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Motion Description Languages and Symbolic Control

Encyclopedia of Systems and Control
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Abstract

The fundamental idea behind symbolic control is to mitigate the complexity of a dynamic system by limiting the set of available controls to a typically finite collection of symbols. Each symbol represents a control law that may be either open or closed loop. With these symbols, a simpler description of the motion of the system can be created, thereby easing the challenges of analysis and control design. In this entry, we provide a high-level description of symbolic control; discuss briefly its history, connections, and applications; and provide a few insights into where the field is going.

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References

  • Abate A, D’Innocenzo A, Di Benedetto MD (2011) Approximate abstractions of stochastic hybrid systems. IEEE Trans Autom Control 56(11):2688–2694

    Article  Google Scholar 

  • Arkin RC (1998) Behavior-based robotics. MIT, Cambridge

    Google Scholar 

  • Baillieul J, Ozcimder K (2012) The control theory of motion-based communication: problems in teaching robots to dance. In: American control conference, Montreal, pp 4319–4326

    Google Scholar 

  • Belta C, Bicchi A, Egerstedt M, Frazzoli E, Klavins E, Pappas GJ (2007) Symbolic planning and control of robot motion [Grand Challenges of Robotics]. IEEE Robot Autom Mag 14(1):61–70

    Article  Google Scholar 

  • Bicchi A, Marigo A, Piccoli B (2002) On the reachability of quantized control systems. IEEE Trans Autom Control 47(4):546–563

    Article  MathSciNet  Google Scholar 

  • Bicchi A, Marigo A, Piccoli B (2006) Feedback encoding for efficient symbolic control of dynamical systems. IEEE Trans Autom Control 51(6):987–1002

    Article  MathSciNet  Google Scholar 

  • Brockett RW (1988) On the computer control of movement. In: IEEE International conference on robotics and automation, Philadelphia, pp 534–540

    Google Scholar 

  • Brockett RW (1993) Hybrid models for motion control systems. In: Trentelman HL, Willems JC (eds) Essays on control. Birkhauser, Boston, pp 29–53

    Chapter  Google Scholar 

  • Brooks R (1986) A robust layered control system for a mobile robot. IEEE J Robot Autom RA-2(1):14–23

    Article  Google Scholar 

  • Egerstedt M (2002) Motion description languages for multi-modal control in robotics. In: Bicchi A, Cristensen H, Prattichizzo D (eds) Control problems in robotics. Springer, pp 75–89

    Google Scholar 

  • Egerstedt M, Brockett RW (2003) Feedback can reduce the specification complexity of motor programs. IEEE Trans Autom Control 48(2):213–223

    Article  MathSciNet  Google Scholar 

  • Fainekos GE, Girard A, Kress-Gazit H, Pappas GJ (2009) Temporal logic motion planning for dynamic robots. Automatica 45(2):343–352

    Article  MATH  MathSciNet  Google Scholar 

  • Frazzoli E, Dahleh MA, Feron E (2005) Maneuver-based motion planning for nonlinear systems with symmetries. IEEE Trans Robot 21(6):1077–1091

    Article  Google Scholar 

  • Girard A, Pappas GJ (2007) Approximation metrics for discrete and continuous systems. IEEE Trans Autom Control 52(5):782–798

    Article  MathSciNet  Google Scholar 

  • Johnson S (2002) Emergence: the connected lives of ants, brains, cities, and software. Scribner, New York

    Google Scholar 

  • Klavins E (2007) Programmable self-assembly. IEEE Control Syst 27(4):43–56

    Article  Google Scholar 

  • Kress-Gazit H (2011) Robot challenges: toward development of verification and synthesis techniques [from the Guest Editors]. IEEE Robot Autom Mag 18(3):22–23

    Article  Google Scholar 

  • Kuipers B (2000) The spatial semantic hierarchy. Artif Intell 119(1–2):191–233

    Article  MATH  MathSciNet  Google Scholar 

  • Lahijanian M, Andersson SB, Belta C (2012) Temporal logic motion planning and control with probabilistic satisfaction guarantees. IEEE Trans Robot 28(2):396–409

    Article  Google Scholar 

  • Manikonda V, Krishnaprasad PS, Hendler J (1998) Languages, behaviors, hybrid architectures, and motion control. In: Baillieul J, Willems JC (eds) Mathematical control theory. Springer, New York, pp 199–226

    Google Scholar 

  • Murray RM, Deno DC, Pister KSJ, Sastry SS (1992) Control primitives for robot systems. IEEE Trans Syst Man Cybern 22(1):183–193

    Article  MATH  Google Scholar 

  • Tabuada P (2006) Symbolic control of linear systems based on symbolic subsystems. IEEE Trans Autom Control 51(6):1003–1013

    Article  MathSciNet  Google Scholar 

  • Tarraf DC, Megretski A, Dahleh MA (2008) A framework for robust stability of systems over finite alphabets. IEEE Trans Autom Control 53(5):1133–1146

    Article  MathSciNet  Google Scholar 

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Andersson, S.B. (2014). Motion Description Languages and Symbolic Control. In: Baillieul, J., Samad, T. (eds) Encyclopedia of Systems and Control. Springer, London. https://doi.org/10.1007/978-1-4471-5102-9_155-1

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  • DOI: https://doi.org/10.1007/978-1-4471-5102-9_155-1

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  • Online ISBN: 978-1-4471-5102-9

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Chapter history

  1. Latest

    Motion Description Languages and Symbolic Control
    Published:
    29 December 2019

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_155-2

  2. Original

    Motion Description Languages and Symbolic Control
    Published:
    12 March 2014

    DOI: https://doi.org/10.1007/978-1-4471-5102-9_155-1