This paper presents a novel path planning algorithm for a car-like mobile robot describing optimal paths using forward and backward motion combined. Path planning for tracking a mobile robot is an important part of an autonomous control system, especially when precision and high energy performance is required, considering several constraints depending on the robot dynamics and the environment. The proposed algorithm uses curves and straight lines, which perfectly describe the desired minimum-length and then applying feedback linearization techniques to design a controller for generating the correct value of robot velocity and steering angle. Simulations are presented to validate the algorithm, leading the mobile robot to describe the optimal trajectory under different working conditions, verifying the effectiveness of the proposed control method.