A geometric model of the trajectory planning for the robot´s arm

A geometric model of robot-arm trajectory planning is described. It is noted that the main task of the intellect in the sensorimotor domain is path planning on the basis of a geometric representation of the space-time, which makes it possible to replace complicated optimization calculation with geometric constructions. In the case of limb control the task involves the interrelations of four spaces, two exterior ones given by the motor task and two for their interior models. How the many-dimensional space could be presented in a machine is considered. It is supposed that the presentation must have the form of a neuron network. The neurons are conceived as specified microprocessors with few functions. There are two (or more) possible approaches to neuron modeling of space. The first one brings into correspondence separate neurons and points of space (more or less fuzzily). In the second approach one takes a finite covering of some domain in the space with balls (receptive fields) which have bell-shaped weight functions under the condition that every point of space be covered with more than n balls, which is the dimension of the space; every point is coded with the collection of its weights in the balls