## Decentralized Scheme for Spacecraft Formation Flying via the Virtual Structure Approach (2003)

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Venue: | AIAA Journal of Guidance, Control, and Dynamics |

Citations: | 57 - 8 self |

### BibTeX

@ARTICLE{Ren03decentralizedscheme,

author = {Wei Ren and Randal W. Beard and Al W. Beard},

title = {Decentralized Scheme for Spacecraft Formation Flying via the Virtual Structure Approach},

journal = {AIAA Journal of Guidance, Control, and Dynamics},

year = {2003},

volume = {27},

pages = {73--82}

}

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### Abstract

this paper. Following a decentralized coordination architecture via the virtual structure approach, decentralized formation control strategies are introduced, which are appropriate when a large number of spacecraft are involved and/or stringent inter-spacecraft communication limitations are exerted. The e#ectiveness of the proposed control strategies is demonstrated through simulation results

### Citations

470 | Behavior-Based Formation Control for Multirobot Teams
- Balch, Arkin
- 1998
(Show Context)
Citation Context ...espectively. The rotational dynamics of each spacecraft relative to F0 (Ref. 16) are dˆqi dt0 =− 1 2 ωi × ˆqi + 1 2 ¯qiωi, dωi Ji dt0 d¯qi dt0 =−ωi × (Jiωi) + τ i � � =− 1 2 ωi · ˆqi REN AND BEARD 75 =-=(2)-=- (3) (4) where Ji and τ i are inertia tensor and control torque associated with the ith spacecraft, respectively. III. Decentralized Architecture via the Virtual Structure Approach In this section we ... |

273 |
BInformation flow and cooperative control of vehicle formations
- Fax, Murray
- 2004
(Show Context)
Citation Context ...coordination vector instantiation satisfies the following rigid-body dynamics: ⎛ ⎞ ⎛ ˙rFi vFi ⎜ ⎜m F ˙vFi ⎟ ⎜ fFi ⎜ ⎟ ⎜ ⎜ ˙qFi ⎟ ⎜ 1 ⎜ ⎟ = ⎜ 2 ⎜JF ˙ωFi⎟ ⎜ ⎜ ⎟ ⎜ ⎝ ⎠ ⎝ �(ωFi)qFi ⎞ ⎟ −ωFi × JFωFi + τ ⎟ =-=(8)-=- Fi⎟ ⎠ where m F and JF are the virtual mass and virtual inertia of the virtual structure, fFi and τ Fi are the virtual force and virtual torque exerted on the ith implementation of the virtual struct... |

110 |
Spacecraft Attitude Dynamics
- Hughes
- 1986
(Show Context)
Citation Context ...hat a unit quaternion is not unique since q and −q represent the same attitude. However, uniqueness can be achieved by restricting the Euler angle φ to the range 0 ≤ φ ≤ π so that ¯q ≥ 0 all the time =-=[10]-=-. In this paper, we assume that ¯q ≥ 0. 0-7803-7896-2/03/$17.00 ©2003 IEEE 1746 Proceedings of the American Control Conference Denver, Colorado June 4-6, 20032.3 The Desired States for Each Spacecraf... |

103 | Coordinated target assignment and intercept for unmanned air vehicles - Beard, McLain, et al. - 2002 |

82 |
High precision formation control of mobile robots using virtual structures. Autonomous Robot
- Lewis, Tan
- 1997
(Show Context)
Citation Context ...ctively. The rotational dynamics of each spacecraft relative to F0 (Ref. 16) are dˆqi dt0 =− 1 2 ωi × ˆqi + 1 2 ¯qiωi, dωi Ji dt0 d¯qi dt0 =−ωi × (Jiωi) + τ i � � =− 1 2 ωi · ˆqi REN AND BEARD 75 (2) =-=(3)-=- (4) where Ji and τ i are inertia tensor and control torque associated with the ith spacecraft, respectively. III. Decentralized Architecture via the Virtual Structure Approach In this section we prop... |

80 | A control Lyapunov function approach to multiagent coordination
- Ogren, Egerstedt, et al.
- 2002
(Show Context)
Citation Context ...ive semidefinite matrices. The proposed control torque τ Fi is given by τ Fi =−kG�q d∗ F qFi − ƔGiωFi − kS�q∗ F(i + 1) qFi � � − DS ωFi − ω F(i + 1) − kS�q∗ F(i − 1) qFi � � − DS ωFi − ω F(i − 1) (9) =-=(10)-=- where kG > 0 and kS ≥ 0 are scalars, ƔGi follows the same definition as just stated, DS is a symmetric positive semidefinite matrix, and ˆq represents the vector part of the quaternion.s78 REN AND BE... |

74 |
Navigation strategies for multiple autonomous mobile robots moving in formation
- Wang
- 1991
(Show Context)
Citation Context ...ensively in the literature with application to the coordination of multiple robots, unmanned air vehicles (UAVs), autonomous underwater vehicles (AUVs), satellites, aircraft, and spacecraft (see e.g. =-=[1, 2, 3, 4, 5, 6]-=-). There are several advantages to using formations of multiple vehicles. These include increased feasibility, accuracy, robustness, flexibility, cost and energy efficiency, and probability of success... |

61 | Formations With a Mission: Stable Coordination of Vehicle Group Maneuvers
- Ogren, Fiorelli, et al.
- 2002
(Show Context)
Citation Context ...hereafter use ξ d instead of ξ d(k) to represent a certain formation pattern to be achieved. Define ˜ξ i = ξi − ξ d = � ˜r T Fi , ˜vT Fi , ˜qT Fi , ˜ωT Fi , ˜λ T Fi , ˙˜λ T Fi �� � T REN AND BEARD 77 =-=(5)-=- (6) as the error state for the ith coordination vector instantiation. There are two objectives for the instantiation of the coordination vector implemented in each spacecraft. The first objective is ... |

61 | The attitude control problem - Wen, Kreutz-Delgado - 1991 |

57 | Hybrid Control of Formations of Robots
- Fierro, Das, et al.
- 2001
(Show Context)
Citation Context ...nd Kri and Kvi are symmetric positive definite matrices. The proposed control torque for the ith spacecraft is given by τ i = Ji ˙ω d 1 i + 2 ωi � × Ji ωi + ωd � i − kqi�q d∗ i qi � − Kωi ωi − ωd � i =-=(7)-=- where Ji is the moment of inertia of the ith spacecraft, kqi is a positive scalar, Kωi is a symmetric positive definite matrix, and ˆq represents the vector part of the quaternion. Equations (6) and ... |

49 |
Coordination and control of multiple microspacecraft moving in formation
- Wang, Hadaegh
- 1996
(Show Context)
Citation Context ...ensively in the literature with application to the coordination of multiple robots, unmanned air vehicles (UAVs), autonomous underwater vehicles (AUVs), satellites, aircraft, and spacecraft (see e.g. =-=[1, 2, 3, 4, 5, 6]-=-). There are several advantages to using formations of multiple vehicles. These include increased feasibility, accuracy, robustness, flexibility, cost and energy efficiency, and probability of success... |

40 | A Decentralized Approach to Elementary Formation Maneuvers
- Lawton, Beard, et al.
- 2000
(Show Context)
Citation Context ...ability of success. Various strategies and approaches have been proposed for formation control. These approaches can be roughly categorized as leader-following (see e.g. [1, 4]), behavioral (see e.g. =-=[2, 7, 8]-=-), and virtual structure (see e.g. [3, 9]) approaches. Each approach has its advantages and disadvantages. The leader-following approach is easy to understand and implement. However, it is a centraliz... |

33 | Closing Ranks in Vehicle Formations Based on Rigidity
- Eren, Belhumeur, et al.
- 2002
(Show Context)
Citation Context ...ositive semidefinite matrices. The proposed control torque τ Fi is given by τ Fi =−kG�q d∗ F qFi − ƔGiωFi − kS�q∗ F(i + 1) qFi � � − DS ωFi − ω F(i + 1) − kS�q∗ F(i − 1) qFi � � − DS ωFi − ω F(i − 1) =-=(9)-=- (10) where kG > 0 and kS ≥ 0 are scalars, ƔGi follows the same definition as just stated, DS is a symmetric positive semidefinite matrix, and ˆq represents the vector part of the quaternion.s78 REN A... |

31 | Quaternion Feedback Regulator for Spacecraft Eigenaxis Rotations - Wie, Weiss, et al. - 1989 |

29 | Formation flying control of multiple spacecraft via graphs, matrix inequalities, and switching - Mesbahi, Hadaegh |

28 | A feedback architecture for formation control
- Beard, Lawton, et al.
- 2000
(Show Context)
Citation Context ...pproaches have been proposed for formation control. These approaches can be roughly categorized as leader-following (see e.g. [1, 4]), behavioral (see e.g. [2, 7, 8]), and virtual structure (see e.g. =-=[3, 9]-=-) approaches. Each approach has its advantages and disadvantages. The leader-following approach is easy to understand and implement. However, it is a centralized implementation, which makes the leader... |

28 | A control scheme for improving multi-vehicle formation maneuvers - Young, Beard, et al. - 2001 |

27 |
Synchronized Multiple Spacecraft Rotations
- Lawton, Beard
- 2002
(Show Context)
Citation Context ...ance principle, �rF i − rd � � F → 0, �vF i� → 0, and � � �rF i − r � F (i+1) → 0, i = 1, · · · , N. Accordingly, � � �vF i − v � F (i+1) → 0, i = 1, · · �=-=� , N. For the rotational dynamics, following [8], consider the Lyapunov function can-=-didate �N � V2 = kG � i=1 qF i − qd � � F 2 �N � � +kS � i=1 qF i − q � F (i+1) 2 + � 1 N 2 i=1 ωT F iJF ωF i. In [12], it is shown that 1749 d dt �q − p�2 = V(p ∗ ... |

25 |
2000), “Autonomous formation flight
- Giuletti, Pollini, et al.
(Show Context)
Citation Context ...he vector part of the quaternion.s6 REN AND BEARD Similar to (9), the proposed control effort νF i is given by νF i = − KG(λF i − λ d F ) − ΓGi ˙ λF i − KS(λF i − λF (i+1)) − DS( =-=˙ λF i − ˙ λF (i+1)) (11) − KS(λF i − �-=-�F (i−1)) − DS( ˙ λF i − ˙ λF (i−1)), where KG is a symmetric positive definite matrix, ΓGi follows the same definition as above, and KS and DS are symmetric positive semi-definite matric... |

24 | Input-to-State Stability on Formation Graphs
- Tanner, Pappas, et al.
- 2002
(Show Context)
Citation Context ... � i (7) where Ji is the moment of inertia of the ith spacecraft, kqi is a positive scalar, Kωi is a symmetric positive definite matrix, and ˆq represents the vector part of the quaternion. Equations =-=(6)-=- and (7) require both Xd i and ˙X d i , which are obtained from ξi and ˙ξ i using Eqs. (1) and (2). B. Formation Control Strategies for Each Virtual Structure Instantiation As in Sec. III.C, ξ i is th... |

24 |
Platoons of underwater vehicles
- Stilwell, Bishop
(Show Context)
Citation Context ... v T FivFi � � �T� � kS qFi − qF(i + 1) qFi − qF(i + 1) N� � i = 1 N� i = 1 N� i = 1 kG ˜q T Fi ˜qFi + 1 2 ωT Fi JFωFi � � �T � � λFi − λF(i + 1) K S λFi − λF(i + 1) � ˜λ T FiKG ˜λFi + ˙λ T Fi ˙λFi � =-=(12)-=- With the proposed control force (6) for each spacecraft, the second equation in the translational dynamics (3) for the ith spacecraft can be rewritten as ˙˜vi =−Kri˜ri − Kvi˜vi. Applying Lemma 1, the... |

16 | Formation Flight as a Cooperative Game - Anderson, Robbins - 1998 |

14 |
Adaptive control of formation flying spacecraft for interferometry
- Hadaegh, Lu, et al.
- 1998
(Show Context)
Citation Context ...ensively in the literature with application to the coordination of multiple robots, unmanned air vehicles (UAVs), autonomous underwater vehicles (AUVs), satellites, aircraft, and spacecraft (see e.g. =-=[1, 2, 3, 4, 5, 6]-=-). There are several advantages to using formations of multiple vehicles. These include increased feasibility, accuracy, robustness, flexibility, cost and energy efficiency, and probability of success... |

14 | Formation Control Strategies for a Separated Spacecraft Interferometer
- Robertson, Inalhan, et al.
(Show Context)
Citation Context |

11 | Co-ordinated attitude control of multi-satellite systems. International fourrial of Robust and Nonlinear Control - Kang, Yeh |

11 | Decentralized control of satellite formations - Carpenter - 1002 |

11 | Virtual structure based spacecraft formation control with formation feedback
- Ren, Beard
(Show Context)
Citation Context ...ation matrix of the frame FO with respect to FF , and [·]O, [·]F , and [·]i are the corresponding coordinate representations. The derivatives of the desired states can be derived correspondingly (see =-=[11]-=-). 2.4 Spacecraft Dynamics The translational and rotational dynamics of each spacecraft relative to FO are dri dto dvi Mi dto dˆqi dto d¯qi dto dωi Ji dto = vi = fi = − 1 2 ωi × ˆqi + 1 2 ¯qiωi (2) = ... |

6 | Information Flow and Cooperative - Fax, Murray - 2002 |

3 |
Decentralized Control of Cooperating Mobile
- Sugar, Kumar
- 1998
(Show Context)
Citation Context ...ely. The rotational dynamics of each spacecraft relative to F0 (Ref. 16) are dˆqi dt0 =− 1 2 ωi × ˆqi + 1 2 ¯qiωi, dωi Ji dt0 d¯qi dt0 =−ωi × (Jiωi) + τ i � � =− 1 2 ωi · ˆqi REN AND BEARD 75 (2) (3) =-=(4)-=- where Ji and τ i are inertia tensor and control torque associated with the ith spacecraft, respectively. III. Decentralized Architecture via the Virtual Structure Approach In this section we propose ... |

2 | Model independent approximate eigenaxis rotations via quaternion feedback
- Lawton, Beard
- 2001
(Show Context)
Citation Context ... · , N. For the rotational dynamics, following [8], consider the Lyapunov function candidate �N � V2 = kG � i=1 qF i − qd � � F 2 �N � � +kS � i=1 qF i − q � F (i+1) 2 + � 1=-= N 2 i=1 ωT F iJF ωF i. In [12], it is shown tha-=-t 1749 d dt �q − p�2 = V(p ∗ q) T (ωq − ωp), (9) where ωq and ωp are the angular velocities corresponding to q and p respectively. Applying (9), the derivative of V2 is ˙V2 = � N i=1 ... |

1 | Synchronized Multiple Spacecraft - Lawton, Beard |

1 |
Navigation Strategies for Multiple Autonomous Mobile Robots Moving in Formation
- 1Wang
- 1991
(Show Context)
Citation Context ...nit quaternion. The conjugate of the unit quaternion q is defined by q ∗ = [−ˆq T , ¯q] T . The conjugate of qp is given by (qp) ∗ = p ∗ q ∗ . The multiplicative identity quaternion is denoted by 1 = =-=[0, 0, 0, 1]-=- T , where qq ∗ = q ∗ q = 1 and q1 = 1q = q. Suppose that q d and q represent the desired and actual attitude respectively, then the attitude error is given by qe = q d∗ q = [ˆq T e , ¯qe] T , which r... |