1. Introduction
In the future, it’s not difficult to image that we will often come across many autonomous mobile robots traversing densely populated place we live in. In such situation, because the autonomous mobile robots need to carry out their tasks in a place with unknown obstacles, the obstacle avoidance is one of the important functions of the robots. With a view to implementation of autonomous mobile robot working in doors, we employ an omni-directional platform as shown in Fig. 1 (left). For experimental verification, an omni-directional mobile robot shown in Fig. 1 (right) is developed. The robot has an omni-directional camera for environmental recognition, and can move to all directions by four omni wheels.
While there are many studies about obstacle avoidance method focusing attention on possibility of avoidance, this paper presents the method focusing on not only possibility but also safer trajectory of avoidance. Even if there are the same situations that the robot needs to avoid a static obstacle, timing of beginning avoidance behaviour should vary according to the robot speed. If the obstacles are moving also, the timing should vary according to the velocities of the obstacles. To cite a case, in a situation that a robot and an obstacle go by each other as shown in Fig. 2, the robot should avoid along the curved line like (iii) according to the speeds of the obstacle and own speed. In order to get to the goal with efficient and safe avoidance behaviour in the unknown environment for the robots, predicting the future obstacles’ positions by their current motions is needed.
This paper introduces a real-time obstacle avoidance method introducing the velocity of obstacle relative to the robot. By means of considering predicted positions of the robot and the obstacle calculated from the time and the relative velocity, the robot can begin the avoidance behaviour at an appropriate time according to the velocity of the obstacle and the robot.
Some researches focus attention on the velocity of obstacle (Ko & Lee, 1996) to avoid moving obstacles efficiently. In this research, virtual distance function is defined based on distance from the obstacle and speed of obstacle, however, only projection of the obstacle velocity on the unit vector from the obstacle to the robot is considered. In other words, the velocity of the robot is not considered.
On the other hand, in (Ge & Cui, 2002), the velocity of the obstacle relative to the robot is considered. Our approach also employs the relative velocity. In addition to this approach, a position vector of the obstacle relative to the robot in the future is calculated by the relative position and the velocity.
In order to solve the real-time motion planning problem, there are effective methods (Khatib, 1986) (Arkin, 1989) (Borenstein & Koren, 1991) (Fox et al., 1997). Fuzzy potential method (FPM) (Tsuzaki & Yoshida, 2003) (Otsuka et al. 2005) is also one of the effective methods. In this research, the method was applied to an autonomous mobile robot which plays soccer. By adequate designing of potential membership function (PMF), it was realized that wheeled robots got to the goal with conveying a soccer ball and avoiding obstacles. This method is easy to understand at a glance. However, in dynamic environment, to avoid moving obstacles efficiently, more specific guideline of designing is desired. In this paper, we introduce design method of PMF considering the predicted positions and discuss the availability by comparing the design of PMF considering the relative velocity and that not considering.
In this paper, for the purpose of avoiding the moving obstacle safely and smoothly, design methods of the potential membership function (PMF), which is considering the velocity of the obstacle relative to the robot, are presented.
2. Fuzzy potential method (FPM)
In the fuzzy potential method (FPM), a current command velocity vector considering element actions is decided in real time. Element actions are represented as potential membership functions (PMFs), and then they are integrated by means of fuzzy inference. Furthermore, by using a state evaluator, the PMFs are modified adaptively according to the situation. The directions on the horizontal axis in Fig. 3 correspond to the directions which are from
PMF idea allows us to represent our knowledge and experiences easily, and furthermore it gives us easy understanding. The grade can be seen as a desire for each direction of the robot. In this paper, to discuss an obstacle avoidance problem, methods for generating of PMF to head to a goal and to avoid moving obstacles are introduced. This method has two steps. First step is generating PMFs. Second step is deciding the command velocity vector by use of fuzzy inference to integrate the PMFs. Hereinafter, design method of PMF considering the obstacle velocity relative to the robot and way to decide the command velocity vector by fuzzy inference are described
3. FPM considering the relative velocity
To realize the obstacle avoidance in dynamic environment, the proposed method employs two different PMFs, one is considering vectors of obstacle’s position and obstacle‘s velocity relative to the robot and the other is to head to the goal. PMF is denoted by
3.1. Design of PMFs
3.1.1. PMF for an obstacle
To avoid moving obstacles safely and efficiently, an inverted triangular PMF by specifying a vertex, height and base width is generated. Because this PMF considers future positions of the robot and the obstacle, the robot can start avoiding the obstacle early and be prompted not to go on to the future collision position. For the purpose of safe avoidance, the PMF
First, in order to predict the future state of both obstacle and robot with the aim of efficient avoidance, a predicted relative position vector, in
where
where
As described above, the predicted relative position vector, at the time
where
Next, as a measure to decide how far the robot should depart from the obstacle,
where
In addition, a base width of inverted triangular PMF is decided by following equation:
where
As mentioned above, by deciding the vertex, the height and the base width of inverted triangle considering the predicted relative position, PMF
3.1.2. PMF for a goal
To head to the goal, a PMF
where
3.2. Calculation of command velocity vector by fuzzy inference
The proposed method employs fuzzy inference to calculate the current command velocity vector. Specifically, The PMF
Finally, by defuzzifier, the command velocity vector
where
where
Based on
3.3. Visualization for PMF on two-dimension surface
It would be convenient to have a visualizer that show us why the robot will go on to the direction. In the proposed method, we can see aspects of the PMFs on two dimension surface and understand easily the reason for choice of the direction. For example, a PMF described on polar coordinate shown in Fig. 8 (left) is comparable to the PMF described on x-y coordinate shown in Fig. 8 (right).
4. Simulation results
To verify the effectiveness of the proposed method that employs PMF considering the velocity of the obstacle of the robot, numerical simulations which assumed an obstacle avoidance of autonomous omni-directional mobile robot were carried out.
In this simulations as shown in Figs. 9-11, the radius of robot and obstacle were supposed to be both 0.3m, therefore,
Figure 9, 10 and 11 show the simulation results when the robot passed the obstacle. Initial positions of the robot and the obstacle were respectively
As shown in Figure 9(a), the robot got close to the obstacle because the relative velocity was not considered. On the other hand, in Figure 9(b), the robot succeeded at the early starting of avoidance behaviour due to generating PMF by use of predicted information based on the relative velocity. In addition to the situation as in Figure 9(b), in Figure 10, the higher limit of the robot speed has been changed:
In Figure 11(a) and (b), the trajectories of the robot, with PMF considering the relative velocity and not considering that, when the obstacle speed
From these simulation results, it is confirmed that by an associating the PMF for avoidance with the relative velocity, higher the obstacle speed is, earlier the timing of the avoidance behaviour of the robot is, therefore the ability of avoiding obstacle can be enhanced.
In order to verify the effectiveness of the proposed method, simplified experiments were also carried out.
In this experiments as shown in Fig.12. A ball was supposed to be a moving obstacle and is rolled toward the robot. The robot recognized the environment by the omni-directional camera. A position of a goal and that of an obstacle relative to the robot were calculated by extracting features based on objects’ colours. The robot size is L 0.4
When the robot used the proposed PMF, which was considering relative velocity, as shown in Fig. 12 (a), it succeeded in avoiding the moving ball with smooth trajectory. On the other hand, the robot with the PMF, which was not considering relative velocity, diverged once as shown in Fig. 12 (b).
5. Conclusion
In this paper, for the purpose of avoiding the moving obstacle safely and smoothly, design methods of the potential membership function (PMF), taking into consideration the velocity of the obstacle relative to the robot have been presented. The proposed PMF for an obstacle and PMF for a goal are unified by fuzzy inference. By defuzzification, the command velocity vector of the robot is calculated and the obstacle. Numerical simulations and simplified experiments, which assumed an obstacle avoidance of an autonomous omni-directional mobile robot, were done. As the result of the comparison between the design method of PMF using relative velocity and not using, it was confirmed that the PMF using relative velocity enhanced the ability of avoiding the moving obstacle.
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