Relative Motion Control Research Articles

Modeling and Control of Reconfigurable Quadrotors Based on Model Reference Adaptive Control

To expand the application prospects of quadrotors in challenging scenes such as those with dense obstacles and narrow corridors, task-driven reconfigurable quadrotors are highly desirable. Aiming to address hazard missions, in this paper, translational reconfigurable quadrotors and rotational reconfigurable quadrotors are proposed with their assumptions and mathematical models. Related motion control laws were designed using model reference adaptive control (MRAC) theory based on Lyapunov stability theory, whose validity was demonstrated by sufficient numerical simulations. The simulation results verify the feasibility of the proposed control laws and reveal the important effect of time delay on the stability of the motion control system. Additionally, the dependence of motion control’s stability on the time constant of reference system was discussed.

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

Observer‐based adaptive neural networks optimal control for spacecraft proximity maneuver with state constraints

AbstractThis article proposes an adaptive neural network (NN) optimal control approach for autonomous relative motion control of non‐cooperative spacecraft in proximity. The proposed method aims to minimize fuel consumption under various challenges including model uncertainty, state constraints, external disturbances, and input saturation. To account for uncertain parameters of non‐cooperative target and external disturbances, we start by designing a NN disturbance observer. Subsequently, a novel optimal control index function is presented. An adaptive NN based on the actor‐critic (A‐C) framework and backstepping theory is then utilized to approximate the solution of Hamilton–Jacobi–Bellman (HJB) equation and obtain an optimal control law. The Lyapunov framework is leveraged to establish the stability of the closed‐loop control system. Finally, numerical simulations are conducted to assess the feasibility and effectiveness of the proposed control scheme in comparison with an existing approach.

Distributed prescribed-time coordinated control of spacecraft formation flying under input saturation

This paper studies the prescribed-time relative motion control problem of spacecraft formation flying under input saturation. Using prescribed-time theory, a prescribed-time sliding mode is designed such that the states on the sliding mode converge to the equilibrium in the prescribed time. Based on the prescribed-time sliding mode, a prescribed-time relative motion tracking controller is developed, which guarantees fast formation maneuvers with feasible fuel consumption and strong robustness under input saturation. Furthermore, a simulation example is carried out to verify the effectiveness of the proposed controller.

An approximate optimal control method for 6-DOF spacecraft

In this paper, an approximate optimal control method based on adaptive dynamic programming (ADP) is proposed for the proximity operations with six degrees of freedom (6-DOF) relative motion control of spacecraft. Firstly, the dynamic model is normalized and dimension-reduced to avoid the excessive gradient change of the neural network. Then, a nonlinear disturbance observer is designed to deal with the disturbance. Finally, using ADP ‘s reinforcement learning idea, a single-critic neural network is constructed to solve the approximate optimal control strategy and minimize the cost function. The simulation results show that the designed controller can achieve the attitude and orbit maneuvering targets, and the overall energy consumption is approximately optimal.

Task-Based Compliance Control for Bottle Screw Manipulation With a Dual-Arm Robot

In this paper, a novel task-based compliance control approach for a dual-arm robot is presented with a bottle screw task. The presented approach aims at overcoming uncertainties from the object model and contact forces during the bottle screw task. A novel framework is proposed to synthesize the task motion planning and compliance control that ensure desired performance of both accuracy and compliant motion. The proposed task-based compliance control approach provides a hierarchical strategy: gross motion planning and fine compliance motion planning. The gross motion planning involves the absolute and relative motion control on a macro scale, while the fine compliance motion planning deals with uncertainties by the compliance control to accomplish a task requiring high precision robustly. A theoretical modeling of the bottle screw task is presented within the proposed framework through the analysis of uncertainties and constraints. The experimental results show that the proposed framework is efficient and robust to operate a set of bottles.

Formation Flying Orbit and Control Concept for Virtual Super Optics Reconfigurable Swarm Mission

The Virtual Super Optics Reconfigurable Swarm (VISORS) mission is a distributed telescope consisting of two 6U CubeSats separated by 40 m that will obtain high-resolution images of active solar regions in the extreme ultraviolet spectrum. This mission is challenging because the CubeSats must autonomously control their relative motion with unprecedented accuracy while operating in close proximity. This paper presents three contributions that enable the VISORS mission to meet its challenging requirements. First, passively safe absolute and relative orbit designs for distributed telescopes that provide regular periods of alignment with inertial targets are developed using relative eccentricity/inclination vector separation. Second, a guidance, navigation, and control system design is proposed to meet the demanding relative motion control requirements. Third, a concept of operations is proposed that minimizes mission operations load when the formation is not actively performing observations. This concept of operations includes a safety plan to address on-orbit anomalies. The performance of the guidance, navigation, and control system is validated through Monte Carlo simulations including all significant error sources and operational constraints. These simulations show that the mission requirements are met with margin, providing a preliminary demonstration of the feasibility of accurate autonomous formation control with CubeSats.

Pareto-optimal control of relative motion in the orbital maneuvering problem of spacecraft with finite thrust

To solve the time-free rendezvous problem of two spacecraft, the multi-criteria optimization of the relative motion trajectory of the linear motion model in an orbiting cylindrical reference frame is studied. The equations for describing the secular and periodic parameters of the relative motion are obtained. The structure of the nominal control program for the longitudinal motion control variant with finite transversal thrust is investigated in some detail, and its analytical solutions are obtained. An algorithm for solving the Pareto-optimal control program for arbitrary boundary conditions and thrust control acceleration values in the standard time including maneuver time and total time is developed. The algorithm uses the Pareto optimal method to achieve two kinds of multi-objective optimization (total time optimization and fuel optimization). The numerical calculation results on the geostationary planar orbit parameter correction variants are given.

Rendezvous and Docking of Co-Operative Target with Dual-Axis Gimbaled Electric Thruster

This paper presents a simulation study on the viability of a dual axis gimbaled electric thruster for the relative orbital position control. Relative attitude of the spacecraft is controlled using reaction wheels (RWs). This study considers proportional derivative (PD) algorithm for orbital position control and nonlinear dynamic inversion for relative attitude control. The relative attitude dynamics is derived assuming that the target spacecraft is cooperative and is inactive, therefore, its relative attitude changes only due to its orbital motion around the central body. The dual-gimbal dynamics is approximated for control design due to coupling between gimbal rates. Numerical simulation results are presented to show the efficacy of the control algorithm as well the viability of the dual-axis gimbaled thruster for relative orbital motion control.

Relative Orbital Motion Control of Spacecraft Based on Multi-Objective Optimization

In this paper, we consider the relative motion of a follower spacecraft orbiting the Earth in a near circular orbit with respect to a leader spacecraft. The relative orbital motion-control problem of the follower spacecraft is studied here. In order to allow the follower spacecraft to succeed in its target orbital motion maneuver, we proposed a multi-objective optimization method to solve the relative orbital motion-control problem. Firstly, a Hill–Clohessy–Wiltshire equation was used to describe the continuous relative orbital motion-control system. Then, the system was discretized into a discrete system using numerical methods. Next, a multi-objective optimization model of the relative orbital motion-control problem was formulated. In the model, two objectives, i.e., the orbital motion error and the energy consumption, were minimized simultaneously. Furthermore, the ε-constraint method was used to solve the multi-objective optimization problem and the Pareto front, which demonstrates that the trade-off between the two objectives can be achieved. Finally, numerical experiments were carried out to validate the effectiveness of the proposed multi-objective optimization approach.

Spacecraft Relative Motion Dynamics and Control Using Fundamental Modal Solution Constants

This paper explores expressing the relative state in the close-proximity satellite relative motion problem in terms of fundamental modal solution constants. The nominal uncontrolled relative state can be expressed in terms of a weighted sum of fundamental and geometrically insightful modal motions. These fundamental motions are obtained using the Lyapunov–Floquet theory. In the case that the dynamics are perturbed by the action of a controller or by unmodeled dynamics, the weights on each fundamental solution are allowed to vary as in a variation-of-parameters approach, and in this manner function as state variables. This methodology reveals interesting insights about satellite relative motion and enables elegant control approaches. This approach can be applied in any dynamical environment as long as the chief orbit is periodic, and this is demonstrated with results for relative motion analysis and control in the eccentric Keplerian problem and in the circular restricted three-body problem. Some commentary on the extension of the methodology beyond the periodic chief orbit case is also provided. This is a promising and widely applicable new approach to the close-proximity satellite relative motion problem.

Finite-time extended state observer based prescribed performance fault tolerance control for spacecraft proximity operations

Relative motion control with six degrees of freedom (6-DOF) for spacecraft proximity operations in prescribed performance control (PPC) framework has become a hot issue in recent years, but actuator failure is seldom involved in controller design. In this paper, we introduce a complete thruster model to describe the actuator characteristics for thruster-only spacecraft, considering efficiency loss, thrust fluctuation and saturation. Besides, the barrier Lyapunov function (BLF) method and homeomorphic mapping method are often used in the PPC framework to constrain transformed errors. However, the two methods have singularity and infinite control effort problem once the constraints are not satisfied because of the actuator failure or other disturbance. In this paper, a novel bounded BLF (BBLF) is proposed to solve this problem. The proposed BBLF can still maintain bounded control effort and guarantee the system stability even if the transformed errors exceed the boundary. Further, the model uncertainty, actuator output uncertainty and external disturbance are summarized as lumped disturbances. A finite-time extended state observer (FTESO) is constructed to estimate the lumped disturbances. Finally, based on the estimated information from FTESO, an adaptive backstepping controller is proposed to track the desired trajectory. Numerical simulation results show the excellent dynamic response and steady-state accuracy of the proposed control strategy.

A planning tool for optimal three-dimensional formation flight maneuvers of satellites in VLEO using aerodynamic lift and drag via yaw angle deviations

Differential drag is a promising option to control the relative motion of distributed satellites in the Very Low Earth Orbit regime which are not equipped with dedicated thrusting devices. A major downside of the methodology, however, is that its control authority is (mainly) limited to the in-plane relative motion control. By additionally applying differential lift, however, all three translational degrees-of-freedom become controllable. In this article, we present a tool to flexibly plan optimal three-dimensional formation flight maneuvers via differential lift and drag. In the planning process, the most significant perturbing effects in this orbital regime, namely the J2 effect and atmospheric forces, are taken into account. Moreover, varying atmospheric densities as well as the co-rotation of the atmosphere are considered. Besides its flexible and high-fidelity nature, the major assets of the proposed methodology are that the in-and out-of-plane relative motion are controlled simultaneously via deviations in the yaw angles of the respective satellites and that the planned trajectory is optimal in a sense that the overall decay during the maneuver is minimized. Thereby, the remaining lifetime of the satellites is maximized and the practicability and sustainability of the methodology significantly increased. To the best of the authors knowledge, a tool with the given capabilities has not yet been presented in literature. The resulting trajectories for three fundamentally different relevant formation flight maneuvers are presented and discussed in detail in order to indicate the vast range of applicability of the tool.

A heaving system with two separated oscillating water column units for wave energy conversion

A theoretical model based on the linear potential theory is presented for two heaving oscillating water column (OWC) devices separated by a gap. The model includes relative motion and phase control between the devices and trapped water columns, and the hydrodynamic performance of the dual-OWC system thence evaluated. Matching conditions are employed along the common interfaces, and the power take-off model and motion equations of the OWC devices are incorporated into the solution procedure. At the top of each chamber, a Wells turbine is installed to extract wave power. To achieve the optimal overall power extraction performance, a numerical strategy of successive approximation is utilized to seek the optimal turbine damping combinations for the separated units. The effects of lip-wall draft and chamber breadth on the performance of a fully-free heaving dual-OWC system are explored. In view of the deficiency of a fully-free heaving system, two alternative optimization strategies are proposed, one focusing on the control of relative motion and phase between the water columns and the heaving devices, the other on utilizing resonance phenomenon inside the gap, achieved by tuning imposed linear spring constants and gap distance, respectively. It is shown that the control between heave motion of devices and water columns inside the chambers is beneficial for extracting more power over a broader range of wave frequencies. Moreover, enhanced extraction is likely over a wider range of wave conditions when the gap distance to wavelength triggers a sloshing mode inside the gap.

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.

Electromagnetic uncoordinated control of a ChipSats swarm using magnetorquers

A swarm of ChipSats equipped with miniature magnetorquers is considered, the electromagnetic interaction force is used for relative motion control at extremely short relative distances up to several centimetres. A ChipSat is a satellite printed on 3.5 × 3.5 cm circuit board with a set of sensors, solar panels, onboard computer, and communication system. Assuming the relative motion between each satellite is known, a Lyapunov-based control algorithm is proposed to achieve bounded relative trajectories. A centralized and a decentralized control approaches are implemented. For the centralized approach, a CubeSat is considered as the main satellite after swarm deployment, producing a high value magnetic dipole moment which interacts with the magnetic dipole of the surrounding ChipSats in order to stop relative drift. For the decentralized approach, the ChipSats are linked in interchangeable pairs in order to apply the electromagnetic control force and reduce the relative drift between the satellites to the vicinity of zero. Two different pairing selection methods are proposed in the paper, based on the closest satellite and on the satellite with highest relative drift. Both translational and rotational motion of satellites are considered. The magnetic dipole moments are used for angular velocity damping when orbit control is not required, and a repulsive collision avoidance electromagnetic control is applied when two ChipSats are within dangerously close proximity to each other. The proposed control schemes performance is studied numerically with different algorithm and ChipSats parameters. The influence of these parameters on the swarm separation is obtained using Monte-Carlo simulations.

Effects of Electric Potential Uncertainty on Electrostatic Tractor Relative Motion Control Equilibria

The electrostatic tractor has been proposed to touchlessly remove space debris from geosynchronous orbit by taking advantage of intercraft Coulomb forces. A controlled spacecraft (tug) emits an electron beam onto an uncooperative or retired satellite (debris). Thus, the tug raises its own electrostatic positive potential to tens of kilovolts, whereas the debris charges negatively. This results in an attractive force called the electrostatic tractor. Prior research investigated the charged relative motion dynamics and control of the electrostatic tractor for two spherical spacecraft and how charge uncertainty affects the relative motion control stability, but attitude effects could not be studied due to the two-sphere model. This work uses the multisphere method to consider general three-dimensional spacecraft shapes, and it investigates how the electric potential uncertainty and debris attitude impact the equilibrium separation distance between the two craft. The results show bounds for safe operations that avoid a collision. State regions are identified where the relative motion is particularly sensitive to potential uncertainty. The relative station-keeping performance using either higher- or lower-fidelity multi-sphere method models are compared to demonstrate that even a lower-fidelity multi-sphere method model can yield good results.

An approach to drastically reduce the required legs DOFs for bipedal robots and lower-limb exoskeletons

AbstractWe present a method to drastically reduce the required number of degrees-of-freedom (DOFs) needed for walking for each leg of bipedal robots and lower-limb exoskeletons. This approach releases more legs DOFs in the null space to do other tasks, instead of unnecessarily constraining them. It uses relative reference frames to control relative motion between the two feet, instead of the usual method of controlling foot movement with respect to fixed reference frames. In its basic form, it controls the bipedal walking holistically using two controllers: (1) world space control using relative feet motion and (2) null-space control of the legs posture.

Electron-Based Touchless Potential Sensing of Shape Primitives and Differentially-Charged Spacecraft

Numerous missions are being proposed which involve multiple spacecraft operating in close proximity in harsh charging environments. In such missions, the ability to sense the electrostatic potential on a nearby object is critical to prevent harmful electrostatic discharges or to leverage Coulomb interactions for relative motion control. The electron method is one such technique for touchless potential measurement which works by measuring low-energy secondary or photoelectrons emitted from the target. Previous work has demonstrated the efficacy of the electron method for touchless sensing, but has been limited to consideration of simple shapes and uniformly charged targets. This paper investigates the electron method for touchless sensing for cases in which the target spacecraft has more complex geometry primitives, including boxes, panels, and dishes. Further, the differential charging case, in which the target object is charged to multiple, different potentials, is also considered. A simulation framework is developed to model electric fields and particle trajectories around such spacecraft geometries. Vacuum chamber experiments validate the simulation results. The study shows how the target geometry can focus or defocus the electron flux into streams of electrons emanating from the surface. This provides critical insight into where to place the servicer vehicle to measure these fluxes and determine the target spacecraft potential.

Відносний рух космічного апарата з аеродинамічним компенсатором у перпендикулярному до площини орбіти напрямку при безконтактному видаленні космічного сміття

The article investigates the feasibility of using an aerodynamic compensator for contactless removal of space debris from low Earth orbits, taking into account aerodynamic disturbances in the direction perpendicular to the orbital plane. The object of the research is a modified scheme of the “ion beam shepherd” de-orbiting concept. The modification consists in replacing an additional electric thruster with an aerodynamic compensator designed to compensate the shepherd spacecraft motion caused by the reaction force of the main electric thruster, the ion plume of which creates a “braking” effect on the space debris object. The shepherd spacecraft with the aerodynamic compensator has a relatively large cross-sectional area. In this case, it is necessary to control the relative motion caused by the aerodynamic disturbances in the direction perpendicular to the orbital plane. This control requires additional propellant for the thrusters of the relative motion control system of the shepherd spacecraft. The article presents the calculation of the propellant consumption using a number of simplifying assumptions. The validity of these assumptions is verified by numerical integration of the equations of relative motion. The feasibility of using the aerodynamic compensator for contactless removal of space debris, taking into account aerodynamic disturbances acting in the direction perpendicular to the orbital plane, is shown.