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Online ISSN 1751-8652 Print ISSN 1751-8644

IET Control Theory & Applications

Volume 1, Issue 2, March 2007

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Volume 1, Issue 2

March 2007

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  • Cooperative control of multiple spacecraft flying in formation

    • Editorial: Cooperative control of multiple spacecraft flying in formation
      Distributed estimation, communication and control for deep space formations
      • Author(s): R.S. Smith  and  F.Y. Hadaegh
      • Source: IET Control Theory & Applications, Volume 1, Issue 2, p. 445 –451
      • DOI:  10.1049/iet-cta:20050460
      • Type: Article
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      • p. 445 –451 (7)
        Spacecraft formations in deep space give a means of implementing science instruments on a physical scale not possible with an individual spacecraft. Interferometric imaging is one application requiring a large spacecraft separation and extremely high relative position precision in order to image planets in other solar systems. Deep-space missions typically also require a high-level of autonomy, and the proposed distributed architectures for control and coordination, that are consistent with these requirements. Each spacecraft estimates the full state of the formation in order to calculate its optimal control action. Disagreements between estimates on the spacecraft lead to unanticipated dynamics and it is shown how communication may be used to ameliorate the effect of these dynamics. The relationship between the communication topology and the closed-loop system dynamics is presented.
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      Acquiring and maintaining persistence of autonomous multi-vehicle formations
      • Author(s): B. Fidan ; C. Yu ; B.D.O. Anderson
      • Source: IET Control Theory & Applications, Volume 1, Issue 2, p. 452 –460
      • DOI:  10.1049/iet-cta:20050409
      • Type: Article
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      • p. 452 –460 (9)
        A set of structural cohesiveness issues raised in control of autonomous multi-vehicle formations is analysed, using a recently developed theoretical framework of graph rigidity and persistence. The general characteristics of rigid and persistent formations and some operational criteria to check the rigidity and persistence of a given formation from the aspect of their use in cohesive motion of vehicle formations, including cohesive formation flight is reviewed. Employing these characteristics and criteria, systematic procedures are provided for acquiring and maintaining the persistence of autonomous formations, which are often found in real-world applications. Although these procedures are provided for certain formation classes (in the case of acquisition) or for certain formation operations (in the case of maintenance), the methodology used to develop these procedures has the potential to generate similar procedures for persistence acquisition and maintenance for other formation classes and operations as well.
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      Formulation and analysis of stability for spacecraft formations
      • Author(s): B. Açıkmeşe ; F.Y. Hadaegh ; D.P. Scharf ; S.R. Ploen
      • Source: IET Control Theory & Applications, Volume 1, Issue 2, p. 461 –474
      • DOI:  10.1049/iet-cta:20050459
      • Type: Article
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      • p. 461 –474 (14)
        A formulation of stability for formation flying spacecraft is presented. First, a formation is defined via control interactions between the spacecraft. Then, stability is formulated on the basis of input-to-output stability with respect to a partitioning of the formation dynamics. The particular form of input-to-output stability used here is based on the peak-to-peak gain of a system from its input to its output. This formulation of stability is shown to be useful in characterising disturbance propagation in the formation as a function of the partition interconnection topology, and also in analysing the robustness of sensing, communication and control topologies. Stability analysis results are presented for hierarchical, cyclic and disturbance attenuating formations in terms of the input-to-output gains of the partitions in the formation. Finally, Lyapunov stability analysis results are provided in terms of linear matrix inequalities for a general class of formations.
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      Load-sharing robust control of spacecraft formations: deep space and low Earth elliptic orbits
      • Author(s): M. Garcia-Sanz  and  F.Y. Hadaegh
      • Source: IET Control Theory & Applications, Volume 1, Issue 2, p. 475 –484
      • DOI:  10.1049/iet-cta:20050395
      • Type: Article
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      • p. 475 –484 (10)
        The design of autonomous and collaborative control strategies to govern the relative distances among multiple spacecraft in formation with no ground intervention is discussed. A coordinated load-sharing control structure for formation flying and a robust methodology to control spacecraft formations under slow time-varying and uncertain parameters are the main objectives. The method shares the load according to frequency specifications and takes into account the uncertainty and the multi-input–multi-output characteristic of the system. The methodology is applied to control spacecraft in formations in both deep space and low Earth elliptic orbits.
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      Multiple spacecraft formation control with thetas–D method
      • Author(s): M. Xin ; S.N. Balakrishnan ; H.J. Pernicka
      • Source: IET Control Theory & Applications, Volume 1, Issue 2, p. 485 –493
      • DOI:  10.1049/iet-cta:20050410
      • Type: Article
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      • p. 485 –493 (9)
        Formation control of multiple spacecraft flying in deep space about the L2 libration point is investigated. Dynamics of the spacecraft is formulated as a circular restricted three-body problem with Sun and Earth as the two primaries. A virtual structure (VS) concept is used as a framework for multiple spacecraft formation in which the centre of the virtual rigid body is assumed to follow a nominal orbit around the L2 libration point. Control is applied to each individual spacecraft so as to keep a constant relative distance from the centre of the VS. The relative formation dynamics is nonlinear and control of this system is carried out using a relatively new suboptimal control technique called as thetas–D technique. The thetas–D method provides approximate analytical solution to the Hamilton–Jacobi–Bellman equation. As it is a feedback control and in a closed form, it is implementable. Simulation results demonstrate that this controller is able to provide millimeter level formation flying accuracy.
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      Formation flying of multiple spacecraft with autonomous rendezvous and docking capability
      • Author(s): P.K.C. Wang  and  F.Y. Hadaegh
      • Source: IET Control Theory & Applications, Volume 1, Issue 2, p. 494 –504
      • DOI:  10.1049/iet-cta:20050411
      • Type: Article
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      • p. 494 –504 (11)
        The idea of incorporating autonomous rendezvous and docking (ARVD) capability into spacecraft flying in formation is explored. The situations where it is advantageous to incorporate ARVD capability into spacecraft formations are identified. Attention is focused on various potential problems pertaining to the control of multiple spacecraft with ARVD capability. Multiple-model-based control laws for formation acquisition and ARVD are developed using generic spacecraft models. In particular, the use of such control laws for simultaneous docking of multiple spacecraft in formation acquisition and reconfiguration is studied. Various optimal formation reconfiguration problems are briefly discussed. The effectiveness of the developed control laws is studied via computer simulation using a six-spacecraft formation model.
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      Consensus strategies for cooperative control of vehicle formations
      • Author(s): W. Ren
      • Source: IET Control Theory & Applications, Volume 1, Issue 2, p. 505 –512
      • DOI:  10.1049/iet-cta:20050401
      • Type: Article
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      • p. 505 –512 (8)
        Extensions of a consensus algorithm are introduced for systems modelled by second-order dynamics. Variants of those consensus algorithms are applied to tackle formation control problems by appropriately choosing information states on which consensus is reached. Even in the absence of centralised leadership, the consensus-based formation control strategies can guarantee accurate formation maintenance in the general case of arbitrary (directed) information flow between vehicles as long as certain mild conditions are satisfied. It is shown that many existing leader–follower, behavioural and virtual structure/virtual leader formation control approaches can be unified in the general framework of consensus building. A multiple micro air vehicle formation flying example is shown in simulation to illustrate the strategies.
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      Hybrid constrained formation flying control of micro-satellites
      • Author(s): F. Bacconi ; E. Mosca ; A. Casavola
      • Source: IET Control Theory & Applications, Volume 1, Issue 2, p. 513 –521
      • DOI:  10.1049/iet-cta:20050397
      • Type: Article
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      • p. 513 –521 (9)
        A solution to the problem of formation reconfiguration and keeping for fleets of micro-satellites in the presence of persistent disturbances and under input-saturation and formation accuracy constraints is proposed. Relative position and attitude dynamics are considered. For suitable initial conditions, the proposed control scheme produces system evolutions that fulfil the coordination constraints at any time and satisfy desirable control performance. This is accomplished by using a bank of command governor units in a switching supervisory control framework. Examples are provided in order to show the effectiveness of the technique.
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      Hybrid mixed-logical linear programming algorithm for collision-free optimal path planning
      • Author(s): B. Cetin ; M. Bikdash ; F.Y. Hadaegh
      • Source: IET Control Theory & Applications, Volume 1, Issue 2, p. 522 –531
      • DOI:  10.1049/iet-cta:20050432
      • Type: Article
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      • p. 522 –531 (10)
        Methods to solve collision-free fuel-optimal path- and motion-planning problems for the reconfiguration of spacecraft formations are presented. First, the motion-planning problem is formulated as a parameter optimisation problem in which the spacecraft are represented by unrotated cubes and the trajectory followed by each spacecraft is discretised in time using cubic splines. In other words, the trajectory is parameterised by the spacecraft positions and velocities at a set of waypoints. Big-M relaxation is then used to formulate the parameter optimisation as a mixed-integer linear program (MILP) whose solution can be obtained using standard MILP solvers. Several concepts are subsequently introduced to obtain the solutions more efficiently and reliably. In particular, the concept of a sequential linear program is introduced in which a sequence of closely-related linear programs are solved until a better local minimum cannot be found without ‘bifurcation’, that is, without qualitatively changing the nature of the solution. An example of such a change is making one spacecraft move in front of an obstacle instead of behind it. To handle these bifurcation points efficiently, the concept of a feasibility MILP (FMILP) is introduced in which the following question is answered: is there a feasible solution whose objective function value is better than that of the current bifurcation point. This is achieved by simply appending a single linear constraint to the set of constraints. A bisection search can be applied to the cost using FMILPs to further speed the proposed method. The method was applied to two standard tests of motion planning with collision avoidance such as swapping (using minimum fuel and along the major diagonals) the positions of eight spacecraft located at the corners of a cube. Preliminary simulations show significant improvement in efficiency by at least one order of magnitude.
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      Optimal guidance and decentralised state estimation applied to a formation flying demonstration mission in GTO
      • Author(s): D. Dumitriu ; S. Marques ; P.U. Lima ; J.C. Bastante ; J. Araújo ; L.F. Peñín ; A. Caramagno ; B. Udrea
      • Source: IET Control Theory & Applications, Volume 1, Issue 2, p. 532 –544
      • DOI:  10.1049/iet-cta:20050425
      • Type: Article
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      • p. 532 –544 (13)
        An integrated approach to guidance, navigation and control (GNC) of formation flying spacecraft (sc) is introduced. The design process considers a three-sc mission in a reference geostationary transfer orbit (GTO). A detailed definition of the mission framework, in terms of GNC modes and corresponding science and technology requirements, is provided. This, together with an analysis of the dynamic environment of the mission, establishes inputs to the design of a low-thrust optimal relative configuration that minimises the fuel consumption and overall complexity. The obtained solution is assessed in detail by means of an analysis considering perturbations acting over a sc in Earth GTO. The GNC closed loop uses the results of the mission analysis and design process as specifications. An algebraic closed-loop algorithm is proposed for the guidance and control (GC) subsystem, minimising the propellant consumption and ensuring collision avoidance. Using Pontryagin's maximum principle, the GC algorithm provides the optimal trajectories from the current state until the target state, as well as the optimal control inputs to follow these trajectories. A full-order decentralised filter implements the navigation algorithm. It estimates the full state of the involved sc and is based on an extended Kalman filter (EKF) for local measurements, and on a covariance intersection (CI) algorithm (plus the EKF prediction part) for the fusion between local state estimates and state estimates communicated by other sc. Results of applying the GNC algorithms to a realistic simulation of the specified mission are presented. The main original contribution of the work presented here is the design of the formation flying mission and algorithms using a top–down approach. From a requirement to maximise the time which can be used for experimentation at the apogee, the orbits of the three sc, as well as the propellant optimal manoeuvres for formation (re)acquisition, have been determined. A novel approach to the CI method has been used to estimate the relative positions between sc. The algorithms have been implemented and tested in an end-to-end mission simulation tool.
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      Leader-following formation control of multiple mobile vehicles
      • Author(s): J. Shao ; G. Xie ; L. Wang
      • Source: IET Control Theory & Applications, Volume 1, Issue 2, p. 545 –552
      • DOI:  10.1049/iet-cta:20050371
      • Type: Article
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      • p. 545 –552 (8)
        A framework for controlling groups of autonomous mobile vehicles to achieve predetermined formations based on a leader-following approach is presented. A three-level hybrid control architecture is proposed to implement both centralised and decentralised cooperative control. Under such architecture, the global-level formation control problem of n vehicles is decomposed into decentralised control problems between n−1 pairs of follower and their designated leader. In the leader–follower control level, two basic controllers are proposed to make the following robot keep a relative position with respect to the leader and avoid collisions in the presence of obstacles. Then, graph theory is introduced to formalise specified formation patterns in a simple but effective way, and two types of switching between these formations are also proposed. Numerical simulations and physical robot experiments show the effectiveness of our approach.
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