SMOOTH TRAJECTORIES FOR HIGH-PERFORMANCE MULTI-AXES AUTOMATIC MACHINES

In this paper, a novel method for the computation of 3D trajectories for high performance automatic machines and robots is presented. This approach, based on the so called smoothing splines, allows to construct a trajectory as smooth as possible (in terms of magnitude of the maximum accelerations produced) while maintaining the deviation of the geometrical path with respect to the given data points below a prescribed tolerance. The main contribution of this paper consists in the procedure for the determination of the free parameters, on which the optimization problem is based, in order to obtain a solution optimal with respect to the characteristics of an automatic machine (dynamical behavior of the mechanical system, purpose of the manufacturing process, etc.). Moreover, the issues tied to the implementation on a computer numerical control have been considered, paying particular attention to the computational complexity of the proposed algorithm. In particular, the computation of the overall trajectory has been subdivided in different parts, whose results are properly merged together to give the desired trajectory.