An original O(N) formulation for simulation of robotic systems

Abstract

In the last decade a significant number of papers have been published on the efficient formulation of the inverse and forward dynamic equations of motion for robotic manipulators and in general for multibody systems, in view of real-time control or real-time simulation of the system. Until recently these dynamic formulations have been confined to serial computers. The breakthrough of parallel computers however causes to reconsider dynamical formulations from this new perspective. This paper presents an original order N formulation for simulation of the dynamics of a robotic manipulator without inversion of the massmatrix. The proposed algorithm differs from the well-known recursive O( N ) methods. Instead of a backward and two forward recursions, this method requires only one forward recursion and the solution of a small linear system of algebraic equations to generate the equations of motion for open-loop systems. The computations within this forward recursion loop can easily be arranged for parallel processing resulting in a very low computational load. The proposed method can be used for rigid multibody systems in tree structure with arbitrary types of joints. This algorithm also proves to be very promising in case of mechanical systems with closed loops.