The method of manipulability control of a robot

Abstract

The paper presents the results of a numerical experiment that demonstrates the effectiveness of a control algo-rithm that maintains a sufficiently high numerical value of the robot's manipulability function , which ensures «remoteness» from a singular configuration. The problem of approaching the end effector of the space manipula-tor Canadarm2, which has seven degrees of freedom (one redundant generalized coordinate), with an object mov-ing along a known trajectory, is considered. To the six parameters that determine the position and orientation of the gripper in absolute space, a «kinematic» function , depending on the relative rotation angles of the links, has been added. In this case, the kinematics equations became closed with respect to the rotation angles. The control law includes a condition for maintaining a certain numerical value that exceeds the minimum allowable value. Illustrations in the form of three-dimensional animation obtained on the basis of numerical integration of the equa-tions of controlled motion of the manipulator and the object were built using the Mathematica computer algebra system.