| 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. |
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