Trajectory Planning And Control For Aerospace Vehicles

As the rapid development of novel aerospace vehicles like hypersonic vehicles and space robots, the requirements for the flexibility, adaptiveness and safety of operations in complex environments are enhanced, promoting the research of mission planning. Compared with other elements of a mission planning system, the trajectory planning and control function is more essential, since it directly determines how the operation performs. Due to the high-dimensional states, multiple constraints, strong nonlinearity and couplings, the trajectory planning and control for aerospace vehicles still remain challenges in both theory and application. In this paper, the trajectory planning and control methods, together with their applications in typical aerospace vehicles, are systematically studied. Based on the research on the fundamental issues, including optimal trajectory planning, online trajectory planning, uncertainty-based trajectory planning, and nonlinear robust trajectory control, a complete set of trajectory planning and control methods is established and applied to the mission design problems of spacecraft electromagnetic formation flying(EMFF) and hypersonic glide vehicles.This paper could be generally divided into two parts: theoretical research and application exploration. The theoretical research mainly focuses on the methods for trajectory planning and control from the aspects of trajectory optimality, computational efficiency, and uncertainty treatment. This part is organized as follows:Firstly, considering the requirements for optimizing the performance criteria, the associated mathematical model for optimal trajectory planning problem is formulated in the framework of optimal control theory, and then transcribed into a nonlinear programming problem by using the multi-phase Radau pseudospectral method(RPM). Concentrating on the numerical difficulties of RPM in solving the Bang-Bang type optimal control problem(OCP), an input structure detection strategy based on the costates mapping theorem and Pontryagin maximum principle is proposed. Then the system trajectories are divided into many segments according to the detection results, and the dynamical constraints on each segment are transformed into algebraic constraints via the Radau integration matrices. Numerical simulations results are presented to verify the feasibility and validity of the improved RPM.Secondly, considering the requirements of computational efficiency and accuracy, an online trajectory planning strategy based on differential flatness is proposed. By utilizing the system’s flatness, the original trajectory planning problem could be mapped into the flat output space, eliminating the differential equations and reducing the dimensionality of the planning space. Then the resulted flat output planning problem is further discretized with a mapped Chebyshev pseudospectral method, which is improved by conformal map and barycentric rational interpolation techniques in order to decrease the side effect of the differentiation matrix’s ill-conditioning on the planning accuracy. In addition, a combined optimization approach based on flatness and analytical homotopy method is studied, where an auxiliary OCP with zero costates is constructed based on the smooth flat output trajectory, eliminating the initialization difficulty and enhancing the applicability of flatness method to non-smooth trajectories.Thirdly, considering the influences of uncertainties on trajectory planning, the main uncertainties in a generic aerospace vehicle are analyzed, and a stochastic collocation based uncertainty propagation analysis approach is proposed, whose estimation accuracy and computation efficiency is validated by comparing with Monte Carlo method. Then the robustness criterion of a given trajectory is formulated, and the uncertainty-based trajectory planning problem is transcribed into a multi-objective optimization problem with a double-level nested planning framework.Fourthly, some feedback tracking control methods are investigated to compensate for the uncertainties. Considering the control energy consumed, a robust optimal tracking control law is designed with the receding-horizon control method, and a differential transformation based approach is proposed to solve the associated two-point boundary value problem in each finite horizon. Taking the convergence time of tracking errors into account, a finite-time tracking control law is designed utilizing the adaptive terminal sliding mode control(ATSMC) method.EMFF and hypersonic glide vehicle are the current hotspot in the field of aerospace, thus the aforementioned trajectory planning and control methods are applied to some typical mission modes of these two aerospace vehicles in the application exploration part.Firstly, the formation reconfiguration mission of EMFF is studied. Due to the couplings of EMFF’s dynamics, the reconfiguration trajectory for the two-satellite formation system is optimized with a combined planning framework integrating free dipole and RPM, while integrating hierarchical strategy and flatness method for the three-satellite formation. Additionally, considering the nonlinearity and uncertainty in the dynamic model, an inner-and-outer loop combined control strategy based on feedback linearization and ATSMC is proposed with finite-time convergence capability and good robust performance.Secondly, the reentry flight mission for the hypersonic glide vehicle is studied. A unified mathematical formulation for the path constraints of heating rate, dynamic pressure and load is developed in the dimensionless altitude-velocity profile, and the corresponding analytical bank angle solution is also obtained. Then the three-dimensional reentry trajectory is generated with a constant-path-constraint strategy. In addition, the nominal reentry trajectory is also planned in the state space using the differential flatness method, and a receding-horizon control approach based robust optimal tracking control law is developed with good robust performance and remarkable computational efficiency.To sum up, this paper systematically studies the trajectory planning and control methods for aerospace vehicles, and applied them to the typical missions of EMFF and hypersonic glide vehicle. Some productions on optimal trajectory planning, online trajectory planning, uncertainty-based trajectory planning, and nonlinear robust trajectory control have been found, provding a good foundation for further research.