Study of the Surfaces Defining the Area Boundaries of the Allowable Configurations of the Mobile Manipulator Mechanism with the Available Forbidden Zones

Abstract

In this work the authors propose a method for analyzing information about the mechanism of the manipulator's positions and use of the restricted area in the field to set permissions in the configuration space of the generalized coordinates. Permissions' configuration reflects a model of the environment and is used in a system, which autonomously generates a robot's movement in accordance with the job description. Features of the manipulator are associated with the execution of the tasks in advance and on the eve of implementation of a virtually simulated movement. If the desired job is virtually modeled, it is executed as a sequence of operations with the use of the force-torque control algorithm and sensitizing system. At the same time, virtual modeling avoids unjustified and unnecessary movement of the manipulator in the presence of a motor redundancy. An approximate method for setting the resolved configurations is used in the collection of the planes and surfaces of the second order, limiting this area. The developed mathematical model of the area made feasible the configurations based on the use of the sets of inequalities and the unit of R-functions. Analysis of the relative position of the manipulator's motion paths and the field configurations admitted in the space of the generalized coordinates, allows predicting deadlocks, in which an arm can move. The results of the computational experiments and studies prove a reduction of the calculation time of the generalized vector of velocity and the trajectory of the manipulator motion in the phase of analysis of the mechanism of virtual manipulator interaction with the known environment. The analytical dependencies can be used in the intelligent control systems for the robots operating autonomously in the presence of the forbidden zones.