a verified hierarchical control architecture for coordinated multi

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  • INTERNATIONAL JOURNAL OF ADAPTIVE CONTROL AND SIGNAL PROCESSINGInt. J. Adapt. Control Signal Process. 2005; 00:16 Prepared using acsauth.cls [Version: 2002/11/11 v1.00]

    A Verified Hierarchical Control Architecture forCoordinated Multi-Vehicle Operations

    Joao Borges de Sousa, Karl H. Johansson, Jorge Silva, Alberto Speranzon

    DEEC, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal. E-mail:jtasso@fe.up.pt

    Electrical Engineering, Royal Institute of Technology, SE-100 44 Stockholm, Sweden. E-mail: {kallej,albspe}@ee.kth.seInstituto Superior de Engenharia do Porto, R. Dr. Antonio Bernardino Almeida 431, 4200 Porto, Portugal. E-mail:

    jes@isep.ipp.pt

    SUMMARY

    A layered control architecture for executing multi-vehicle team coordination algorithms is presented along with thespecifications for team behavior. The control architecture consists of three layers: team control, vehicle supervisionand maneuver control. It is shown that the controller implementation is consistent with the system specificationon the desired team behavior. Computer simulations with accurate models of autonomous underwater vehiclesillustrate the overall approach in the coordinated search for the minimum of a scalar field. The coordinated searchis based on the simplex optimization algorithm. Copyright c 2005 John Wiley & Sons, Ltd.

    KEY WORDS: Hierarchical control; Multi-robot systems; Autonomous underwater vehicle; Transition systems;Formal methods; Hybrid systems.

    1. INTRODUCTION

    The last decade has witnessed unprecedented interactions between technological developments incomputing, communications and control which have led to the design and implementation of roboticsystems consisting of networked vehicles and sensors. These developments enable researchers andengineers not only to design new robotic systems but also to develop visions for systems that couldhave not been imagined before.

    1.1. Multi-vehicle operations

    Today, there are automotive vehicles in various stages of automation ranging from automated highwaysystems [57, 24], to coordinated adaptive cruise control systems [1], to platooning of passenger andmilitary vehicles. Other examples for ground vehicles include border patrol, search and rescue, and

    J. Borges de Sousa and J. Silva are partially supported by Agencia de Inovacao through the PISCIS project. K. H. Johanssonand A. Speranzon are partially supported by the European Commission through the RECSYS, HYCON and RUNES projects,by the Swedish Foundation for Strategic Research through an Individual Grant for the Advancement of Research Leaders andby the Swedish Research Council.

    ReceivedCopyright c 2005 John Wiley & Sons, Ltd. Revised

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    games such as robotic soccer [58, 12] or the RobotFlag [13]. There are numerous applications forautonomous underwater vehicles, such as oceanographic surveys [51, 60, 29], operations in hazardousenvironments, inspection of underwater structures, mine search [23], and the Autonomous OceanSampling Network [10, 11], to name just a few. The Mobile Offshore Base illustrates the problemof coordinating the motions of sea-going vehicles [44, 14]. The application pull for the coordinationand control of teams of unmanned air vehicles is driven mainly by military requirements [7]; sometechnologies have already been field tested [4, 50, 27] while others are being developed and testedin simulation [17]. A promising technological push comes from the inter-operation of multi-vehiclesystems and sensor networks [9].

    1.2. Approach and contributions

    In this paper we present a control architecture for the implementation of a class of coordinationstrategies by a team of autonomous vehicles. This class is characterized by the alternation betweentwo phases: a communication phase where the team exchanges messages to define waypoints foreach vehicle; and a motion phase where the vehicles move to the designated waypoints, where a newcommunication phase will take place. The strategy specification is encoded as an automaton.

    Several difficulties must be faced in developing a control architecture for the implementation ofthis class of coordination strategies. We illustrate these difficulties and discuss our contributions inthe context of the coordinated search for the minimum of a scalar field by a team of autonomousunderwater vehicles with limited communication capabilities. The coordination strategy is inspired bya class of optimization algorithms with phased operations: each phase starts with the selection of pointsto sample and terminates when these points are sampled.

    First, there are severe limitations on communications. For example, autonomous underwater vehiclesuse acoustic communications which pose significant restrictions on range and bandwidth [48, 30]. Thisprecludes the use of communications for low-level feedback control. We address this difficulty byrestricting communications to the exchange of a few coordination messages.

    The second difficulty is in that the design space of the team search is large and heterogeneous. Thedesign involves generating sampling points and arrival times to ensure communications at the endof each phase; assigning vehicles to the sampling points; and designing real-time feedback strategiesfor each vehicle. We address this difficulty by structuring the design into two pieces: generation ofsampling points and execution control. We present conditions for the generation of sampling pointsand arrival times with the required properties; this is done in the setting of dynamic optimization andreach set computations. We introduce a layered design for the execution control. This is done in theframework of hybrid automata: there is a team controller, a vehicle supervisor and several maneuvercontrollers per vehicle. The coordination strategy is implemented through the interactions of the teamcontrollers during the coordination phase. In this phase, one team controller, the master controller,receives the samples sent by the other team controllers, calculates the sampling points and arrival timesfor the next motion phase and sends them to the other team controllers. The motion phase is executedindependently by each vehicle.

    The third difficulty originates in the requirement that the execution control must indeed implementthe search strategy. We addressed this difficulty by layering the execution control and designingeach layer to ensure that their controllers produce guaranteed results under the assumption that thecontrollers at the adjacent layers also produce guaranteed results. This is done in a modular fashion.The vehicle supervisor and the maneuver controllers guarantee that each sampling point is visitedwithin a given tolerance of the arrival time. Under these assumptions the composition of the team

    Copyright c 2005 John Wiley & Sons, Ltd. Int. J. Adapt. Control Signal Process. 2005; 00:16Prepared using acsauth.cls

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    controllers is shown to implement the specification. This is done using automata-based techniques.Our contributions concern the design of a modular architecture and the proof that the modules and

    the interactions within the architecture implement a given specification. This is done in the frameworkof automata-theoretic techniques and reach set analysis.

    Summarizing, our design touches upon several related problems: finding the minimizer of a scalarfield through the coordinated motions of multiple vehicles; guaranteed maneuver design; waypointbased coordination schemes, and control architectures. Next, we briefly compare our approach torelated work on these problems.

    1.3. Related work

    The problem of finding the minimum of a scalar field with the coordinated motions of autonomousvehicles with sampling capabilities has received large attention in the last decade. A significant bodyof this work concerns the adaptation of optimization algorithms to single- or multi-vehicle searchstrategies. Search strategies for single vehicle operations inspired by different optimization algorithmsare reported in [6] along with illustrative examples. Pure gradient-based methods for scenarios wherea vehicle platoon searches the minimum of general convex and smooth scalar fields are presentedin [3]. Lyapunov-based arguments are used in [3, 19] for the gradient descent of a scalar field. Theseapproaches result in feedback control laws that require closing the control loop around communicatedmeasurements. We take the view of considering limited and sporadic communications, which precludethe use of these techniques.

    The problem of guaranteed maneuver design with logic switching is a difficult one, and has receivedsignificant attention from researchers in hybrid systems. Techniques from optimal control and gametheory are used in [39] and [52] to design controllers for safety specifications in hybrid systems. Theirmethodology consists of three phases. First, they translate safety specifications into restrictions on theset of reachable sets. Second, they formulate a differential game and derive Hamilton-Jacobi-Bellmanequations whose solutions describe the boundaries of reachable sets. Third, they synthesize the hybridcontroller from these equations. The controller assumes the form of a feedback control law for thecontinuous and discrete variables, which guarantees that the hybrid system remains in the safe subsetof the reachable set. This formulation is strongly related to the problem of reach set computation.Several techniques for reachability analysis of dynamic systems have been proposed. An approachfor reach set computation for linear systems based on the Pontryagin maximum principle of optimalcontrol theory and the separation property is presented in [55]. Dynamic programming techniquesare used in [32] to describe reach sets and related problems of