Abstract—Nowadays, mobile robotics is becoming one of the most open research areas due to the fact that it includes many quite complex advanced mechanisms that are difficult to get a thorough mastery of. In fact, the control task becomes much more complex. The problem is how to guarantee safety for the robot while moving toward a known goal. For this reason, simulation plays a very important role in robotics. It is believed to be the most suitable procedure that may offer a fast prototyping of mobile robots, by considering all options even before fixing the technological devices. Multi-agent simulation models are widely used to solve problems in mobile robotic. In fact, there are similarities between the agent and the robot. However, the most popular methods are based on reactive local navigation schemes that tightly couple the robot actions to the sensor information. But the robot needs not only to avoid collision at real time, but also to anticipate environment evolution in order to take suitable decisions. In this paper, we present a multi-agent simulation model of an autonomous robot that takes into account the reactivity and the anticipation of blocking situations in dynamic and uncertain environments by using only ultrasonic sensors.
I. INTRODUCTION The act of moving towards a specific goal in an
uncertain and dynamic environment involves many mechanisms such as: object detection, perception, internal building model, decision making, prediction of the future state of the environment, and on-line navigation.
Thus, the control task is the most complex one, as it is often difficult to master perfectly every existing technology. For this reason, simulation plays a very important role in robotic. In fact, simulation is believed to be the most suitable procedure that may offer a fast prototyping of mobile robots, by considering all the options even before fixing the technological devices.
Multi-agent simulation models are widely used to solve problems in mobile robotic. Indeed, the term “agent” has been defined as a hardware or a software system with certain properties such as autonomy, social ability, reactivity and proactivity [20]. From this definition, we can note that the robot and the agent share the same characteristics. So, a robot can be represented by an agent.
In this paper, we present a multi-agent simulation model of robot’s behavior in the case of a dynamic and uncertain environment.
To face the dynamicity, the robot should be reactive to act rapidly to the changes of the environment. It should also be able to anticipate the future state of its environment.
To deal with the uncertainty of the environment, the Bayesian inference has been widely used especially in localization and mapping, but it is very slow and complex (NP-Complex) [21]. Since, the fuzzy logic control (FLC) has been investigated by several researchers to treat the problem of reactive navigation and obstacle avoidance. It has the ability to treat uncertain and imprecise information using simple linguistic rules [22]. It offers the possibility of combining many behaviors and it is also faster than Bayesian networks (see Table I).
Although fuzzy logic techniques may simplify navigation problems in uncertain environments, there are situations where a fuzzy logic approach fails in taking appropriate action [12]. These troublesome situations happen when the environment is composed of multiple static and moving obstacles. To overcome this problem, we present a simulation model based on fuzzy logic that takes into account the reactive navigation in an environment composed of a local minimum. It is composed of two fuzzy controllers. The first is to control the angel orientation (the robot should have an idea about the type of obstacles around it). The second is to control the speed (the robot should adjust its velocity in order to avoid collision with the obstacles). Moreover, this method allows the anticipation of the blocking situation and the prediction of the nature of the obstacle and its position in the future.
TABLE I. COMPARISON BETWEEN FUZZY LOGIC AND BAYESIAN NETWORKS
experimental results. In Section 5, we conclude and we give perspectives for this work.
II. RELEATED WORK A wide range of approaches have been adopted to
suggest solutions to the problem of on-line navigation in order to attend a known goal. Most of them are based on reactive strategies.
We mention: Potential Fields Approach [1][13], Vector Field Histogram [2], Dynamic Window [3], curvature velocity [4], Nearness Diagram [5], fuzzy logic approach [12]. The main drawback of these strategies is that the robot gets into an infinite loop or a local minimum. To face this limit, many methods like memory state method [6], minimum risk approach [7][8], virtual wall method [16] are proposed. However these strategies do not take into account the dynamic nature of the environment and the uncertainty of perception, which means that the robot can be driven into dangerous or blocking situations.
Hence, other approaches applied in dynamic environments are proposed with the idea of combining the reactive techniques with global planning methods [9]. These approaches need a priori complete information about the environment. Some other approaches appeared to combine the reactivity and the anticipation [10]. These approaches need a movement planning that requires an important computation time to find the most appropriate way. But in a dynamic and uncertain environment, often the path cannot be executed if there is an unexpected change in the environment.
In the field of multi-agent systems, several works have encouraged researchers to develop models of simulating robot’s behaviors in order to achieve a known target. In fact, there are similarities between the robot and the agent. Accordingly, many approaches are using multi-agent systems to simulate and control autonomous mobile robot. For example, [17] proposes a multi-agent system for autonomous robot navigation in unknown environments. But in this approach, the robot avoids only static obstacles. Ono [18] also proposed a multi-agent architecture to control an intelligent wheelchair. However, it cannot combine many behaviors together and it is applied only in a static environment. Innocenti [19] proposed a multi-agent system to control the robot’s navigation in static and dynamic environments.
Therefore, the object of our work is to propose a multi-agent model based on fuzzy logic to simulate robot navigation in order to combine reactivity (able to avoid rapidly moving obstacles) and anticipation (predict the nature of obstacles and their positions) in a dynamic and uncertain environment.
III. PROPOSED APPROCH A multi-agents system is composed of [20]: (1) An
environment ‘E’, (2) A set of fixed objects ‘O’ in ‘E’, (3) A set of mobile agents ‘A’ in ‘E’, (4) A set of relationships ‘R’ between agents, (5) A set of operation ‘op’ enabling agents ‘A’ to collect, produce, consume and manipulate objects of ‘O’.
According to this definition, we identify our multi-agent system as a set of objects, which represents the static objects present in the environment and a set of agents that represent the dynamic objects and the robot. In our model, the principle agent is the “robot”. It should be able to navigate by minimizing interactions with the other objects and agents navigating in the same space in order to avoid conflict with obstacles and to achieve a known goal.
Our model is able to avoid collision at real time, anticipate future states of the environment through the velocity of each obstacle and reach a known goal.
The behavior of the robot depends on its model of perception. We use ultrasonic sensors to navigate in nearest areas.
Typically ultrasonic sensors calculate the distance between the robot and the obstacle and therefore they do not provide information about the obstacle’s nature (mobile or static) and its position in the future state. However, this kind of information is necessary in order to predict the conflict situations in the future. To overcome this problem, in our work, the robot uses this distance to calculate new information called “Time Collision”. It represents the time left for the robot before a collision occurs with an obstacle in order to predict the nature of the obstacle and its position in the future. The TC (Time collision) can be obtained by applying (1), where Di represents the distance between robot and obstacle at time i, and υRi represents the velocity of the robot. With this information, the robot avoids not only collisions with obstacles (a reactive behavior), but also anticipates their natures and positions (an anticipative behavior).
TC =Di/υRi (1)
If TC is equal to zero, it means that the obstacle in the trajectory of the robot is static. In this situation, robot should change its direction. If TC is infinity, it means that the robot navigates in a free subspace. If TC is positive, then the obstacle is considered as a mobile one. In this situation, the robot can anticipate that the trajectory will be free in a few times. If TC is negative, then the obstacle is mobile and it is going toward the robot. In this situation, the robot should minimize its velocity in order to avoid collision with this obstacle, and then decide to change completely the direction if it’s possible (moves to another subspace which makes the robot’s safety). Or wait until this mobile object moves away (the current subspace will be free in a few time), if there is no another free subspace. The advantage of this information is that it allows the robot not only to avoid collision at real time with obstacles around it, but also to anticipate their natures and their positions in the future so as to predict the conflict situations.
The cinematic model (velocity, acceleration and orientation angle of the robot) will be assured by the fuzzy logic (see Table II).
Fuzzy logic has been widely used in robotic to solve the problem of navigation in a static environment, based on reactive techniques [12]. Fuzzy logic is the representation of, and reasoning with, imprecise and uncertain information.
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But the majority existing fuzzy logic methods deal only with static environments, and use only the distance between the robot and the obstacle to avoid collision. In this case, we propose a fuzzy model for navigation in a dynamic uncertain environment based on TC and the velocity of obstacles. For example, if there is an obstacle in front of the robot, hence it is more interesting to reason about its velocity in order to have an idea about its state in the future. In contrast, the distance between the robot and the obstacle allows it to change immediately the trajectory, while the velocity allows the robot to predict the environment evolution. So the fuzzy logic controller should make a compromise between obstacle avoidance behaviors and goal seeking behavior.
TABLE II. THE CHARACTERISTICS OF THE ROBOT
Characteristics Role Utility Velocity Allows the robot to
navigate. Speed of the two wheels
Orientation Allows the robot to change its trajectory.
The orientation angle between robot and its target.
In this way, we propose tow fuzzy controller systems to
coordinate and combine reactive and anticipative behaviors in order to produce a suitable decision.
A. The fuzzy controller for the angular velocity The first controller (Figure 1.a) is the heading control
activity. It is used to determine the heading angular change Δθ. The inputs of this controller are the difference time collision in the left (DTCL), the difference time collision in the front (DTCF), the difference time collision in the right (DTCR), and the current target orientation between the robot and its goal (TO). These inputs are based on TC. They give an idea about the nature of obstacles in front, left, and right areas. So, this controller uses the input information in order to predict the nature of each obstacle and choose the suitable path in the future by minimizing interaction and anticipating collision.
B. The fuzzy controller for the linear velocity The second controller (Figure 1.b) is the speed
controller. It determines whether the robot speed should be increased or decreased. It is used to determine the speed change Δυ.
The D, υO, and the υR represent the distance between the robot and the nearest obstacle in the front area, the velocity of the nearest obstacle in the front area, and the current velocity of the robot, respectively. If the nature of the obstacle is static, then its velocity is equal to zero. If it is mobile, then its velocity can be obtained by (2), where D represents the distance traveled by the obstacle in the time interval Δ.
υO=D/Δ (2)
The distance is calculated from (3), where Xc and Yc represents the coordinates of the obstacles at time ti and Xc’
and Yc’ represents the coordinates of the obstacle at ti+Δ. The coordinates are obtained by (4) and (5).
D = 22 )''()( YcXcYcXc −+− (3)
Xc= Xa + (Xb – Xa) cosΘ – (Yb – Ya) sinΘ. (4)
Yc= Ya + (Yb – Ya) cosΘ + (Xb – Xa) sinΘ. (5)
Defuzzified output for angular velocity and linear velocity can be obtained from (6), where y represents the constant of output membership function.
Δθ= ∑
∑ ×
b
ay
b
ayy
)(
)(
μ
μ (6)
C. Fuzzy rules The reasoning of the robot navigation is based on fuzzy
rules which represent the human reasoning. The motion control variables of the mobile robot are the translational speed and the rotational turn angle. The robot speed is represented by three linguistic fuzzy sets {Low, No change, High}. The robot turn angle is represented by five linguistic fuzzy sets {Large Left Turn, Small Left Turn, No Turn, Small Right Turn, Large Right Turn}. Therefore there are 8 if-else rules for the first controller (Figure 2.a), based on the type of each obstacle in order to predict the environment evolution in the future, and 8 if-else rules for the second controller (Figure 2.b), based on velocity of the nearest obstacle in order to determine the linear velocity.
This architecture allows avoiding collision and anticipating the future state of the environment.
IV. EXPERIMENTATION AND RESULTS To test our method, we have used the Simbad simulation
platform, programmed in JAVA.
A. The parameters of the robot and the controller in simulation In the simulation, the parameters of the robot are:
b=0.4m (b is the half distance between the two driving wheels), r= 0.05m (r is the radius of the wheel). The Δ interval time between two successive perceptions is 0.4s, the linear velocity is limited to υ = 1m/s, and the angular velocity is limited to ω = 45°/s.
The controllers are based on 16-fuzzy rules (represent the reasoning). The small number of rules is advantageous in dynamic environments (short execution and high frequency of sensor readings).
2020
Figure 1. (a) Fuzzy controller of heading angular, (b) Fuzzy controller of speed change.
Figure 2. (a) The fuzzy rules for the angular velocity, (b) the fuzzy rules for the linear velocity.
Figure 3. Experimental results in static environment composed of multiple traps.
B. Experimental Results The main objective is to obtain a robot control
architecture that provides coherent and rational conduct aimed at achieving a known goal and at the same time, preserving the real-time response to the immediate physical environment. In this sense, multi-agent systems provide the basic architecture.
This section presents scenarios used to test the performance of our control architecture in a dynamic and uncertain environment.
1) Experimental results in static environments: By using the designed controllers described in Section 3, different starting positions are selected for the robot with various initial poses. The robot can avoid the obstacle
successfully for any starting situation. The simulation environment is a square area composed on multiple traps like U-shape and T-shape.
We present in Figure 3 an experimental result of our model and we give a comparison between our method and other methods dealing with the same problem.
Scenario 1 (see Figure 3.a): in this setting, an obstacle is introduced into the path of the robot. There is a wall with a length of 12 m located 6 m from the robot. The robot detects that TC=0 (static obstacle), so it changes its direction by choosing the path with fewer constraints to reach its goal. However, in the minimum risk method based on trial-return behavior phenomenon, the robot searches the nearest exit [7]. Therefore when the nearest exit is blocked by a long wall, the nearest exit will be the opening at the right hand
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side where the wall ends. This method takes a large time to find the free end of the wall. However the problem with trial-return motion is high power consumption and the time spent from start to target is long when the obstacle is composed of complex traps like U-shape and T-shape. But in our model, the same situation as shown in scenario 2 (see Figure 3.b), the robot moves away from the U-shape obstacle because it detects that TC=0, so it should change immediately its direction to find a path free towards its target. In scenario 3 (see Figure 3.c), the robot can detect easily the multiple “dead cycle” by using the time collision. The robot calculates for each trap a TC and the decision depends on the nature of the obstacle (e.g., the obstacle is static if its TC is equal to zero). However in the memory state method, the dead cycle problem is resolved by using a state memory strategy [6]. Therefore there are situations where the robot cannot go straight towards the target. It has to keep turning around the obstacle if the distance between the robot and the obstacle is shorter than the distance between the robot and the target. In scenario 4, we test our method in environment composed of corridors. As shown in Figure 3.d, the robot moves in a corridor in order to reach its target. The problem is how to ensure the motion’s stability without oscillation. When the robot navigates along a very narrow corridor, the TC in left and right areas are equal to zero, and the TC in the front is infinity, which means that the front area is free. The robot can reach its target easily without oscillation. The average speed was 0.4 m/s. While in sensor-based motion control, the same scenario was shown that the robot can reach its target in 127 s and the average speed was 0.204 m/s [23].
So, by using the TC in order to find the nature of each obstacle, the robot chose the trajectory with fewer constraints in order to reach its goal without collision.
2) Experimental results in dynamic environment: We have tested our method in environments including moving obstacles (agents). The robot has no information about the speed and direction of obstacles around it. It should predict
the nature and the velocity of each obstacle in order to choose the suitable free path to reach its target without collision. The minimum speed of the obstacles is υO = 0 m/s (i.e., a static obstacle) and the maximum speed is υO = 0.7 m/s.
In scenario 1 (see Figure 4.a), the robot navigates with multiple moving obstacles. Each obstacle has its own speed. The robot adjusts its velocity (in point ‘a’) with the speed of the nearest obstacle. In point ‘b’, the robot changes its direction because it detects a free area in the right (DTCR is equal to infinity). In point ‘c’ the robot avoids collision with a static obstacle. Then, it accelerates because the path is becoming free (DTCF is equal to infinity). The average speed was 0.205 m/s. However in sensor-based motion control, the robot can detect and avoid collision with moving obstacle without anticipating the future state of the environment [23]. The average speed was 0.196 m/s.
In scenario 2 (Figure 4.b), the robot navigates in an environment composed of corridors with a moving obstacle. At the first time the corridor is narrow; in this setting the robot should adjust only its velocity to avoid collision with the obstacle without changing the direction because the goal is in the front area and there is no free area neither in the left, nor in the right (TC is equal to zero in the left and the right, and different to zero in the front). When the corridor becomes large, the robot changes direction because there is a free area in the right. In point ‘a’, the robot decreases its velocity and change the orientation to the right area (the free area), and in point ‘b’, it accelerates because the path is becoming free. In this scenario, the robot reaches easily its target without losing time.
In scenario 3 (Figure 4.c), we test our method in a dynamic environment composed of multiple traps. In region 1, the robot moves away from a U-shape obstacle because it detects that the TC is equal to zero (see Figure 3.d, when the TC decreases until zero). In region 2, the robot is in a large
Figure 4. Experimental results in dynamic environment.
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corridor with moving obstacles, it calculates the TC relative to every moving obstacle in order to predict the free path and adjust its velocity to avoid collision with them. In this region (see Figure 4.d), TC values are between +30 and -30, which means that the obstacles are moving. In region 3, the robot is in narrow corridor, it calculates the TC in order to have an idea about the nature of each obstacle around it and to decide about the direction that will be chosen. The TC of the nearest front obstacle is positive, which means that the obstacle is moving away. So, the robot keeps the same direction. The velocity of the nearest moving obstacle is 0.4 mm/ms; the robot adjusts its velocity (0.2 mm/ms) with the velocity of this obstacle in order to avoid collision. In region 4 (Figure 4.d), the robot is in a free area to reach its target (the TC increases until infinity and the heading angular is 0°). In this situation, the robot can maximize its velocity until 0.8 mm/ms. In this experiment, the whole path from the start position up to the end position was covered in 32000 ms. The average speed in each region is presented in Table III.
CONCLUSION AND FUTUR WORK A multi agent model simulation for robot navigation in
dynamic environments has been presented. We have used the fuzzy logic to develop a control system that enables the robot to navigate even in dynamic and uncertain environments. The robot not only has a reactive behavior but also an anticipative behavior when it takes decision. Our model uses the velocity of obstacles in order to combine reactivity and anticipation. In this stage, our system is composed of tow fuzzy controllers: the heading controller and the speed controller. The fuzzy logic body (inference) produces necessary rules for the robot to achieve a known goal with an intelligent decision. Experimental results using the proposed method to navigate in uncertain and dynamic environments have shown that the robot can successfully achieve its goal without collision. In perspective we try to represent the decision of the robot by reactive agents and cognitive agents that communicate with each other to generate intelligent behavior.
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