and attitude control schemes are investigated for probe hovering tumbling small bodies, respectively. The orbital motion of the probe near a tumbling small body is modelled with the uncertainties of small body’s rotation and gravitational field. The effects of external disturbances, such as the solar radiation pressure and the gravity of other celestial bodies, are also considered. A robust LQR control scheme based on the adaptive feedback linearization is proposed, which ensures the stabilization of probe hovering. A sliding mode guidance is employed to generate the transition process trajectory. By doing so, the actuator saturation problem, which is caused by initial error, is mitigated. Based on the error quaternion, the probe attitude dynamics is modeled with multi-uncertainties, which includes the rotation perturbation and the gravity moment of the small body, and the probe’s inertial perturbation. A continuous control scheme, which is based on the non-singular terminal sliding mode and a novel adaptive super-twisting algorithm, is proposed to ensure the finite-time convergence of probe’s attitude error. The proposed scheme does not require any knowledge on the uncertainties, and it is anti-chattering and anti-singularity. Moreover, it makes the attitude error converge to zero at a faster rate than traditional sliding mode control.更多还原