COMPUTED TORQUE CONTROL OF UNDER-ACTUATED DYNAMICAL SYSTEMS MODELED BY NATURAL COORDINATES

The under-actuated systems have less control inputs than degrees of freedom. We assume that the investigated under-actuated systems have desired outputs of the same number as inputs. In spite of the fact that the inverse dynamical calculation leads to the solution of a system of differential algebraic equations (DAE), the desired control inputs can be determined uniquely by the method of computed torques. We often use natural (Cartesian) coordinates to describe the configuration of the robot, while a set of algebraic equations represents the geometric constraints. In this modeling approach the mathematical model of the dynamical system itself is also a DAE. The method of computed torque control with a PD controller is applied to under- actuated systems described by natural coordinates. The inverse dynamics is solved via the backward Euler discretization of the DAE system for which a general formalism is proposed. Some results are presented in the form of a case study for a cart-pole system and confirmed by numerical simulation.