## 2 Related Work  
Several previous studies on active maneuvering not directly related to emergency maneuvers can be found in the open literature. In the case of [6], we can find a mathematical evaluation in which some interesting properties of active maneuvering are obtained by applying _Optimal Control theory_ (OC) to the calculation of optimum trajectories in order to obtain a given final heading. Satisfying either minimum time or minimum distance, the results in [6] showed that trajectory tracing for just one vehicle when looking for a specific heading can be useful when dealing with general robots, but not as much when talking about vehicles, which essentially would expect to avoid an accident, regardless of the final heading. In [7] the authors proposed an approach to solve the problem of tracing the trajectory for a car between two fixed points. This type of problem is a BVP (_Boundary Value Problem_) in which the main concern is to study the trajectory between two fixed points while optimizing the time employed to complete this trajectory according to some physical constraints in terms of maximum acceleration. This evaluation gave a useful hint on the analysis of OC problems by providing a mathematical functional based on nearly-time optimality for the solution of the problem. However, this formulation of the problem suffers from convergence issues as well as tight constraints in values for mobility parameters (such as speed). Furthermore, fixed final boundaries are rarely met under real circumstances due to the obvious variability of the environmental conditions. Another approach for the establishment of an optimal control law for a pair of [PERSON]'s vehicles (cars moving characterized by a sinusoidal differential equations model) is found in [8], where authors obtain trajectories that transfer the two [PERSON]'s vehicles from pre-established initial positions to fixed final locations in space. The optimization goals in [8] included the minimization of acceleration, speed and distance along the trajectory and the maximization of the distance between the two vehicles during the maneuver. This is essentially a BVP where there is some sort of cooperative trajectory optimization. A more closely related work is found in [4], where the collision avoidance problem is formulated as an IVP (_Initial Value Problem_) in which a vehicle divides the trajectory tracing procedure into three stages (each one with its own functional). The first one consists of steering to simply avoid the collision against the obstacle; the second phase affords the reorientation of the trajectory to avoid colliding against the lateral protections; and the last one deals with relocating the car in the same lane it was circulating before. Moreover, this work provided a realistic mobility model of the vehicle. In fact, the goal of the paper was to study the advantages of additional actuated degrees of freedom. According to general path planning techniques, we find in the literature some important works regarding online trajectory tracing by using fuzzy logic. That is the case of the research led by [PERSON] in [9], where a power-steering control architecture for autonomous driving is proposed. Integrated into two different layers (target position calculation and vehicle positioning), the offered architecture showed by experimentation that the combination of different sensing sources (GPS, vision...) by artificial intelligence provides a reliable behavior of the car in transit. Another work of the same authors was presented in [10], where the associated AUTOIA architecture was introduced in detail, including the recent advances in terms of specific car maneuvers designed for autonomous car control in such vehicles.