Source-linked AI summary
Formation Keeping Control for Deorbiting an Uncooperative Satellite by Laser Ablation
Shun Isobe, Yasuhiro Yoshimura, Toshiya Hanada, Yuki Itaya, Tadanori Fukushima
TL;DR
Laser-ablation deorbiting requires a chaser to maintain formation as it decelerates its target, a setting beyond conventional assumptions that only the chaser maneuvers. This paper derives powered-flight relative motion and a formation-keeping control law, and simulations verify it under perturbations and ablation uncertainty while both vehicles deorbit and maintain relative motion.
Problem
Because laser ablation decelerates the target while the chaser must maintain formation, conventional assumptions that only the chaser maneuvers do not cover this simultaneous-deorbit setting.
Source: §1 · p. 2, §4 · p. 10Method
The paper derives powered-flight relative motion and an analytical solution, then uses them to schedule laser-ablation and electrical-thrust timings and directions for periodic return to a desired formation.
Source: §1 · p. 2, §4 · p. 10Results
Simulations verified the control law under orbit perturbations and laser-ablation uncertainty, with both vehicles deorbiting while maintaining relative motion under disturbances.
Source: §4 · p. 10Takeaways & Limitations
The controller’s flexibility is presented as relevant to mission-operation and laser-system design.
Source: §4 · p. 10The paper leaves controller comparisons by deorbiting time or fuel consumption and extension to multiple-target deorbiting for future work.
Source: §4 · p. 10
Abstract
from arXiv · showhide
This paper proposes the formation keeping control law for deorbiting debris by a laser ablation. Laser ablation is vital technology for contactless active debris removal, where a chaser satellite with a laser system irradiates laser pulses to a target object to generate the ablation force for deorbiting. The deorbiting force decelerates the target, and the chaser must maintain its relative position and continue irradiating. In other words, both the chaser and the target are supposed to be deorbited simultaneously, where both have accelerations. Although conventional formation flying missions assume that only a chaser maneuvers, the formation flying in this paper considers that both a chaser and a target have accelerations. Thus, this paper derives the relative equations of motion between the chaser and the target in powered flight and their analytical solution using relative orbital elements. A control law based on the analytical solution is proposed, which determines the timings and directions of the laser ablation and the electrical thrust so that the formation periodically returns to a desired formation. Numerical simulations first examine the control law in two cases with different maneuver timings. Then, a Monte Carlo simulation is performed to verify the effectiveness of the control law for a variety of desired formations.
1. Introduction
Laser-ablation debris removal requires a chaser to maintain formation while both it and the target accelerate. The paper derives powered relative-motion equations and a control law for simultaneous deorbiting that returns the formation to a desired configuration.
Introduction
- Laser-based ADR enables contactless debris removal, reducing the risk of functional loss from accidental collisions associated with direct-contact methods.Direct-contact approaches can also be difficult to use when debris is uncooperative.Source: §1 · p. 1
- Chang et al. (2014) found that the ablation plume grows nearly perpendicular to the target surface regardless of laser irradiation angle, enabling force direction to be selected by choosing the irradiation point.The text notes that orbit transfer without changing attitude can be achieved by selecting the surface intersection with the perpendicular line from the center of mass.Source: §1 · p. 2
- The chaser must maintain formation as laser pulses decelerate the target, making this a powered formation-flying mission in which both spacecraft accelerate.The chaser uses electrical propulsion while the target experiences laser-ablation force.Source: §1 · p. 2
- The paper derives powered-flight relative-motion equations and an analytical solution, then uses them to choose ablation and electrical-thrust timings and directions for periodic return to a desired formation.The chaser’s low continuous electrical thrust and the target’s ablation force are the assumed external accelerations.Source: §1 · p. 2
- The controller compensates for uncertainty in ablation magnitude and orbital perturbations, and accommodates different desired formations and maneuver timings.The chaser’s laser ablation and electric propulsion are assumed not to operate simultaneously because of power constraints.Source: §1 · p. 3
2. Preliminaries
The preliminaries define the inertial and Hill frames, formulate powered relative motion, and introduce relative orbital elements (ROE) and their conversion to Hill-frame position and velocity. They also describe how ROE encode bounded relative-orbit geometry.
2.1. Orbital Motion
- Under a near-circular-orbit assumption, the paper uses Gauss’ variational equations to derive linear relative equations of motion in powered flight.The Hill frame is centered on the chaser, with radial, along-track, and orbit-normal axes.Source: §2.1 · pp. 3–4
2.2. Relative Motion
- Assuming a circular chaser orbit and separation small relative to orbital radius, the paper expresses target-relative motion in Hill coordinates and formulates the Hill–Clohessy–Wiltshire equations with external forces.The relative-motion formulation follows by taking the difference between the chaser and target equations of motion.Source: §2.2 · p. 4
2.3. Relative Orbital Elements
- ROE parameterize relative motion: δa = 0 denotes bounded motion, δa, δλ, and δe describe in-plane motion, and δi describes out-of-plane motion.The paper notes that ROE make relative-motion geometry visible and support orbit control planning using the GVE.Source: §2.3 · pp. 5–6
2.4. Transformation matrix of ROE–Hill frame
- The ROE-to-Hill transformation gives relative position and velocity; for δa = 0, the in-plane orbit is an ellipse and cross-track motion is harmonic.The ellipse has along-track semi-major axis 2aδe and radial semi-minor axis aδe; cross-track oscillation has amplitude aδi and phase u − ϑ.Source: §2.4 · p. 6
3. Equations of relative motion in powered flight
This section develops the powered-flight relative-motion model and ROE-based analytical solution, then reports Monte Carlo evidence of controller performance across desired formations.
3.1. Formulation
- The powered-flight relative dynamics are linearized about the near-circular chaser orbit using first-order Taylor expansion, while maneuver-driven orbital-element changes are accounted for.The dynamics are formulated using the GVE.Source: §3 · p. 6, §3.1 · pp. 6–7
3.2. Analytical solution
- Assuming constant maneuver magnitude, the study derives the powered-flight ROE analytical solution from orbital-element evolution; the mean-argument solution assumes in-plane maneuvers.The relative-motion solution is obtained using variation of parameters.Source: §3 · p. 6, §3.2 · pp. 7–8
3.3. Monte Carlo simulations
- Relative-orbit errors stayed below 8.2 m from M = 4 to M = 10, and control succeeded in all 100 Monte Carlo runs across varied desired formations.Desired formations were sampled from a uniform distribution.Source: Figure 3 · p. 9, §3.3 · p. 9
4. Conclusions
The paper derives powered-flight relative motion for an accelerating chaser and target and uses its analytical solution to control their simultaneous deorbit. Simulations show the control law maintains relative motion under disturbances while both deorbit.
Conclusions
- The paper derives powered-flight relative equations of motion and an analytical solution for a chaser and target that both accelerate.This differs from conventional formation-flying assumptions in which only the chaser maneuvers.Source: §4 · p. 10
- The control law selects laser-ablation and electrical-thrust timings and directions to periodically restore a desired formation, with flexible formation and maneuver timing.Two maneuver strategies were examined for returning to the desired formation within one orbital revolution.Source: §4 · p. 10
- Simulations verified that periodic control lets both satellites deorbit while maintaining their relative motion despite orbit perturbations and laser-ablation uncertainty.The control law’s flexibility may inform mission-operation and laser-system specifications, including focal length, irradiation angle, and camera angle.Source: §4 · p. 10
- Future work will optimize the controller for deorbiting time or fuel consumption and extend deorbiting to multiple targets using one chaser.Source: §4 · p. 10
Appendix A.
Appendix A derives nonlinear relative-motion dynamics using the GVE and obtains linear dynamics through a first-order Taylor expansion around the chaser orbit.
Appendix A.
- Substituting Eqs. (1)–(6) into Eq. (24) yields the nonlinear relative-motion dynamics using the GVE.Source: Appendix A · p. 10
- The passage lists elements of matrix B′, defines f as true anomaly and θ as true argument of latitude, and states that a first-order Taylor expansion is performed.Source: Appendix A · pp. 11–12
Appendix B.
Appendix B gives derivation details for the transformation from Eq. (60) to Eq. (??), including matrix Γ expressions and a stated omission of out-of-plane chaser maneuvering.
Appendix B.
- The appendix details the transformation from Eq. (60) to Eq. (??).The supplied passage identifies this as the section’s focus but gives no further transformation steps.Source: Appendix B · p. 12
- Neglecting the chaser’s out-of-plane maneuver, the appendix sets γ52, γ62, γ13, γ23, γ33, and γ43 to zero.These zero coefficients are listed in Eq. (B.26).Source: Appendix B · pp. 12, 14
- The paper states that the elements of matrix Γ can be expressed using Eqs. (36), (39), and (48), together with the approximation in Eq. (B.3).Source: Appendix B · p. 13