Case studies for computed torque control of constrained underactuated systems

Abstract

Computed torque control (CTC) method is an efficient technique for trajectory tracking control of robot manipulators. As a model-based control, CTC needs the inverse dynamics calculation of the dynamical system. A special group of these systems is formed by the underactuated ones, in which the number of independent control inputs is lower than the degrees of freedom of the system. In these systems, the inverse dynamics calculation is a challenging task, because the inverse calculation leads to the solution of a differential-algebraic equation (DAE). Complex robotic structures like the ones with closed kinematic loops are generally modeled by redundant descriptor coordinates instead of the Lagrangian approach when a minimum set of generalized coordinates are chosen. The use of non-minimum set of descriptor coordinates requires the introduction of a set of geometric constraints, which are expressed in the form of algebraic equations. Thus, the mathematical model of the robotic structure itself is also a DAE. A few different CTC method based algorithms are studied. The control algorithms are compared in the case of the simplest possible linear dynamical system with special attention to the choice of the descriptor coordinate set.