Model-based trajectory planning and control of underactuated mechanical systems

The problem of trajectory planning and control design for underactuated mechanicalsystems is a nontrivial task due to the presence of passive degrees of freedom in them. Inthis thesis, the virtual holonomic constraint approach is used for the trajectory planningand control design of a typical double link underactuated mechanical system, called thePendubot. The goal is to create synchronous oscillations of both links. After modeling thesystem using Euler-Lagrangian equations of motion, the parameters of the model areidentified with optimization techniques. Using this model, the trajectory planning is donevia Virtual Holonomic Constraint approach on the basis of re-parameterization of themotion according to geometrical relations among the generalized coordinates of thesystem. And finally control design is done on the basis of a time periodic linearapproximation of the nonlinear model which is called transverse linearization in whichasymptotic stability of the origin in this linear system ensures orbital exponential stabilityof the periodic motions of the nonlinear system. Results of simulations for some of themotions are given in the last section