On the statistical and Fourier modelling of robot motion

A method for the study and optimization of manipulator trajectories is developed. The novel feature resides in the modelling formulation. Standard system descriptions are based on a set of differential equations which, in general, require laborious computations and may be difficult to analyze. Moreover, the derived algorithms are suited to ´deterministic´ tasks, such as those appearing in a repetitive work, and are not well adapted to a ´random´ operation that occurs in intelligent systems interacting with an unstructured and changing environment. These facts motivate the development of alternative models based on distinct concepts. The proposed embedding of statistics and a Fourier transform gives a new perspective towards the calculation and optimization of the robot trajectories in manipulating tasks.