In recent years, artificial neural networks have received a great deal of attention for their ability to perform nonlinear mappings. In trajectory control of robotic devices, neural networks provide a fast method of autonomously learning the relation between a set of output states and a set of input states. In this paper, we will apply the cognitive approach to solve the problems related to the position controller using the inverse geometrical model. In order to control a robot manipulator to accomplish a task, trajectory planning is required in advance or in real time. The desired trajectory is usually described in Cartesian coordinates and needs to be converted to joint space for the purpose of analyzing and controlling the system behavior. In this paper, we use the memory neural network MNN to solve the optimization problem concerning the inverse of the direct geometrical model of the redundant manipulator subject to some constraints. Our approach offers substantially better accuracy, avoids the computation of the inverse or pseudoinverse Jacobian matrix and do not produce problems such as singularity, redundancy, and considerably increased computational complexity, etc.