Iterative calculation method for constraint motion by extended Newton-Euler method and application for forward dynamics

Abstract

There are two principal methods to derivate motion of equation of robot manipulator, which are Newton-Euler (NE) method and Lagrange method. NE method treats each linkage as rigid linkage and it is possible to calculate internal force and torque not generating real motion of robot manipulator, which is a merit of NE method that Lagrange method does not have. So far, NE method has been applied to a robot of open-loop serial-linkage structure. However, the adaptation has been limited to a motion without contact of hand with environment. Although robot task based on contact with environment, for example assembly task, grinding task, is important, it is not formulated in the way of NE method. So, this paper proposes iterative calculation method for representing constraint dynamical motion of robot manipulator utilizing inverse dynamic calculation method-NE method, leading and enabling the forward dynamics calculation of constraint motions to be dealt recursively through proposed extended NE method for constraint motions, with no use of explicit representation of equation of motions. We applied this method to 2-linkage and 3-linkage manipulators and evaluated its validity by numerical simulations. Also, we calculated inertia force acting on each linkage during constraint motion and evaluated validity of those values.

Keywords

• newton-euler method
• constraint motion
• iterative calculation
• manipulator
• internal force