GROUP THEORETICAL APPROACH IN USING CANONICAL-TRANSFORMATIONS AND SYMPLECTIC-GEOMETRY IN THE CONTROL OF APPROXIMATELY MODELED MECHANICAL SYSTEMS INTERACTING WITH AN UNMODELLED ENVIRONMENT

In spite of its simpler structure than that of the Euler-Lagrange equa tions-based model, the Hamiltonian formulation of Classical Mechanics (CM) gained only Limited application in the Computed Torque Control (C TC) of the rather conventional robots. A possible reason for this situ ation may be, that while the independent variables of the Lagrangian m odel are directly measurable by common industrial sensors and encoders , the Hamiltonian canonical coordinates are not measurable and can als o not be computed in the lack of detailed information on the dynamics of the system under control. As a consequence, transparent and lucid m athematical methods bound to the Hamiltonian model utilizing the speci al properties of such concepts as Canonical Transformations, Symplecti c Geometry, Symplectic Group, Symplectizing Algorithm, etc. remain out of the reach of Dynamic Control approaches based on the Lagrangian mo del. In this paper the preliminary results of certain recent investiga tions aiming at the introduction of these methods in dynamic control a re summarized and illustrated by simulation results. The proposed appl ication of the Hamiltonian model makes it possible to achieve a rigoro us deductive analytical treatment up to a well defined point exactly v alid for a quite wide range of many different mechanical systems. From this point on it reveals such an ample assortment of possible non-ded uctive, intuitive developments and approaches even within the investig ations aiming at a particular paradigm that publication of these very preliminary and early results seems to have definite reason, too.