资源描述
Application of switching control for automatic pre-crashcoll ision avoidance in cars
Abstract：In recent years, a number of European Com-mission funded projects have investigated how the ob-jective of increasing pedestrians’ safety can be attainedby means of intelligent driver assistance systems. Theresults already available show that, while in the long range case, a warning system, to alert the driver as soon as a vulnerable road user (VRU) is detected and classified by the sensors, can be sufficient to reduce the mandatory in pre–crash situations. The generation of collision avoidance manoeuvres appears to be a suit-able application for switching control. In this paper, in particular, an automatic pre–crash collision avoidance
strategy for cars based on sliding mode control is pre-sented. It produces a collision avoidance manoeuvre, if feasible, or, otherwise, an emergency braking to reduce the energy at the impact. Experimental results based on a scaled radio–controlled car are provided.
Keywords ：Automatic manoeuvre Switched control waring system emergency braking
1. Introduction
There are two types of automatic actions that a driver as-sistance system can accomplish so as to attain collision avoidance or injury severity mitigation: an emergency braking or a collision avoidancemanoeuvre. The effect of collision velocity on injury severity is well–known,and a number of research projects have been devoted to design warning systems to alert the driver, in case of possible collision with pedestrians, so as to reduce the energy at the impact [1, 3, 10]. Nevertheless, the benefits of an emergency braking have been analyzed on a statistical basis in [9], under the assumptions that the driver assistance system is able to react faster than the attentive driver, and capable of performing a full braking, while the average driver usually exploits only the 60% of the maximum deceleration of the vehicle.In a previous work, the second type of automatic action, namely the generation of collision avoidance manoeuvres, has been analyzedwith reference to a pas-senger car [6]. The car is supposed to be equipped with sensors able to measure the relative position and rela-tive velocity between the car and a number of moving VRUs.In the present paper a more general automatic pre–crash collision avoidance strategy is analyzed. It is based on the assumption that the car is equipped withfront and lateral sensors (radar, laser or stereo vision systems, for instance), so that both the pedestrians crossing the road and other moving or static objects(like cars arriving in the opposite direction or from behind, parked cars, pavements or road borders) can be detected. The automatic strategy is realized only when,on the basis of the data available at the current time instant, it turns out that a future collision is going to occur in 1 s or less, assuming that the time necessary to practically generate the automatic action is around 0.3–0.4 s, and that a lower bound of the driver reaction time is 1.2 s. Otherwise, it is supposed that a warning generation strategy could be activated。
The designed control system, depicted in Fig. 1, ischaracterized by a supervisor which receives the data from the car sensors, detects the possible collision, and makes the decision on which action, between the emer-gency braking and the collision avoidance manoeuvre,is the appropriate choice in the current situation. It can be viewed as a development of the scheme described in[5]. In case a collision avoidance manoeuvre is neces-sary and feasible, the supervisor activates a high levelcontrollerwhich, on the basis of the data received at any sampling instant from the sensors, and of some com-puted quantities, establishes if the car has to perform the movement to avoid the obstacle, or if it has to re-turn to the original driving direction, since the obstacle
has been avoided. This implies that there are two low level controllers capable of attaining the two different aims.Both of themare designed through a slidingmode control approach [11], acting on two control variables:traction/braking force and wheels steering angle. Thevariations of both the control variables have to complywith safety rules and physical limits.
On the whole, the controlled system results in being an interesting applicative example of switching control. It has been verified in simulation and tested on a scaled(1:10) radio–controlled (R/C) car. Some results of thisexperimentation are here reported. Even if the clear limitations of the available experimental set–up and its differences with respect to a real car let the necessity of experimentation on a car prototype open, this study has been important to have a first confirmation of the possibility of actually applying an automatic switch-ing control system to the peculiar context of collision avoidance and collision mitigation in cars.
2. Collision detection
In the sequel, the following two assumptions will be considered: (A1) both the vehicle and the obstacles are moving on a two-dimensional space; (A2) their veloc-ities (modulus and direction), during the sampling in-terval, can be regarded as constant quantities.
2.1. The collision cone
The collision detection task is performed relying on the so-called collision cone. The theory underlying the construction of this cone can be briefly summarized as follows. Let us consider two point objects moving by translation on a plane (Fig. 2): let O represent the car,and F the obstacle to be avoided; let VF and VO be the respective velocities. In a polar-coordinates reference frame centered on the vehicle O, the motion of the object F with respect to the car O is described by the two speed components Vr and Vθ Vr = ˙ r = VF cos (β − θ) − VO cos (α − θ)
Vθ = r ˙ θ = VF sin (β − θ) − VO sin (α − θ)
(1)in which describe also the kinematic behavior of the seg-
mentOF. Relying on the assumption of constant speed,
it is easy to prove that
Vr0 and Vθ0 being the initial conditions, so that it can be claimed that the possibility that a collision occurs de-pends only on the initial conditions. More specifically,it is possible to prove that, under the assumption that the two considered points O and F are moving with con-
stant velocities, Vθ0 = 0 and Vr0 < 0 are a necessary and sufficient condition for collision . So, if one con-siders an initial geometry defined by the two points Oand F, with specified values for r0 and θ0, VO and VF ,and β, it is possible to determine the value of α suchthat a collision can occur in the future.
In the more complete case of collision detection be-tween a point object O and a circular one F, character-ized by a ray R (Fig. 2), the entire range of values of α which verify the condition of future collision takes thename of collision cone. In this case, the collision be-tween the two objects will occur if there exists a pointC belonging to the circle F which verifies the colli-sion condition previously mentioned. Thus, rewriting
(1) for the line OC, one has
(Vr )OC=VF cos (β−(θ + φ))−VO cos (α−(θ+φ))
(Vθ )OC=VF sin (β−(θ + φ))−VO sin (α−(θ + φ))
(3)
2.2. Application of the collision cone theory
To apply the collision cone concept to the detection of possible collisions between a car and the pedestrians crossing the road, the area occupied by the car plus some margins is represented by means of circles suit-ably positioned on the vehicle as indicated in Fig. 3(note that the front and rear circles pass through the car vertexes, while the center C2 of the circle in the middle is the medium point between C1 and C3), where also a pedestrian is depicted as a circular object. The radius
of the circle representing the pedestrian is 0.5m.
As for road borders, the collision cone idea can be extended relying on trigonometric considerations.Making reference to Fig. 4, and assuming for the timebeing that the car is represented by a single circle of radius Rcar passing through its vertexes, the resulting collision cone with respect to the left road border will be given by the set of angles
NLrb = {ϕ − ψ, αlim}（4），
（5）
in which d is the minimum distance between the car and the left road border, |Vcar| is the module of the car velocity vector, treaction is the minimum reaction time of the driver assumed equal to 1.2 s, ϕ is the maximum allowed angle between the car direction and the roadborder, and ψ is the angle between the current car di-rection and the road border.Coming back to the considered case in which the car is represented by three circles, αlim is still calculated by means of (5) the value of which is a code associated with the various situations that is used by the supervisor to generate the suitable corresponding action. The values assumed in the considered case are listed below:
4: the collision cannot be avoided acting only on α;
3: future collision with the road border detected;
2: future collision with the obstacle detected;
1: collision detected with timpact > treaction;
0: no collision detected.
Taking into account the values of the collision vari- ables associated with the various obstacles detected at a certain time instant, an appropriate set of angles for which a collision is predicted is created. Such set is obtained by the union of the collision cones that have the collision variable value greater than or equal to 2. From now onwards, for the sake of simplicity, this set will be called collision cone. The extreme of this set nearest to the velocity vector phase will be passed to the controller in charge of the generation of the colli-sion avoidance manoeuvre as a new set point for the direction of the velocity vector, the collision avoidance manoeuvre being oriented to steer the car direction out-side the overall forbidden region.
3. The control module
To design the multi–level controller, one needs to refer to a simple mathematical model of the car, to identify the different control phases, and to design the two low level controllers capable, respectively, to generate the movement to avoid the obstacle, and to make the car recover the original driving direction. These issues will be described in the following subsections.
3.1. A simple car model
For the sake of simplicity, let us rely on the so–called
bicycle model [8] of the car vehicle
where M is the mass of the vehicle, f , c f and cr are friction coefficients, K1, K2 are aerodynamics-related quantities, hg is the height of the center of mass and all other quantities are as in Fig. 3. The two control signals are δ, the wheels steering angle, and T , the traction force at the contact point between the tire and the ground. These two signals are saturated for phys- ical and comfort reasons, i.e., −δmax ≤ δ ≤ δmax and Tmin ≤ T ≤ Tmax.For δmax it can be found an explicit expression function of the geometry of the vehicle and the environment parameters, such as the status of theroad surface [7].
3.2. The control actions
Acollision avoidance control systems for pre–crash ap-plication is a critical system, in the sense that a number of physical aspects and constraints need to be taken into account in order to generate a safe manoeuvre. This is the reason why a supervisor has been included in the
control scheme: its aim is to determine, on the basis of the information available at each sampling instant, if a collision with some VRU or with some other obstacle detected by the sensors is going to occur in the near
future, as well as to establish if a collision avoidance manoeuvre is applicable (or, in contrast, if, by making the manoeuvre, a collision with a different obstacle is likely). If the manoeuvre is not feasible, an emergency braking is produced so as to reduce, at least, the en-ergy at the impact. Otherwise, a high level controller in charge of the generation of the manoeuvre is activated.
To produce a correct manoeuvre, the controller re-quires that a reference trajectory is available at any time instant during the by–passing movement. To simplify the reference trajectory generation, the movement of the car during the collision avoidance manoeuvre has been divided into two phases: Phase 1, collision avoid-ance movement; Phase 2, re–entry movement
3.3. The sliding–mode based low level controllers
The two low level controllers in Fig. 1 have been de-signed relying on a sliding–mode control approach[11]. The controller which is activated in Phase 1 (lowlevel controller 1) makes the car track the collision avoidance curve approximated, during the interval be-tween the arrivals of two subsequent pieces of data from the sensors, with its tangent line. Such a curve is deter-mined on the basis of the angle α received fromthe col-lision avoidance algorithm. Indeed the position of the current velocity vector of the vehicle inside the conegives indications on how a collision could be avoided. The simplest strategy is to steer the car in such a way that the driving direction moves outside the cone, tak-ing into account safety and comfort bounds. On the other hand, a safer and more efficient manoeuvre can be attained by acting, contemporarily on the steering wheels and on the car speed. This second approach is the one adopted in our proposal.The controller which is activated in Phase 2 (low level controller 2)makesthe car track the reference tra-jectory given by a line parallel to the road border anddistant from it of an offset equal to 1.5m. Moreover,both the controllers produce, as a control action, the appropriate traction/braking force so that a reference velocity ud is tracked during both phases. The choice of ud can bemade on the basis of dynamical considera-tions, taking into account themaximumdeceleration of the vehicle, and constraints, due to passengers’ safety,
4. Simulation results
The automatic pre-crash collision avoidance system presented in this paper has been tested in simulation, considering a situation in which three pedestrians are moving on the road. Their accelerations on the road
plane aremodelled as pseudo-randomvariables relying on the Random Number generator of Simulink. Note that the corresponding pedestrian positions are suit-ably saturated so that themovements of the pedestrians always take place on the road or close to it (e.g., on thepavement).The trajectory of the controlled car and of the pedes-trians is illustrated in Fig. 6, while the corresponding steering control input is reported in Fig. 7. The carspeed and the distance with respect to the pedestrians(aggregated into a single variable, by giving to this vari-able the value of the minimum of the relative distances determined with respect to the three pedestrians) are illustrated in Figs. 8 and 9, respectively. The minimum relative distance is zoomed so as to appreciate the fact that it is always different from zero (no collision hasoccurred).
图6
图7
图8
图9
The automatic driving system has been tested on a arge amount (1200) of different situations so as to col-ect data for a
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