Dynamic modeling of SCARA robot based on Udwadia–Kalaba theory

With the aim of dynamic modeling of the SCARA robot subjected to space trajectory constraint to satisfy repetitive tasks with higher accuracy, a succinct and explicit equation of motion based on Udwadia–Kalaba theory is established. The trajectory constraint, which is regarded as the external constraints imposed on the system, is integrated into the dynamic modeling of the system dexterously. The explicit expression of constraint torques required to satisfy constraints and explicit dynamic equation of the system without Lagrange multiplier are obtained. However, constraint violation arises when the initial conditions are incompatible with the constraint equations. Baumgarte stabilization method is considered for constraint violation suppression. Simulations of the varying law of the generalized coordinate variables and the trajectories of the SCARA robot are performed to demonstrate the simplicity and accuracy of the method.

[1]  Firdaus E. Udwadia,et al.  Methodology for Satellite Formation-Keeping in the Presence of System Uncertainties , 2014 .

[2]  Ettore Pennestrì,et al.  An application of the Udwadia-Kalaba dynamic formulation to flexible multibody systems , 2010, J. Frankl. Inst..

[3]  W. Blajer.  Methods for constraint violation suppression in the numerical simulation of constrained multibody systems – A comparative study , 2011 .

[4]  C. Pappalardo.  A natural absolute coordinate formulation for the kinematic and dynamic analysis of rigid multibody systems , 2015 .

[5]  Parviz E. Nikravesh,et al.  Some Methods for Dynamic Analysis of Constrained Mechanical Systems: A Survey , 1984 .

[6]  R. Oprea.  A constrained motion perspective of railway vehicles collision , 2013 .

[7]  J. Baumgarte.  Stabilization of constraints and integrals of motion in dynamical systems , 1972 .

[8]  Jin Huang,et al.  Udwadia-Kalaba Approach for Parallel Manipulator Dynamics , 2013 .

[9]  Firdaus E. Udwadia,et al.  Control of Uncertain Nonlinear Multibody Mechanical Systems , 2014 .

[10]  Firdaus E. Udwadia,et al.  What is the General Form of the Explicit Equations of Motion for Constrained Mechanical Systems , 2002 .

[11]  T. Kane.  Dynamics of Nonholonomic Systems , 1961 .

[12]  R. Kalaba,et al.  A new perspective on constrained motion , 1992, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[13]  Firdaus E. Udwadia,et al.  A Closed-Form Approach to Tracking Control of Nonlinear Uncertain Systems Using the Fundamental Equation , 2012 .

[14]  D. J. Braun,et al.  Eliminating Constraint Drift in the Numerical Simulation of Constrained Dynamical Systems , 2009 .

[15]  Moharam Habibnejad Korayem,et al.  A new approach for dynamic modeling of n-viscoelastic-link robotic manipulators mounted on a mobile base , 2015 .

[16]  R. Kalaba,et al.  On the foundations of analytical dynamics , 2002 .

[17]  Firdaus E. Udwadia,et al.  Explicit solution to the full nonlinear problem for satellite formation-keeping , 2010 .

[18]  Aaron D. Schutte,et al.  Constrained Motion of Tethered Satellites , 2005 .

[19]  Richard M. Murray,et al.  A Mathematical Introduction to Robotic Manipulation , 1994 .

[20]  Han Zhao,et al.  Application of the Udwadia–Kalaba approach to tracking control of mobile robots , 2016 .

[21]  Shih-Tin Lin,et al.  A PID Type Constraint Stabilization Method for Numerical Integration of Multibody Systems , 2011 .

[22]  Jia Liu,et al.  Simple method to the dynamic modeling of industrial robot subject to constraint , 2016 .

[23]  Firdaus E. Udwadia,et al.  Dynamics and control of a multi-body planar pendulum , 2015 .

[24]  Han Zhao,et al.  Dynamic modeling and simulation of multi-body systems using the Udwadia-Kalaba theory , 2013 .