Neural Networks’ Based Inverse Kinematics Solution for Serial Robot Manipulators Passing Through Singularities

Abstract

Before moving a robot arm, it is of considerable interest to know whether there are any obstacles present in its path. Computer-based robots are usually served in the joint space, whereas objects to be manipulated are usually expressed in the Cartesian space because it is easier to visualize the correct end-effector position in Cartesian coordinates than in joint coordinates. In order to control the position of the end-effector of the robot, an inverse kinematics (IK) solution routine should be called upon to make the necessary conversion (Fu et al., 1987). Solving the inverse kinematics problem for serial robot manipulators is a difficult task; the complexity in the solution arises from the nonlinear equations (trigonometric equations) occurring during transformation between joint and Cartesian spaces. The common approach for solving the IK problem is to obtain an analytical close-form solution to the inverse transformation, unfortunately, close-form solution can only be found for robots of simple kinematics structure. For robots whose kinematics structures are not solvable in close-form; several numerical techniques have been proposed; however, there still remains several problems in those techniques such as incorrect initial estimation, convergence to the correct solution can not be guarantied, multiple solutions may exist and no solution could be found if the Jacobian matrix was in singular configuration (Kuroe et al., 1994; Bingual et al., 2005). A velocity singular configuration is a configuration in which a robot manipulator has lost at least one motion degree of freedom DOF. In such configuration, the inverse Jacobian will not exist, and the joint velocities of the manipulator will become unacceptably large that often exceed the physical limits of the joint actuators. Therefore, to analyze the singular conditions of a manipulator and develop effective algorithm to resolve the inverse kinematics problem in the singular configurations is of great importance (Hu et al., 2002). Many research efforts have been devoted towards solving this problem, one of the first algorithms employed was the Resolved Motion Rate-Control method (Whitney, 1969), which uses the pseudoinverse of the Jacobian matrix to obtain the joint velocities corresponding to a given end-effector velocity, an important drawback of this method was