Trajectory Planning And Control For Spacecraft Proximity Relative Motion

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.