Tracking Control of Fully-actuated Mechanical port-Hamiltonian Systems using Sliding Manifolds and Contraction

In this paper, we propose a novel trajectory tracking controller for fully-actuated mechanical port-Hamiltonian (pH) systems, which is based on recent advances in contraction-based control theory. Our proposed controller renders a desired sliding manifold (where the reference trajectory lies) attractive by making the corresponding error system partially contracting. Finally, we present numerical simulation results where a SCARA robot is commanded by our proposed tracking control law.

[1]  Jacquelien M. A. Scherpen,et al.  Adaptive tracking control of fully actuated port-Hamiltonian mechanical systems , 2010, 2010 IEEE International Conference on Control Applications.

[2]  Kazunori Sakurama,et al.  Trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations , 2001, Autom..

[3]  Kvetoslav Belda,et al.  Mathematical modeling of industrial robots based on Hamiltonian mechanics , 2016, 2016 17th International Carpathian Control Conference (ICCC).

[4]  Arjan van der Schaft,et al.  Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems , 2002, Autom..

[5]  Lorenzo Marconi,et al.  Incremental passivity and output regulation , 2006, CDC.

[6]  Rodolphe Sepulchre,et al.  A Differential Lyapunov Framework for Contraction Analysis , 2012, IEEE Transactions on Automatic Control.

[7]  Arjan van der Schaft,et al.  Speed Observation and Position Feedback Stabilization of Partially Linearizable Mechanical Systems , 2010, IEEE Transactions on Automatic Control.

[8]  Jean-Jacques E. Slotine,et al.  On partial contraction analysis for coupled nonlinear oscillators , 2004, Biological Cybernetics.

[9]  Rob Dekkers,et al.  Control of Robot Manipulators in Joint Space , 2005 .

[10]  A. Schaft,et al.  Variational and Hamiltonian Control Systems , 1987 .

[11]  Vadim I. Utkin,et al.  Sliding mode control , 2004 .

[12]  A. Schaft,et al.  The Hamiltonian formulation of energy conserving physical systems with external ports , 1995 .

[13]  M. Spong,et al.  Integral manifolds of singularly perturbed systems with application to rigid-link flexible-joint multibody systems , 2000 .

[14]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[15]  Arjan van der Schaft,et al.  Port-Hamiltonian Systems Theory: An Introductory Overview , 2014, Found. Trends Syst. Control..

[16]  B. Jayawardhana.  Tracking and disturbance rejection for passive nonlinear systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[17]  Jean-Jacques E. Slotine,et al.  On Contraction Analysis for Non-linear Systems , 1998, Autom..

[18]  Romeo Ortega,et al.  A globally exponentially stable tracking controller for mechanical systems using position feedback , 2013, 2013 American Control Conference.

[19]  Thor I. Fossen,et al.  A Tutorial on Incremental Stability Analysis using Contraction Theory , 2010 .

[20]  Romeo Ortega,et al.  Immersion and Invariance Stabilization of Nonlinear Systems Via Virtual and Horizontal Contraction , 2017, IEEE Transactions on Automatic Control.

[21]  Ricardo G. Sanfelice,et al.  Convergence of Nonlinear Observers on $\BBR^{n}$ With a Riemannian Metric (Part I) , 2012, IEEE Transactions on Automatic Control.

[22]  Mohammad Javad Yazdanpanah,et al.  Trajectory tracking of a class of port Hamiltonian systems using Timed IDA-PBC technique , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[23]  Ronald J. Patton,et al.  A Note on Hurwitz Stability of Matrices , 1998, Autom..

[24]  Bayu Jayawardhana,et al.  Tracking and disturbance rejection for fully actuated mechanical systems , 2008, Autom..

[25]  Romeo Ortega,et al.  Passivity-based Control of Euler-Lagrange Systems , 1998 .

[26]  Vadim I. Utkin,et al.  Sliding Modes in Control and Optimization , 1992, Communications and Control Engineering Series.

[27]  Suguru Arimoto.  Control Theory of Nonlinear Mechanical Systems , 1996 .

[28]  Mohamed I. El-Hawwary,et al.  Reduction theorems for stability of closed sets with application to backstepping control design , 2013, Autom..

[29]  David Navarro-Alarcon,et al.  Passivity-based tracking controllers for mechanical systems with active disturbance rejection , 2015 .

[30]  Bayu Jayawardhana,et al.  Transverse Exponential Stability and Applications , 2016, IEEE Transactions on Automatic Control.

[31]  J. Slotine,et al.  On the Adaptive Control of Robot Manipulators , 1987 .

[32]  Arjan van der Schaft,et al.  Control by Interconnection and Standard Passivity-Based Control of Port-Hamiltonian Systems , 2008, IEEE Transactions on Automatic Control.

[33]  Romeo Ortega,et al.  Passivity of Nonlinear Incremental Systems: Application to PI Stabilization of Nonlinear RLC Circuits , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.