This paper tackles the problem of motion planning and control of a car-like robot in an obstacle-ridden workspace. A kinematic model of the vehicle, governed by a homogeneous system of first-order differential equations, is used. A solution to the multi-tasking problem of target convergence, obstacle avoidance, and posture control is then proposed. The approach of solving the problem is two-fold. Firstly, a novel velocity algorithm is proposed to drive the car-like robot from its initial position to the target position. Secondly, a single layer artificial neural network is trained to avoid disc-shaped obstacles and provide corresponding weights, which are then used to develop a function for the steering angles. Thus, our method does not need a priori knowledge of the environment except for the goal position. With the help of the Direct Method of Lyapunov, it is shown that the proposed forms of the velocity and steering angle ensure point stability. For posture stability, we model the two parallel boundaries of a row-structured parking bay as continua of disk-shaped obstacles. Thus, our method is extendable to ensuring posture stability, which gives the desired final orientation. Computer simulations of the generated path are presented to illustrate the effectiveness of the method.