# New State Transition Matrices for Spacecraft Relative Motion in Perturbed Orbits

@article{Koenig2017NewST, title={New State Transition Matrices for Spacecraft Relative Motion in Perturbed Orbits}, author={Adam W. Koenig and Tommaso Guffanti and Simone D’Amico}, journal={Journal of Guidance Control and Dynamics}, year={2017}, volume={40}, pages={1749-1768} }

This paper presents new state transition matrices that model the relative motion of two spacecraft in arbitrarily eccentric orbits perturbed by J2 and differential drag for three state definitions ...

#### Figures and Tables from this paper

#### 59 Citations

State-Transition Matrix for Satellite Relative Motion in the Presence of Gravitational Perturbations

- Physics
- 2019

A state-transition matrix (STM) for the relative motion of artificial satellites is presented in this work that is valid in the presence of the gravitational spherical harmonic perturbations. The p...

Robust and Safe N-Spacecraft Swarming in Perturbed Near-Circular Orbits

- Computer Science
- 2018

This paper presents a new guidance and control methodology for spacecraft swarms based on relative orbital elements, that generalizes flight-proven techniques used for binary formations to accommod...

Linear Models for Spacecraft Relative Motion Perturbed by Solar Radiation Pressure

- Physics
- 2019

Many scientific applications require the implementation of spacecraft formation-flying around Earth and other celestial bodies. The control of these formations calls for simple relative dynamics mo...

Closed-Form Optimal Impulsive Control of Spacecraft Formations Using Reachable Set Theory

- Computer Science
- 2021

This paper addresses the spacecraft relative orbit reconfiguration problem of minimizing the delta-v cost of impulsive control actions while achieving a desired state in fixed time. The problem is ...

Analytical Framework for Precise Relative Motion in Low Earth Orbits

- Physics
- 2020

This work presents a practical and efficient analytical framework for the precise modeling of the relative motion in low Earth orbits. Developed to support the design and verification of relative g...

Nonlinear analytical uncertainty propagation for relative motion near J2 -perturbed elliptic orbits

- Physics
- 2017

A nonlinear analytical uncertainty propagation method using state transition tensors is developed for satellite relative motion near J2-perturbed elliptic orbits. The improved state transition tens...

Nonlinear Kalman Filtering for Improved Angles-Only Navigation Using Relative Orbital Elements

- Mathematics
- 2017

This paper addresses the design and validation of an accurate estimation architecture for autonomous angles-only navigation in orbits of arbitrary eccentricity. The proposed filtering strategy over...

A simple method to design non-collision relative orbits for close spacecraft formation flying

- Physics
- 2018

A set of linearized relative motion equations of spacecraft flying on unperturbed elliptical orbits are specialized for particular cases, where the leader orbit is circular or equatorial. Based on… Expand

Spacecraft formation flying reconfiguration with extended and impulsive maneuvers

- Computer Science
- J. Frankl. Inst.
- 2019

The proposed approach for the derivation of the control solutions is based on the inversion of the linearized equations of relative motion parameterized using the mean relative orbit elements, which eases the inclusion of perturbing accelerations and offers an immediate insight into the relative motion geometry. Expand

Autonomous Trajectory Planning for Satellite RPO and Safety of Flight Using Convex Optimization

- Computer Science
- 2018

Autonomous Trajectory Planning for Satellite RPO and Safety of Flight using Convex Optimization and autonomous trajectory planning for satellite RPO usingconvex optimization. Expand

#### References

SHOWING 1-10 OF 43 REFERENCES

New State Transition Matrix for Relative Motion on an Arbitrary Elliptical Orbit

- Mathematics
- 2002

A new state transition matrix is described for the nonlinear problem of relative motion on an arbitrary elliptical orbit. A linearization is performed, leading to a set of linear differential… Expand

State Transition Matrix of Relative Motion for the Perturbed Noncircular Reference Orbit

- Mathematics
- 2003

A precise analytic solution that includes the effects of the reference orbit eccentricity and differential perturbations is needed for the relative motion of formation-flying satellites. As a result… Expand

GUIDANCE FOR RELATIVE MOTION OF LOW EARTH ORBIT SPACECRAFT BASED ON RELATIVE ORBIT ELEMENTS

- Geography
- 2004

In this paper a multiple-impulse maneuver algorithm for relative motion trajectory reconfiguration based on the Clohessy-Wiltshire-Hill’s equations is reviewed from previous work. This algorithm is… Expand

Satellite Relative Motion Using Differential Equinoctial Elements

- Mathematics
- 2005

For precise control, to minimize the fuel consumption, and to maximize the lifetime of satellite formations a precise analytic solution is needed for the relative motion of satellites. Based on the… Expand

Formation flying linear modelling

- Engineering
- 2005

Paper given at Dynamics and Control of Systems and Structures in Space (DCSSS), 5th conference, Kings College, Cambridge, July 2002

FLIGHT DYNAMICS ASPECTS OF THE GRACE FORMATION FLYING

- Geography
- 2001

Three key items have been studied at the mission control center (GSOC) for the build-up and control of the GRACE formation (along-track separation of about 220±50 km): 1. The safe ejection of both… Expand

Proximity Operations of Formation-Flying Spacecraft Using an Eccentricity/Inclination Vector Separation

- Mathematics
- 2006

The implementation of synthetic apertures by means of a distributed satellite system requires tight control of the relative motion of the participating satellites. This paper investigates a… Expand

Model of $$J_2$$J2 perturbed satellite relative motion with time-varying differential drag

- Physics
- 2015

This work revisits the modeling of the relative motion between satellites flying in near-circular low-Earth-orbits. The motion is described through relative orbital elements and both Earth’s… Expand

High-Fidelity Linearized J Model for Satellite Formation Flight

- Physics
- 2002

With the recent flurry of research on satellite formation flight, a need has become apparent for a set of linearized equations that describe the relative motion of satellites under the effect of the… Expand

E/I-vector separation for safe switching of the GRACE formation

- Physics, Computer Science
- 2006

The paper provides a conceptual outline and mathematical description of the e/i-vector separation for spacecraft formations in low Earth orbit and discusses the GRACE longitude swap maneuvers. Expand