Visualization of Linear Shifts of Nodal Points during Implementation of Instantaneous States of Various Configurations of an Android Robot Arm

During planning the movement of an android robot arm in an organized space, there is a need in reducing calculation time of the trajectory in the space of generalized coordinates. The indicated time significantly depends on calculation time the vector of increments of the generalized coordinates at each step of calculations in the synthesis of movements along the velocity vector. In this paper, geometric studies were carried out based on the visualization of patterns of changes in the average displacement of the nodal points of the hand mechanism of an android robot while implementing instantaneous states. On the basis of the geometric analysis of the indicated displacements, a method is proposed which makes it possible to reduce the time of iterative search for the increment vector of generalized coordinates. Also images are shown of multiple positions of arm mechanism links on the frontal and horizontal projections when implementing instantaneous states. This images allows to make a graphic interpretation of manipulator mechanism maneuverability at each point of the configuration space. Hypersurfaces in four-dimensional space are used to establish the analytical dependencies reflecting the relationship of the average displacement of manipulator mechanism nodal points and the generalized coordinates that defining the positions of the manipulator configurations. For this purpose, the equations of interpolating polynomials located in three mutually perpendicular planes are used. Based on these three interpolating polynomials, a third-order hypersurface equation is obtained, which reflects the interrelation of geometric and kinematic parameters. The article also presents the results of virtual modeling of android robot hand mechanism movement, taking into account the position of the restricted area in the AutoCAD system. The results of calculations using the obtained analytical dependencies showed a reduction in the calculation time of test tasks. The conducted studies can be used in the development of intelligent motion control systems for autonomously functioning android robots in an organized environment without the participation of a human operator.