This paper gives details regarding a mathematical framework to achieve reactive autonomous navigation of electric cyber-vehicles that interact in urban environments. The framework combines continuoustime kinematic equations with social potential fields that yield repulsive and attractive forces. On one hand, lane lines, parked cars, traffic signals/signs and so forth define repulsive forces against static obstacles. On the other hand, walking people, moving cars/bikes, etc, determine dynamic obstacles. In addition, attractive potential forces are artificially generated in relation to a set of goal destinations. Generally, potential fields are modeled considering the vehicle as a particle in motion; the proposed scheme integrates a general forward-kinematics solution for different inertial systems, which is combined with the vehicle geometric constraints. The proposed motion model combines a scheme for controlling both: the desired and the maximal allowed vehicle’s velocity. The latter, is because of potential fields raise so large when suddenly situations associated to accidents happen. A multi-sensor fusion scheme is proposed in terms of redundancy of observed features to adaptively compute numeric weights to contribute on yielding a more suitable navigation function. The magnitudes of weights are correlated with the perception vehicle’s angle of motion. The proposed model allows an easy implementation to achieve reliability and security in autonomous driving control, and the capability of free-collision navigation in highly dynamic environments. Simulation results are shown.