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Distributed Controls of Multiple Robotic Systems, An Optimization Approach

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Encyclopedia of Complexity and Systems Science

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This chapter describes an integrated approach for designing communication, sensing, and control systems for mobile distributedsystems. A three‐step process is used to create locally optimal distributed controls for multiple robot vehicles. The first step is to definea global performance index whose extremum produces a desired cooperative result. The second step is to partition and eliminate terms in theperformance index so that only terms of local neighbors are included. This step minimizes communication amongst robots and improves system robustness. The thirdstep is to define a control law that is the gradient of the partitioned performance index. This control drives the system towards the local extremum of thepartitioned performance index. Graph theoretic methods are then used to analyze the input/output reachability and structural controllability and observabilityof the decentralized system. Connective stability of the resulting controls is evaluated with...

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Abbreviations

Multiple robotic system:

Multiple robotic systems are a collective of multiple robotic vehicles (e. g.ground‐based, aerial, underwater, and/or some combination thereof) whereineach robot has assigned tasks designed to help the entire system achieve itsoverall goals.

Provably convergent cooperative controls:

Provablyconvergent cooperative controls is a distribution of control laws amongthe agents of a multiple robotic system with the objective that global stability is preserved and a global performance index is optimized. The controllaws take into account the physics of the individual robots, the communication protocols and information exchange between the robots, the overall terrain, andthe goals/constraints of the entire collective.

Connective stability:

A  system is connectively stable if it is stable in the sense of Lyapunov forall structural perturbations of the interconnection matrix that describesthe system (see [63]). These structural perturbations include attenuation,degradation, and loss of communication between nodes in the network.

Vehicle communication protocols:

In a multiple robotic system, vehicle communication protocols refer to thetype of communication algorithm used by the vehicles to share informationamongst each other. These protocols are crucial in determining stability andperformance properties.

Time division multiple access (TDMA):

TDMA is a channel access method for shared medium (usually radio) networks. It allows several users to share the samefrequency channel by dividing the signal into timeslots. The users transmit in rapid succession, one after the other, each using their own timeslot. Thisallows multiple stations (e. g. robots) to share the same transmission medium (e. g. radio frequency channel) while using only part of itsbandwidth.

Carrier sense multiple access (CSMA):

CSMA is also a channel access method for shared medium networks where thestation first listens to the channel for a predetermined amount of time soas to check for any activity on the channel. If the channel is sensed “idle”then the station is permitted to transmit. If the channel is sensed as“busy” the station defers its transmission. This access method is used inwired TCP/IP networks.

Linear TDMA broadcast:

The number of time slots in the TDMA network is equal to the total number ofnodes in the network.

Polylogarithmic TDMA broadcast:

The number of time slots in the TDMA network is less than the total numberof nodes because of spatial reuse. This method only applies as long as thedegree of the network (the number of nodes within communication range) issmall (see [66]).

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Acknowledgments

The authors greatly appreciate the help of Steven Eskridge, John Hurtado,Chris Lewis, John Harrington, and Nekton Research, LLC, in implementing andtesting these algorithms on a variety of robot platforms.This work was supported in part by the Sandia National Laboratories. Sandiais a multiprogram laboratory operated by Sandia Corporation, a LockheedMartin Company, for the United States Department of Energy under contractDE–AC04–94AL85000. In addition, this research was partially funded by theInformation Processing Technology Office and Microsystems Technology Officeof the Defense Advanced Research Projects Agency.

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Authors and Affiliations

  1. Sandia National Laboratories, Albuquerque, USA

    John T. Feddema, David A. Schoenwald, Rush D. Robinett & Raymond H. Byrne

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  1. RAMTECH LIMITED, 122 Escalle Lane, Larkspur, CA, 94939, USA

    Robert A. Meyers Ph. D. (Editor-in-Chief) (Editor-in-Chief)

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Feddema, J.T., Schoenwald, D.A., Robinett, R.D., Byrne, R.H. (2009). Distributed Controls of Multiple Robotic Systems, An Optimization Approach. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_129

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