A Lie group formulation of the dynamics of cooperating robot systems

Abstract

In this article we formulate the dynamics of cooperating robot systems using standard ideas and notation from the theory of Lie groups. Utilizing the geometric framework introduced in Park et al. (1995), we develop the equations of motion for a system of N cooperating robots manipulating a common workpiece. In the resulting dynamic equations the Jacobian, mass matrix, Coriolis, and gravity terms of the closed chain system admit succinct block-triangular factorizations in terms of the basic linear operators on se(3), the Lie algebra of the Euclidean group SE(3). The resulting closed-form equations provide a high-level description of the equations of motion that reduces the symbolic complexity without sacrificing computational efficiency.