A geometrical formulation of the dynamical equations describing kinematic chains

Abstract

A general expression for the kinetic energy associated with a kinematic chain is developed and it is used to derive the dynamical equations. In the authors' expression for the kinetic energy, the dependence on the chain's parameters is particularly transparent. Such a representation is desirable in applications such as adaptive control and robot calibration. The kinetic energy is expressed using standard geometric operations, e.g., group multiplication, exponentiation, and adjoint mappings. Lie-theoretic identities are used to simplify the expressions for those derivatives of the inertia matrix which appear in Lagrange's equations. An elegant expression for the Coriolis terms is provided. The equations of motion for a serial chain are written in a general form which requires no adaptation for specific problems. This representation to classify dynamically balanced chains.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>