Abstract
In this paper, we consider the problem of generating optimized, executable control code from high-level, symbolic specifications. In particular, we construct symbolic control programs using strings from a motion description language with a nominal set of motion parameters, such as temporal duration and energy, embedded within each mode. These parameters are then optimized over, using tools from optimal switch-time control and decentralized optimization of separable network problems. The resulting methodology is applied to the problem of controlling robotic marionettes, and we demonstrate its operation on an example scenario involving symbolic puppet plays defined for multiple puppets.
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References
Armijo, L.: Minimization of Functions Having Lipschitz Continuous First-Partial Derivatives. Pacific Journal of Mathematics 16, 1–3 (1966)
Arrow, K., Hurwicz, L., Uzawa, H.: Studies in Nonlinear Programming. Stanford University Press, Stanford (1958)
Attia, S.A., Alamir, M., Canudas de Wit, C.: Sub Optimal Control of Switched Nonlinear Systems Under Location and Switching Constraints. In: Proc. 16th IFAC World Congress, Prague, Czech Republic, July 3-8 (2005)
Baird, B.: The Art of the Puppet. Mcmillan Company, New York (1965)
Belta, C., Bicchi, A., Egerstedt, M., Frazzoli, E., Klavins, E., Pappas, G.: Symbolic Planning and Control of Robot Motion. IEEE Robotics and Automation Magazine (March 2007)
Brockett, R.W.: On the Computer Control of Movement. In: Proceedings of the 1988 IEEE Conference on Robotics and Automation, New York, April 1988, pp. 534–540 (1988)
Egerstedt, M., Brockett, R.W.: Feedback Can Reduce the Specification Complexity of Motor Programs. IEEE Transactions on Automatic Control 48(2), 213–223 (2003)
Egerstedt, M., Murphey, T., Ludwig, J.: Motion Programs for Puppet Choreography and Control. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 190–202. Springer, Heidelberg (2007)
Egerstedt, M., Wardi, Y., Axelsson, H.: Transition-Time Optimization for Switched-Mode Dynamical Systems. IEEE Trans. on Automatic Control AC-51, 110–115 (2006)
Frazzoli, E.: Explicit Solutions for Optimal Maneuver-based Motion Planning. In: Proceedings of 42nd IEEE Conference on Decision and Control, vol. 4, pp. 3372–3377 (2003)
Frazzoli, E., Dahleh, M.A., Feron, E.: Maneuver-Based Motion Planning for Nonlinear Systems with Symmetries. IEEE Transactions on Robotics 21(6), 1077–1091 (2005)
Johnson, E., Murphey, T.: Dynamic Modeling and Motion Planning for Marionettes: Rigid Bodies Articulated by Massless Strings. In: International Conference on Robotics and Automation, April 2007, pp. 330–335 (2007)
Kloetzer, M., Belta, C.: A Fully Automated Framework for Control of Linear Systems From Temporal Logic Specifications. IEEE Transactions on Automatic Control 53(1), 287–297 (2008)
Manikonda, V., Krishnaprasad, P.S., Hendler, J.: Languages, behaviors, hybrid architectures and motion control. In: Willems, J.C., Baillieul, J. (eds.) Mathematical Control Theory. Springer, Heidelberg (1998)
Martin, P., Egerstedt, M.: Optimal Timing Control of Interconnected, Switched Systems with Applications to Robotic Marionettes. In: Workshop on Discrete Event Systems, Gothenburg, Sweden (May 2008)
Martin, P., de la Croix, J.P., Egerstedt, M.: MDLn: A Motion Description Language for Networked Systems. In: Proceedings of 47th IEEE Conference on Decision and Control (December 2008)
Moeseke, P.V., de Ghellinck, G.: Decentralization in Separable Programming. Econometrica 37(1), 73–78 (1969)
Rantzer, A.: On Price Mechnanisms in Linear Quadratic Team Theory. In: IEEE Conference on Decision and Control, New Orleans, LA (December 2007)
Shaikh, M.S., Caines, P.: On Trajectory Optimization for Hybrid Systems: Theory and Algorithms for Fixed Schedules. In: IEEE Conference on Decision and Control (2002)
Tabuada, P., Pappas, G.J.: Linear Time Logic Control of Discrete-time Linear Systems. IEEE Transactions on Automatic Control 51(12), 1862–1877 (2006)
Xu, X., Antsaklis, P.J.: Optimal Control of Switched Systems via Nonlinear Optimization Based on Direct Differentiations of Value Functions. Int. J. of Control 75, 1406–1426 (2002)
Yamane, K., Hodgins, J.K., Brown, H.B.: Controlling a Marionette with Human Motion Capture Data. In: International Conference on Robotics and Automation, vol. 3, pp. 3834–3841 (2003)
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Martin, P., Egerstedt, M. (2009). Optimization of Multi-agent Motion Programs with Applications to Robotic Marionettes. In: Majumdar, R., Tabuada, P. (eds) Hybrid Systems: Computation and Control. HSCC 2009. Lecture Notes in Computer Science, vol 5469. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00602-9_19
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DOI: https://doi.org/10.1007/978-3-642-00602-9_19
Publisher Name: Springer, Berlin, Heidelberg
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