Relative Motion Control Research Articles

Lyapunov-Floquet control of satellite relative motion in elliptic orbits

This paper proposes a method for continuous-thrust control of satellite formations in elliptic orbits. A previously calculated Lyapunov-Floquet transformation relates the linearized equations of relative motion for elliptic chief orbits to the Hill-Clohessy-Wiltshire equations describing circular chiefs. Using a control law based on Lyapunov-Floquet theory, a time-varying feedback gain is computed that drives a deputy satellite toward rendezvous with an elliptic chief. This control law stabilizes the relative motion across a wide range of chief eccentricities.

6-DOF integrated adaptive backstepping control for spacecraft proximity operations

Relative motion control with 6 degrees of freedom (6 DOF) is investigated for a chaser spacecraft with parametric uncertainties to approach an unknown tumbling space target. Unlike the conventional relative motion model described in the target orbital frame, the relative motion model formulated in the chaser's body-fixed frame can simplify modeling and control design for spacecraft proximity operations, while the chaser's thrust misalignment and the natural couplings between relative translation and relative rotation are considered in the 6-DOF integrated dynamics. After the coupled relative motion dynamics are modeled, a 6-DOF integrated state feedback controller is designed by combining the classical backstepping technique with a simple norm-estimation adaptive method to achieve good control performance and decrease the computational burden. The chaser's and target's unknown inertial parameters, unknown thrust misalignment, and upper bound of unknown disturbances are estimated by online adaptive laws. Ultimately, uniformly bounded convergence of the relative position and relative attitude is proved via Lyapunov analysis. The performance of the proposed controller is demonstrated through numerical simulations.

Model Predictive Control for Spacecraft Rendezvous and Docking: Strategies for Handling Constraints and Case Studies

This paper presents a strategy and case studies of spacecraft relative motion guidance and control based on the application of linear quadratic model predictive control (MPC) with dynamically reconfigurable constraints. The controller is designed to transition between the MPC guidance during a spacecraft rendezvous phase and MPC guidance during a spacecraft docking phase, with each phase having distinct requirements, constraints, and sampling rates. Obstacle avoidance is considered in the rendezvous phase, while a line-of-sight cone constraint, bandwidth constraints on the spacecraft attitude control system, and exhaust plume direction constraints are addressed during the docking phase. The MPC controller is demonstrated in simulation studies using a nonlinear model of spacecraft orbital motion. The implementation uses estimates of spacecraft states derived from relative angle and range measurements, and is robust to estimator dynamics and measurement noise.

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.

S1340103 固定砥粒加工工具による梨地面創成法の開発 : 相対速度差±10%時における表面の影響

This study is dealt with the new method to fabricate a mat-surface by using fixed abrasive tool. Mat-surface is generally fabricated by using chemical or electrical etching, or loose abrasive lapping, or shot blasting. These conventional processes require pre-masking of work-piece and relatively large scale back-up facility. At first, the mechanism to fabricate mat-surface is discussed in this paper. After discussion, paying our attention on the relative motion control between tool and work, the new method to produce mat-surface by using fixed abrasive tool is proposed. New designed fixed-abrasive-tool is utilized for various basic experiments of mat-surface fabrication, the results of the experiments clarifies that it is feasible not only to fabricate mat-surface without masking locally, but also to provide fish-scale-like surface-structure by controlling relative motion of the tool and the work-piece.

Relative Motion Control of Nano-Satellites Constellation

The article is dedicated to research of possibility of monitoring (control and measurement) of nano-satellites relative motion at the constellation to get data for mapping the gravity anomalies and solving other tasks. The model of gravity anomalies is offered. The paper considers the relevance and possible methods of satellites motion control in constellation and various models of gravity anomalies and approaches to their monitoring using small satellites.

1P2-T02 タンブリング衛星捕獲のための相対回転制御に向けた接触ダイナミクス

Space debris mitigation is a key technology for on-orbit servicing. In order for secure capture of space debris by a space robot, contact control with translational and rotational motion is necessary for detumbling and grasping the debris. This paper elaborates on collision experiments in micro-gravity and numerical simulations based on contact dynamics model. We examined contact characteristics with/without mechanical compliance, which is equipped on the space robot and needed for contact control by its robotic arms. On the basis of these analyses, we introduce theoretical contact conditions for relatively detumbling. The validity of the conditions is experimentally shown by using air-floating test beds in planar micro-gravity. The result contributes to relative motion control after contact.

HTHL Space Vehicles: Concepts and Control Problems

Integrated launch systems that include aerospace plane (ASP) and another heavy winged vehicle (plane or better Wing-in-Ground effect vehicle) as a booster are reviewed. It is shown that WIG-vehicle with a mass of 1500 ton or more is capable to carry ASP with initial mass of 500 ton and landing mass of 60-70 ton. Ekranoplane can provide ASP with the primary speed of Mach 0.5-0.65 in the required direction that allows lowering the design requirements to ASP's wing area and engines. A number of other advantages from the offered transport system are linked to possible use of WIG-vehicle at ASP landing. Heavy WIG-vehicle is unique vehicle for realizing the progressive idea of docking to descending ASP, allowing expanding opportunities of its landing. The problem of ASP horizontal landing without undercarriage by docking with other flying vehicle at the last stage of decent and the requirements to control systems for relative motion control of both vehicles are discussed. The progressive idea of joining space launch technologies with marine technologies is developed. It is especially important for countries with strongly limited areas of land territory but with easy access to the ocean.

Relative Motion Guidance, Navigation and Control for Autonomous Orbital Rendezvous

In this paper, the dynamics of the relative motion problem in a perturbed orbital environment are exploited based on Gauss’ variational equations. The relative coordinate frame (Hill frame) is studied to describe the relative motion. A linear high fidelity model is developed to describe the relative motion. This model takes into account primary gravitational and atmospheric drag perturbations. In addition, this model is used in the design of a control, guidance, and navigation 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 and velocity of the chaser vehicle with respect to the target vehicle and the chaser attitude and gyros biases. This filter uses the range and angle measurements of the target relative to the chaser from a simulated LIDAR system along with the star tracker and gyro measurements of the chaser. 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 navigations errors, trajectory dispersions, and attitude 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.

Kinematically Coupled Relative Spacecraft Motion Control Using the State-Dependent Riccati Equation Method

AbstractThis paper presents kinematically coupled relative spacecraft motion control in the close proximity of a tumbling target using the state-dependent Riccati equation method for proximity operation mission. In general, a rigid-body dynamics can be expressed as both translation and rotation about the center of mass. However, a kinematic coupling between the rotational and translational dynamics occurs when it is not expressed about the center of mass. Thus, kinematically coupled relative spacecraft motion model is derived to describe the relative motion about the selected arbitrary points on both the target and spacecraft. Then, spacecraft relative motion is represented by combining the relative translational and rotational dynamics of arbitrary points on the spacecraft. The spacecraft is required to achieve the desired position and attitude to track a tumbling spacecraft quickly in the effect of kinematic translation and rotation coupling. The state-dependent Riccati equation method is implemented to...

Modeling and Analysis of Relative Hovering Control for Spacecraft

This paper deals with the spacecraft relative hovering control problem, which is an important problem of space flight dynamics and one of the critical aspects of satellite relative motion control. Initially, the precise analytic models of the relative hovering control for an active spacecraft with respect to a target spacecraft both in circular and/or elliptical reference orbit with the influence of perturbation are established. According to the models, the maximum- and minimum-force positions for the relative hovering under a given range are determined by the well-known optimization technique of Lagrange multipliers. In view of the long-term onboard operational requirement, the formula for calculating fuel consumption in an orbital period is derived. Most important, the maximum- and minimum-fuel positions for the relative hovering under a given range are found by the same optimization technique as well. A number of useful numerical examples are provided, illustrating the validness of theoretical results. These closed-form solutions of the minimum-force and minimum-fuel positions can facilitate the practical operation of relative hovering, which could make progress in the design of future relative hovering missions.

Satellite formation flying control by mass exchange

Novel approach for formation flying relative motion control is proposed and studied. It is based on a mass exchange between satellites. A certain mass is separated from one satellite in a given direction with a given velocity. It impacts absolutely inelastically another satellite to impart a pulse. The mass exchange causes desired change in a relative motion trajectory of both satellites. The feasibility of such a control approach is shown in the paper. The Hill–Clohessy–Wiltshire equations are used for relative motion representation. The resulting trajectory equations after mass exchange are analytically derived. The control approach is applied to formation reconfiguration, drift-stop and also to relative motion trajectory maintenance under perturbation effect J2. The mass exchange approach is verified by numerical simulations.

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.

A Simple Time Domain Collocation Method to Precisely Search for the Periodic Orbits of Satellite Relative Motion

A numerical approach for obtaining periodic orbits of satellite relative motion is proposed, based on using the time domain collocation (TDC) method to search for the periodic solutions of an exactJ2nonlinear relative model. The initial conditions for periodic relative orbits of the Clohessy-Wiltshire (C-W) equations or Tschauner-Hempel (T-H) equations can be refined with this approach to generate nearly bounded orbits. With these orbits, a method based on the least-squares principle is then proposed to generate projected closed orbit (PCO), which is a reference for the relative motion control. Numerical simulations reveal that the presented TDC searching scheme is effective and simple, and the projected closed orbit is very fuel saving.

Nonlinear Robust Adaptive Control for Spacecraft Proximity Operations

The relative motion control for an uncertain chaser spacecraft to approach a tumbling space target is investigated in this paper. The nonlinear coupled dynamics for relative translational and rotational motions of the two spacecrafts are modeled. Based on the model, relative position and attitude controllers are designed by a unified nonlinear robust adaptive control method without using the target inertial parameter information. Asymptotic stability of the six degrees-of-freedom closed-loop system is proved. Theoretical results are demonstrated by a numerical simulation.

Nonlinear Adaptive Feedback Control for Spacecraft Proximity Formation Flying

Spacecraft proximity formation flying is essential for future autonomous space mission such as autonomous rendezvous and docking and assembly of space system on-orbit. In order to improve the autonomy of relative motion control between two spacecrafts and concerning the effect of perturbation by bounded uncertain disturbance, a novel nonlinear adaptive feedback controller is developed based on sliding mode control law to maintain the desired reference trajectory as precisely as possible. The simulation results demonstrate the control scheme can effectively carry out the relative motion maintenance and have better asymptotically stability.

High-precision single-input control of relative motion in spacecraft formation

A Newton-type method is proposed to improve the accuracy of control for relative motion of two satellites in close formation. We assume that the deputy satellite is equipped with a passive attitude control system that provides one-axis stabilization, and one or two orbit control thrusters are installed along the stabilized axis. Previous studies show that it is possible to construct periodic relative trajectories both in case of passive magnetic and spin stabilization. However, the accuracy of the numerically obtained control is quite low due to modeling errors caused by linearization of the equations of relative motion. Therefore, a correction procedure is required to compensate for nonlinear effects. To this end we suggest a recently developed algorithm based on the Newton method for solving nonlinear systems with geometric constraints. Being implemented, this algorithm allows decreasing the modeling error by up to ten times. The previously found control and trajectory of the linearized system are used as initial approximations.

A028 Motion Path Evaluation based on Energy Consumption of Feed Drive System in NC Machine Tool

NC machine tools generate desired shapes by relative motion control between tool and workpiece. Since several tool paths exist in machining products with NC machine tools, it is difficult to plan the suitable motion path for the machining. This study investigates the energy consumption of feed drive systems of NC machine tools during the machining operation. In this study, an evaluation method to predict the energy consumption for a given motion path patterns is proposed. The results of this study confirmed that the proposed method can evaluate the power efficiency of each motion path based on its energy consumption.

Relative Motion Control For Two-Spacecraft Electrostatic Orbit Corrections

The charged relative-motion dynamics and control of a two-craft system is investigated if one vehicle is performing a low-thrust orbit correction using inertial thrusters. The nominal motion is an along-track configuration where active electrostatic charge control is maintaining an attractive force between the two vehicles. In this study the charging is held fixed and the inertial thruster of the tugging vehicle is controlled to stabilize the relative motion to a nominal fixed separation distance. Using a candidate Lyapunov function, the relative orbit control law is shown to be asymptotically stable. Analysis of the control system gains is performed in order to achieve a desired settling time and damping ratio. The effects of uncertainties in the vehicle charges are also examined. Using numerical simulation, the performance of the proposed control system is investigated for a formation in geosynchronous earth orbit.