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This article deals with the reactive control of an autonomous robot, which moves safely in a crowded real-world unknown environment and reaches a specified target by avoiding static as well as dynamic obstacles. The inputs to the proposed neural controller consist of left, right, and front obstacle distance to its locations and the target angle between a robot and a specified target acquired by an array of sensors. A four-layer neural network has been used to design and develop the neural controller to solve the path and time optimization problem of mobile robots, which deals with cognitive tasks such as learning, adaptation, generalization, and optimization. The back-propagation method is used to train the network. This article analyses the kinematical modelling of mobile robots as well as the design of control systems for the autonomous motion of the robot. Training of the neural net and control performances analysis were carried out in a real experimental set-up. The simulation results are compared with the experimental results and they show very good agreement.