The purpose of this study is to minimize the arc length for the path described by the model of a robot platform when the path is constrained to have smooth transitions given by sigmoid functions. The optimization required a proof of stability for the resulting control law, the selection of the best sigmoid function among ten functions, and the definition of two gains necessary to parameterize the control law. The optimization was carried out by simulating the system under several kinematic and dynamical conditions, and the best sigmoid function was a hyperbolic tangent. Thus, the motion control first implied the simulation of a reference model to define an optimal path, and later the control of an actual robot platform, which followed the optimal path. The use of the optimized path reduced the complexity of the controller while allowing natural and intuitive paths for the robot platform.