Smoothing the robot center mass trajectory by genetic selection

Abstract

The paper examines a calculating method for an articulated construction kinematics and application of a genetic algorithm to provide the required trajectory of the specified structure points. First, we describe all types of articulated constructions segments, their mathematical description and construction on their basis of nonlinear equations systems that describing the articulated construction kinematics. The obtained nonlinear systems are solved by repeated application of Newton's method for nonlinear equations. The built algorithm is used to calculate the kinematics of the articulated construction which is a limb model of kinetic sculptures by Theo Jansen. The calculation purpose is optimum parameters selection of a limb which will allow applying it for a robot model with four supporting extremities. We built a reference point trajectory fitness function and constructed the best trajectory which provides rectilinear movement of a robot body relative to the ground by the method of genetic selection. Theoretical calculations are supported by numerical modeling and visualization. There is a graph illustrating the successful application of the developed model at the article end. A real prototype of a stepping robot with four extremities by means of 3D printing of components and subsequent assemblage is created on the basis of theoretical considerations.