Parameters and constants for the simulation.
The collision avoidance control has been one of the key technology for future transportation. Recently, many unmanned systems are developed in shapes of robots, cars, ships, aircraft, etc. In these environments, proper navigation and control systems including collision avoidance is needed. This paper is on collision avoidance control law for air vehicles under uncertain information. The control law uses information amount as one of the physical parameter for control system.
In the field of guidance, navigation, and control, collision avoidance of automated transportation system has been one of main interest of researchers. Many researches started from collision avoidance of ships (Ciletti et al., 1997) where collision avoidance has been one of the problems due to the increasing demand for the naval transportations. Wide varieties of studies on collision avoidance are treated in fields of robots (Fukuda & Kubota, 1999), cars (Hiraoka et al., 2009a, 2009b) and satellites. Some of these researches treat avoidance problems with the formation control which requires the cooperative information control (Slater et al., 2006; Stipanovic et al., 2007).
In the field of aeronautics, the Traffic alert and Collision Avoidance System (TCAS) has been one of the references for the collision avoidance. TCAS exchanges the information of aircrafts and advises the aircraft to avoid in vertical direction. For the conflicts in collision avoidance control, Frazzoli et al. (2001) have shown feasible strategy to treat the conflict problem. Gates (2009) has proposed rule-based collision avoidance control strategies for real-time online collision avoidance. Miele et al. (2010) has proposed collision avoidance control for case of abort landing with low computational load which can be calculated by on-board computer.
Conventional avoidance problems assume that all information about avoidance (intruders and environments) is certain. Therefore, control law is designed based on certain information. However in real cases, all information may not be correct and most of it is uncertain. These uncertainty of information differes by the relative position of the evader and intruder or the absolute position of intruder. There has been no research on control law to deal with uncertain information. This paper proposes control law that treats uncertain information. New parameters quantifying information amount are defined for this purpose. The proposed control law provides new performance by enabling the aircraft to obtain information and to check the certainty of the information.
Two different cases of numerical simulations are used to investigate the usage of the information amount. The first case defines the problem as the uncertainty of the information changes by the relative position of the evader and the target. The problem treats the case where the amount of infomation changes by relative position, for example, the flight in fog or smoke. The information is clearer as the evader gets closer to the fog. These uncertainties are quantified and used as parameters for collision avoidance control law. The second case defines the problem as the uncertainty of the infomation is given as absolute position. The infomation can or cannot be obtained by the position itself, for example, the flight around urban buildings or moutains. In both cases, the information amount is obtained from focused area assigned by the user. Using the information amount, the control law is designed for safer flight of the air vehicles.
2. Information amount
In this study, amounts of information are treated as parameters for the control law. First, the focused area : SE is treated as the region of the area that the user focuses. This area can be large if the vehicle is moving fast or very small if the vehicle is in urban area moving very slowly. The cleared area : SC is the area where the information are certain. In the cleared area, all of the infomation is available, meaning if there is an intruder in that region, the evader can obtain all the infomation of the intruder. In the other hand, the blurred area : SB is the area where infomation is uncertain.
From these parameters of the areas, the infomation amount is derived qunatatively as physical value to be used. One of the important factor used in this paper is information localization :
and the schematic image of this areas are shown in Fig.1.
Another important factor for the information amount is information acquisition requirement :
The infomation amounts can be changed according to the users request and experience. If the evader is moving fast, the
3. Collision avoidance law
The total system of collision avoidance law in this paper consists of three types of control laws. They are actual collision avoidance, information gathering, and cource keeping. They are switched by the risk of collision and amount of infomation obtained. All of the simulation are in 2-dimensions and either acceralation or angular velocity of the vehicle is used as input variables. Fig.2 shows the basic definition of variables and constants used in this paper.
The risk of collision is described numerically for collision avoidance control law. Two values are introduced in this paper. One is Range to Closest Point to Approach:
Then, the relative position and range at closest point of approach is given as,
The risk function is defined as the following equation.
The collision avoidance control law satisfies the following equation.
The first factor of the right hand side is the angular velocity of the evader, so by eliminating this factor, the following can be derived by taking the derivative of the relative velocity.
As total, the angular velocity for collision avoidance can be derived as,
This collision avoidance control law activates when the risk is high. In other words, other 2 control laws, infomation gathering and course keeping laws are used when the risk is low. In the following 2 sections, the different types of infomation gathering control laws are introduced depending on the difference of the uncertainties up ahead. The course keeping control law is used to keep the original course, which is not important in this paper, so will not be explained in details.
4. Uncertainty depending on relative position
The information gathering control with uncertainty depending on relative position is introduced in this section. The uncertainty depending on relative position stands for the cases where the infomation that can be obtained are defined as function of relative distance to an uncertainty. This is applicable for the flights in the fog or smokes where the uncertainty differs by the distance, closer you are, clear infomation you can obtain. The control target is fixed wing aircraft and the control input is angular velocity. The control law is designed from fuzzy logic to realize the fuzziness of the infomation. First, the additional parameters of the uncertain infomation is explained in this section. Followed by the control law and control results.
4.1. Uncertain parameters
The control law uses additional parameters for infomation in this section. The basic parameters were
4.1.1. Information probability -
Infomation probability is a parameter describing the probability, possibility or likelihood of the target existence.
4.1.2. Information clarity -
Infomation clarity is a parameter describing the clarity of target existence.
4.1.3. Information truth -
Infomation truth is a parameter describing truth of the target existence. The value determines whether the target exists or not. It takes a value of either 0 or 1. When
4.1.4. Information location accuracy -
Infomation location accuracy is a measure of the area in which the target exists. For example, in a 2D model,
4.2. Application to control law
The control law using the uncertain infomation is introduced. From the viewpoint of complexity and difficulty, it is wrong to design a whole new control law adopting
uncertainty. Therefore, the control law to deal with uncertainty simply by introducing technique to the conventional control law with only minor modification is proposed.
4.2.1. Uncertainty coefficient
As a first step in designing a control law to deal with uncertainty, the uncertainty coefficient
As shown in Fig. 6,
In the situation in Fig. 4, when each uncertain parameter is given, the value of
4.2.2. Information acquisition requirement
4.3. Simulation result of relative position - in-fog problem
An example of avoidance problem is uncertainty of information defined in the relative coordinate (body fixed) system is shown. The problem is assumed to be in-fog problem, where there is area where the information is uncertain upahead.
4.3.1. Statement of problem
The evader cannot see the target beyond a certain distance because visibility is obscured by an obstacle like fog. The problem is defined as two-dimensional in the horizontal plane. The evader flies on a straight course with constant velocity towards a target that may exist in existence zone as shown in Fig. 9. Visibility is defined as a function of relative distance from the evader. When the relative distance is smaller than a certain distance, for example 4000m, the evader can see the target clearly. However, the evader cannot see the target when the relative distance is larger than a certain distance, for example 5000m. Visibility changes gradually between these two areas. The information clearness
4.3.2. Initial conditions and requirement
The initial position of the evader and target existence zone are shown in Fig. 9. Other constants are shown in Table 1. Figure 4 is used for
4.3.3. Initial conditions and requirement
Figures 10 and 11 show the avoidance trajectory and angular velocity, respectively. Solid lines represent the results for the proposed control law; dashed lines represent the results for the conventional control law. The figure shows two cases for the conventional control law: avoidance with correct information; and avoidance with incorrect information where target appears suddenly without information.
The avoidance trajectories in Fig. 10 show that avoidance using the conventional control law with incorrect information causes significant delay because the evader does not avoid until the target is found. On the other hand, the avoidance trajectories produced by the proposed
|Initial position||(0, 0)||Shown in Fig. 4|
|Radius of existence zone||1000[m]||1|
|Center of existence zone||(25000, 2000)||Shown in Fig.5|
|True position of target||(25500, 2500)||0.2, 0.9|
control law depend on the value of
Both of the figures show that the proposed control law was able to increase the safetiness and reliability of the flight in uncertain information defined in relative position from the evader.
5. Uncertainty depending on absolute position
In this section, the uncertainty depending on absolute position is treated. Different from the uncertainty that differs by relative position as explained in section 4, the information does not change due to the environment. For example, when aircraft is going around a mountain or a helicopter going around the buildings, the information does not change due to relative position.
The information parameters
5.1. Design of information gathering control law
Design of information gathering control law is derived using a model in Fig.12 and Fig.13. Figure 12 is the vehicle in the ground fixed coordinate and Fig.13 shows the vehicle in body fixed coodinate. Focused area depends on the speed and direction of the vehicle, so the distance
The shadow area cannot be seen from the vehicle. So, the area of shadow area is assumed as the following equation using the focused area.
The time derivatives of the
Therefore, the information amount of safety can be changed by
In the case of
This control law uses the same feedback gain in the cases of
5.2. Simulation result of absolute position
The simulation result using the collision avoidance control with IAFB is introduced. Two different cases of similation will be shown in this scetion. The first case is the case with the helicopters. The velocity of the vehicle can be changed directly by the control law. The second case is the case with the fixed wing aircraft. The input is given as the angular velocity and the velocity itself is kept as constant.
5.2.1. Simulation result of helicopters
Figure 14 shows the initial condition of the evader and intruder. The intruder cannot be seen from evader at beginning of the control. The intruder is incoming from behind the obstacle with velocity of 10[m/s] and 20[m] away from the obstacle. The evader starts from 150[m] away from the obstacle with various position defined by
In the first half of the control, the evader starts to obtain the information behind the obstacle. After the intruder is found approaching, the evader decides to evade either in front or back of the intruder depending on the estimated trajectory of the intruder passing in the way. In this case, the results were split into exactly two groups where evader decelerates and passes behind the intruder or accelerates and passes in front of intruder. In Fig.16, the case without IAFB, the first half of the information gathering does not occur, so the helicopter avoids the intruder after they find the incoming vehicle. Figure 17 is comparison of the minimum distance when the two vehicles pass each other. The result with IAFB shows higher level of avoidance due to the earlier motion of gathering information which leads to easier avoidance and faster recognition of the intruder.
5.2.2. Simulation result of fixed wing aircraft
For fixed wing type aircraft, it is not easy and efficient to change the velocity so often. The control input for these types are changed to angular velocity input. Basic input is same as the one described in section 5.1. Most of the conditions are same as that of the case of the helicopters except that the cruising speed of evader and intruder is 100[m/s] and the results are compared with different
Figure 18 shows the trajectory of evader with different
Figure 19 shows the time history of the relative distance of the vehicles. The results show that the relative distance decreases very quickly in the case without IAFB and the minimum distance between the vehicles are shorter than the others. This clearly shows the effectiveness of the IAFB.
Figure 20 shows the trajectory of evader when the intruder starts from different positions. The
Two cases of collision avoidance control is simulated to see the effect of the information amount as parameter for control. One was that uncertainty of the information changes by the relative position of the evader and the target and the other was that uncertainty of the infomation is given as absolute position. Both cases have shown smoother and safer trajectories than the conventional control laws. The simulation results have shown that the control laws using information amounts does not rely on the coodinates. The motion of the aircraft show similar trajectories to that of humans to obtain safe margin to gain information when they do not have enough information.