A LIE GROUP FORMULATION OF THE NEWTON-EULER EQUATIONS AND ITS APPLICATION TO ROBOT DYNAMICS

Based on the screw theory, this paper presents a Lie group formulation for robot dynamics. Regarding the screws and co-screws as elements of se(3) and its dual se* (3), the shifting law and change-of-coordinates of screw quantities can be uniformly interpreted as the adjoint transformations associated with pure translation and rotation of rigid displacements, respectively. The acceleration screw which enables the Newton-Euler equations of a rigid body to behave in a screw-like manner, is defined with intuitive interpretations. As a result, the advantages of Lie group formulation in robot kinematics can be extended to dynamics, so that both kinematics and dynamics can be formulated about an arbitrary point initially and then transformed to any other. Based on the principle of virtual work, the system N-E equations can be solved conveniently for both forward and inverse dynamics of serial robots. By taking advantage of the adjoint representations for the Lie algebra and its operations, only matrix calculations are required, avoiding the ad hoc definitions and notational conventions, to derive the system dynamic equations.