Abstract
A measure differential inclusion (MDI) based modeling approach for rigidbody mechanical systems will be introduced, that can exhibit autonomous or controlled mode transitions, accompanied by discontinuities on velocity and acceleration level. The hybrid optimal control necessitates the consideration of an uncommon concept of control, namely, controls of unbounded, impulsive and set-valued type. Examples to manipulators and wheeled robots are presented.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others

References
Alart, P., Curnier, A.: A mixed formulation of frictional contact problems prone to newton-like solution methods. Computer Methods in Applied Mechanics and Engineering 92, 353–375 (1991)
Aubin, J.-P., et al.: Impulse Differential Inclusions: A Viability Approach to Hybrid Systems. IEEE Trans. on Automatic Control 47, 2–20 (2002)
Bemporad, A., Morari, M.: Control of systems integrating logic, dynamic, and constraints. Automatica 35, 407–427 (1999)
Bengea, S.C., DeCarlo, R.A.: Optimal Control of switching systems. Automatica 41, 11–27 (2005)
Borelli, F., et al.: Dynamic programming for constrained optimal control of discrete-time linear hybrid systems. Automatica 41, 1709–1721 (2005)
Branicky, M.S., Borkar, V.S., Mitter, S.M.: A unified framework for hybrid control: Model and optimal theory. IEEE Transactions on Automatic Control 43, 31–45 (1998)
Brogliato, B.: Non-smooth Impact Mechanics. Lecture Notes in Control and Information Sciences. Springer, Heidelberg (1996)
Brogliato, B., et al.: On the equivalence between complementarity systems, projected systems and differential inclusions. Systems and Control Letters 55, 45–51 (2006)
Clarke, F.H.: Optimization and Nonsmooth Analysis. SIAM Classics in Applied Mathematics. Wiley, New York (1983)
Cottle, R.W., Pang, J.-S., Stone, R.E.: The Linear Complementarity Problem. Academic Press, Boston (1992)
De Schutter, B., Heemels, W.P.M.H., Bemporad, A.: On the equivalence of linear complementarity problems. Operations Research Letters 30, 211–222 (2002)
Ferrari-Trecate, G., et al.: Analysis of discrete-time piecewise affine and hybrid systems. Automatica 38, 2139–2146 (2002)
Heemels, W.P.M.H., De Schutter, B., Bemporad, A.: Equivalence of hybrid dynamical models. Automatica 37, 1085–1091 (2001)
Glocker, C.: Set-Valued Force Laws, Dynamics of Non-Smooth Systems. Lecture Notes in Applied Mechanics, vol. 1. Springer, Berlin (2001)
Glocker, C.: On Frictionless Impact Models in Rigid-Body Systems. Phil. Trans. Royal Soc. Lond. A359, 2385–2404 (2001)
Glocker, C., Pfeiffer, F.: Multiple Impacts with Friction in Rigid Multibody Systems. Nonlinear Dynamics 7, 471–497 (1995)
Glocker, C.: The Geometry of Newtonian Impacts with Global Dissipation Index for Moving Sets. In: Proc. of the Int. Conf. on Nonsmooth/ Nonconvex Mechanics, Thessaloniki, pp. 283–290 (2002)
Miller, B.M., Bentsman, J.: Optimal control problems in hybrid systems with active singularities. Nonlinear Analysis 65, 999–1017 (2006)
Moreau, J.J.: Quadratic programming in mechanics: Dynamics of one-sided constraints. SIAM Journal of Control 4, 153–158 (1966)
Moreau, J.J.: Bounded Variations in time. In: Moreau, J.J., Panagiotopoulos, P.D., Strang, G. (eds.) Topics in Non-smooth Mechanics, pp. 1–74. Birkhäuser, Basel (1988)
Moreau, J.J.: Unilateral Contact and Dry Friction in Finite Freedom Dynamics. In: Non-smooth Mechanics and Applications. CISM Courses and Lectures, vol. 302, Springer, Wien (1988)
Murty, K.G.: Linear Complementarity, Linear and Nonlinear Programming. Helderman-Verlag, Berlin (1988)
Potočnik, B., et al.: Hybrid Modelling and optimal control of a multiproduct Batch plant. Control Engineering Practice 12, 1127–1137 (2004)
Rockafellar, R.T.: Convex Analysis, Princeton Landmarks in Mathematics. Princeton University Press, Princeton (1970)
Shahid Shaikh, M., Caines, P.E.: On the optimal control of hybrid systems: Optimization of trajectories, switching times, and location schedules. In: Maler, O., Pnueli, A. (eds.) HSCC 2003. LNCS, vol. 2623, pp. 466–481. Springer, Heidelberg (2003)
Yunt, K., Glocker, C.: Trajectory Optimization of Hybrid Mechanical Systems using SUMT. In: IEEE Proc. of Advanced Motion Control, Istanbul, pp. 665–671. IEEE Computer Society Press, Los Alamitos (2006)
Yunt, K., Glocker, C.: Time-Optimal Trajectories of a Differential-Drive Robot. In: Proceedings of the 2005 ENOC Conference, Eindhoven, Netherlands (2005)
Yunt, K., Glocker, C.: A combined continuation and penalty method for the determination of optimal hybrid mechanical trajectories. In: IUTAM Symposium on Dynamics and Control of Nonlinear Systems with Uncertainty, Nanjing, China, 2006. IUTAM Bookseries, vol. 2, Springer, Heidelberg (2007)
Yunt, K.: Trajectory Optimization of structure-variant mechanical Systems. In: Proc. on of Int. Workshop on Variable Structure Systems, Alghero, Italy, pp. 298–303 (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Yunt, K., Glocker, C. (2007). Modeling and Optimal Control of Hybrid Rigidbody Mechanical Systems. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds) Hybrid Systems: Computation and Control. HSCC 2007. Lecture Notes in Computer Science, vol 4416. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71493-4_47
Download citation
DOI: https://doi.org/10.1007/978-3-540-71493-4_47
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-71492-7
Online ISBN: 978-3-540-71493-4
eBook Packages: Computer ScienceComputer Science (R0)