Spacecraft Relative Motion Control Research Articles

Spacecraft Relative Motion Control Near an Asteroid With Uncertainties: A Lyapunov Redesign Approach

Spacecraft Relative Motion Control Near an Asteroid With Uncertainties: A Lyapunov Redesign Approach

Feedback tracking control of optimal reference trajectories for spacecraft relative motion

In this paper, first the optimal trajectories are defined by a fixed end-time, continuous-thrust trajectory which minimizes a terminal cost at the end of an inter-planetary trajectory by appending the multi-body dynamic equations defining the motion by a set of Lagrange multipliers or co-states. The solution of these co-states and the optimal trajectories for a fixed end-time are obtained by solving a two-point boundary value problem along with a steering control law, which is used to provide a reference trajectory. Inspired by the general expression for the gravitation potential and the Q-law, a tracking control law is designed to track the reference trajectory. As the steering controller is not a feedback controller, a feedback tracking control law is proposed to continuously correct the spacecraft's actual relative motion trajectory so it tracks the reference relative motion trajectory. The nonlinear relative motion tracking control law is reduced to a linear feedback control law, when the spacecraft is sufficiently close to the reference relative motion trajectory. The feedback laws demonstrate the feasibility of developing practical tracking laws for continuous trajectory correction manoeuvre control of spacecraft relative motion, for implementing low-thrust inter-planetary trajectory following control in electrically propelled spacecraft, in practice.

Control of Spacecraft Relative Motion in a Tandem Flight Configuration

The article discusses the problems of controlling the relative motion of spacecraft (SC) in a tandem flight configuration. Flight configurations of two SC that form the so-called ballistically linked group and fly at a relatively small distance from each other are described. The effect of the evolution of orbital elements on the nature of the relative motion of SC in tandem is analyzed. The problems of orbit correction for maintaining the given tandem configuration are considered. Correction energy costs are estimated.

Nonlinear model predictive control of spacecraft relative motion

This investigation deals with the problem of spacecraft relative motion control, which is typically associated with the spacecraft rendezvous and proximity maneuvers. Relative position and linear velocity are considered. A distinguishing attribute of the presented approach is consideration of definitely larger relative distance between the satellites than it is commonly addressed in the literature. The presented control method is applicable in the case where the chief satellite moves in a known, highly elliptical orbit. A quasi-optimal control is found by a model predictive control algorithm, where the nonlinear optimization problem is reduced to quadratic optimization by preliminary estimation of the future control trajectory. Significance of the method has been verified using a computer simulation.

New Closed-Form Solutions for Optimal Impulsive Control of Spacecraft Relative Motion

This paper addresses energy-optimal guidance and control of satellite relative motion for formation flying and rendezvous using impulsive maneuvers. To meet the requirements of future multisatellite missions, closed-form solutions of the inverse relative dynamics are sought in arbitrary orbits. Time constraints dictated by mission operations and relevant perturbations acting on the formation are accounted for by splitting the optimal reconfiguration into guidance (long-term) and control (short-term) layers. Both problems are cast in relative orbit element space, which allows the simple inclusion of secular and long-periodic perturbations through a state-transition matrix and the translation of the energy-optimal optimization into a minimum-length path-planning problem. From the choice of state variables, both guidance and control problems can be solved in closed form, leading to optimal, predictable maneuvering schemes for simple onboard implementation. Besides generalizing previous work, this paper finds five new in-plane and out-of-plane closed-form solutions to the relative motion control problem in unperturbed eccentric and perturbed near-circular orbits. A delta-v lower bound is formulated, which provides insight into the optimality of the control solutions. Finally, the functionality and performance of the new maneuvering schemes are rigorously assessed through numerical integration of the equations of motion and systematic comparison with primer vector optimal control.

Modeling, Dynamics and Control of Spacecraft Relative Motion in a Perturbed Keplerian Orbit

The dynamics of relative motion in a perturbed orbital environment are exploited based on Gauss' and Cowell's variational equations. The inertial coordinate frame and relative coordinate frame (Hill frame) are used, and a linear high fidelity model is developed to describe the relative motion. This model takes into account the primary gravitational and atmospheric drag perturbations. Then, this model is used in the design of a navigation, guidance, and control system of a chaser vehicle to approach towards and to depart from a target vehicle in proximity operations. Relative navigation uses an extended Kalman filter based on this relative model to estimate the relative position/velocity of the chaser vehicle with respect to the target vehicle. This filter uses the range and angle measurements of the target relative to the chaser from a simulated LIDAR system. The corresponding measurement models, process noise matrix, and other filter parameters are provided. Numerical simulations are performed to assess the precision of this model with respect to the full nonlinear model. The analyses include the navigation errors and trajectory dispersions.

Safe Positively Invariant Sets for Spacecraft Obstacle Avoidance

This paper presents an obstacle avoidance method for spacecraft relative motion control. In this approach, a connectivity graph is constructed for a set of relative frame points, which form a virtual net centered around a nominal orbital position. The connectivity between points in the virtual net is determined based on the use of safe positively invariant sets for guaranteed collision free maneuvering. A graph search algorithm is then applied to find a maneuver that avoids specified obstacles and adheres to specified thrust limits. As compared to conventional open-loop trajectory optimization, this approach enables the handling of bounded disturbances, which can represent the effects of perturbing forces and model uncertainty, while rigorously guaranteeing that nonconvex and possibly time-varying obstacle avoidance constraints are satisfied. Details for handling a single stationary obstacle, multiple stationary obstacles, moving obstacles, and bounded disturbances are reported and illustrated with simulation case studies.

Adaptive tracking control of spacecraft relative motion with mass and thruster uncertainties

This study presents adaptive tracking controls of relative position between two spacecraft in the presence of uncertainties in the thrust alignments and gains, and the active spacecraft's mass. The proposed methods are based on the equations of motion expressed in the general second-order form with trajectory-controllable Hamiltonian systems, which makes it possible to use some useful physical properties in the control law design. Unlike most of the previous works, the control laws are presented not only for the Cartesian coordinates, but also for the spherical coordinates in Keplerian orbits whose dynamic equation is highly complicated but reflects the actual measurement environment (laser/microwave based) and thus is more suitable in real applications. The proposed adaptive algorithms are developed utilizing the smooth-projection algorithm in order to deal with the uncertainties in the actuator model. Numerical simulations show that the proposed adaptive scheme successfully achieves the relative position tracking within a small level of error in the whole process, compared with the non-adaptive scheme.