1. Introduction
Obstacle avoidance methods for mobile robots have proposed in a broad range of studies and the availabilities have been discussed. Most of these studies regard the robots as points or circles and control methods of the translational movements are discussed. In these studies, it is pointed out that a non-circle robot can be transformed into a point robot by expanding the obstacles by the largest radius or maximum size of the robot. The effectiveness of avoiding obstacles by these approaches have been confirmed, however, according to the shape of the robot, these approaches reduce and waste the available free-space and can decrease the likelihood of getting to the goal. If wide-robots, which are horizontally long, are regarded as circles according as conventional approaches, they have possibilities not to go through between two divided objects due to the largest radius of the robot, even if they ought to be able to go through by using their shortest radius. This suggests necessity of suitable orientation angle at the moment of avoidance. Consequently, to enable wide-robots to avoid obstacles safely and efficiently, it is necessary to control not only the translational movement but also the rotational movement. In our current research, wide-robots with omni-directional platform have been employed, as shown in Fig.1. In situations like Fig.1, both wide-robots can go through only by changing the orientation angle in real time.
Some researches focus attention on the orientation angle of the robot (Kavraki, 1995)(Wang & Chirikjian, 2000). In these studies, by convolving the robot and the obstacle at every orientation and constructing the C-space, the suitable orientation angles of the robot for path planning are decided. However, these methods need environmental map and do not show the effectiveness for autonomous mobile robots about avoidance of unknown obstacles in these studies. Therefore, in order to avoid unknown obstacles reactively considering the orientation angle, the wide-robot needs an algorithm that can decide the orientation angle and rotational velocity command on the spot based on the current obstacle information.
Meanwhile, decision methods of the translational movement have been proposed in many studies (Wang et al., 2000) (Du et al. 2007) (Khatib, 1986) (Borenstein & Koren, 1991) (Dieter, 1997), we employ fuzzy potential method (FPM) (Tsuzaki & Yoshida, 2003). This method realizes some tasks in dynamic environment by fuzzy calculation about desire for each direction of the robot. In this research, it was shown that wheeled robots succeeded getting to the goal with conveying a soccer ball and avoiding obstacles.
In this paper, a control method using a capsule-shaped case is described for both translational and rotational movement based on the FPM, and it takes into consideration the width of the robot. With this new approach, real-time control of the orientation angle is easily achieved. Conventional FPM has only been able to deal with translational velocity. The proposed method is able to control the rotational and translational velocity simultaneously within the framework of FPM.
2. Capsule case
2.1. Need to consider the width of mobile robot
In recent years, non-circle robots have been developed, of which vertically long robots, wide-robots, appear. In studies of humanoid robots, the robots have two arms mounted to the stationary torso with wheels because these robots can be used in terms of mobility, manipulation, whole-body activities, and human-robot interaction (Ambrose et al., 2004) (Du et al., 2007). During last two decades, vast number of algorithms of obstacle avoidance for mobile robot, and recently some researches and developments of the mobile robot in practical use have been reported. These robots have problems that conventional methods are inconvenient for applying for the wide-robot because most of conventional methods of obstacle avoidance regard the robot as points or circles. Or due to the postulate of the conventional methods, the robots have needed to be designed in a circle. We also have developed the wide -robot, which has torso with two arms and a head, for making the robot perform not only moving but also communication with human by means of gestures or speeches based on a perspective of human interaction. This robot is also horizontally long. In addition, when the robot opens an arm slightly, as shown in Fig. 1, or both arms, it becomes increasingly harder to apply conventional methods. If these wide-robots are regarded as circles according as conventional approaches, they have possibilities not to go through between two divided objects due to the largest radius of the robot, even if they ought to be able to go through by using their shortest radius. In this study, enable the wide-robots, which move automatically, to move smoothly and safely in the environment with obstacles, a capsule case is introduced.
2.2. Design of capsule case
The capsule shaped case is modeled by two circles and two lines tangent to the circles as shown in Fig.2.
This closed contour is defined as
where
In the proposed method,
3. Fuzzy potential method (FPM) using capsule case
3.1. Concept
In the fuzzy potential method (FPM), a current command velocity vector that takes into consideration element actions is decided by fuzzy inference. Element actions are represented as potential membership functions (PMFs), and then they are integrated by means of fuzzy inference. The directions on the horizontal axis in Fig. 3 correspond to the directions, which are from -
3.2. PMF for translational motions
3.2.1. PMF for obstacles
In order to enable a wide-robot to avoid obstacles safely and efficiently in real time, a concave shaped PMF
First,
Next, as a measure to decide how far the robot should depart from the obstacle,
where
If the current obstacle position is ins
ide of a circle with radius
where
The PMF
As mentioned above, by deciding the depth and the base width of concave, PMF
3.2.2. PMF for a goal
To head to the goal, a PMF
where
3.3. Calculation of translational command velocity
The proposed method employs fuzzy inference to calculate the current command velocity vector. Specifically, The PMF
Finally, by defuzzifier, the command velocity vector is calculated as a traveling direction
Based on
where
3.4. PMF for rotational motions
3.4.1. PMF for obstacles
In order to enable a wide-robot to decide the appropriate angle of the direction for obstacle avoidance in real time, PMF
The aim of the PMF
3.5. Calculation of rotational command velocity
As for the rotational movement, like the translational movement, the proposed method employs fuzzy inference to calculate the current rotational command velocity vector. Specifically, The PMF
Finally, by defuzzifier, the command velocity vector is calculated as a traveling direction
where
where
3.6. Calculation of wheel speeds
To realize the movement, in this study, an omni-directional platform is employed for a autonomous mobile robot. The command velocity vector is realized by four DC motors and omni wheels using following equations:
where
4. Simulation results
The effectiveness of the proposed method was verified by numerical simulations intended for omni-directional autonomous mobile robots. As postulates, the robot supposed to be
able to detect obstacles and has information about the relative position vector. The measuring range was assumed to be 4.0m at all directions. Each parameter was as follows:
The wide-robot size was assumed as L=0.4m, W=1.0m, which are in Fig.10. Considering this L and W, Ca, CL and CR in Fig.2 were all set at 0.3m.
4.1. Performance of capsule case
In this section, the effectiveness of using capsule case and the design method of PMF based on the capsule case are verified, by comparing the results of chosen direction of movement at following two different situations about the orientation angle for a wide-robot. As common assumption, the positions of the robot and two obstacles were immobilized on each point respectively (1.0m, 2.0m), (1.5m, 0.5m) and (3.0m, 2.0m), as shown in Fig.11.
4.1.1. Situation I
The orientation angle of the robot was fixed to
4.1.2. Situation II
The orientation angle of the robot is fixed to
Through these two results, the effectiveness of the capsule case is confirmed. The wide-robot can decide the direction of translational motion with considering the own orientation, goal position and obstacle positions simultaneously in real time.
4.2. Capability of going through between objects
The effectiveness of the proposed method was tested by comparing two design methods, I and II, based on PMF, for obstacle avoidance problem. Start and goal point of the robot are respectively (0.0m,0.0m) and (8.0m,0.0m). The trajectory of the robot and the aspects considering the orientation angle on the position every 1 second are plotted in Fig. 13 and Fig. 14. Obstacles positions are respectively (2.5m,
On the other hand, in the Method II, the capsule case and real-time control based on FPM were used. As shown in Fig. 14, the robot performed translational and rotational motions simultaneously and succeeded in going between two objects. In addition, the robot succeeded in getting to the goal with the orientation angle 0 radian using PMF for rotational motion.
The effectiveness of the proposed method was verified also by simplified experiments using omni-directional autonomous mobile robots as shown in Fig.15. In each picture of the Fig.15, aspects of the robot every 1 second are plotted. The robot recognized environment by the omni-directional camera. A position of a goal and that of obstacles relative to the robot were calculated by extracting features in images based on objects’ colours. A ball was assumed as the goal and columns were assumed as obstacles, as shown in Fig.15. A dashed circle enveloping a column in Fig.15 corresponds to a dashed circle in Fig.5. As shown in Fig. 15(a), the robot was not able to between two objects without the capsule case. However, as shown in Fig. 15(b), the robot with the capsule case performed translational and rotational motion simultaneously in real time and succeeded in going between two obstacles.
These results showed that motion control without a capsule case made it difficult for the robot to go between two objects due to the largest radius of the robot, even if it would be able to go through by using its shortest radius. Applying the capsule case to a wide robot enhances the possibility of going between two objects.
5. Conclusion
In this paper, the real time control method of simultaneously translational and rotational motions for an autonomous mobile robot, which is horizontally long, has been introduced. This method employs omni-directional platform for the drive system and is based on the fuzzy potential method (FPM). The novel design method of potential membership function (PMF), which is considered the width of the robot by using the capsule case, has been shown. According to this proposed method, the wide-robot can decide the current direction of translational motion to avoid obstacles safely by using capsule case. In addition, by controlling the rotational motion in parallel with the translational motion in real time, the wide-robot can go through narrow distance between two objects. The effectiveness has been verified by numerical simulations and simplified experiments. It has been shown that the proposed method enables simultaneous control of the translational and rotational velocity within the framework of FPM.
References
- 1.
Kavraki L. 1995 Computation of Configuration Space Obstacles Using the Fast Fourier Transform ,11 3 408 413 - 2.
Wang Y. Chirikjian G. S. 2000 A New Potential Field Method for Robot Path Planning , San Francisco, CA,977 982 - 3.
Ambrose R. O. Savely R. T. Goza S. M. Strawser P. Diftler M. A. Spain I. Radford N. 2004 Mobile manipulation using NASA’s robonaut ,2104 2109 - 4.
Du Z. Qu D. Yu F. Xu D. 2007 A Hybrid Approach for Mobile Robot Path Planning in Dynamic Environments, ,1058 1063 - 5.
Khatib O. 1986 Real-time Obstacle Avoidance for Manipulators and Mobile Robots ,5 1 90 98 - 6.
Borenstein J. Koren Y. 1989 Real-Time Obstacle Avoidance for Fast Mobile Robots, ,19 5 1179 1187 - 7.
Borenstein J. Koren Y. 1991 The Vector Field Histogram Fast Obstacle Avoidance for Mobile Robots ,7 3 278 288 - 8.
Lumelsky V. J. Cheung E. 1993 Real Time Obstacle Collistion Avoidance in Teleoperated Whole Sensitive Robot Arm Manipulators, ,23 1 194 203 - 9.
Dieter F. Wolfram B. Sebastian T. 1997 The Dynamic Window Approach to Collision Avoidance ,4 1 1 23 - 10.
Tsuzaki R. Yoshida K. 2003 Motion Control Based on Fuzzy Potential Method for Autonomous Mobile Robot with Omnidirectional Vision ,21 6 656 662 Takahashi, M., Suzuki, T., 2009. Multi Scale Moving Control Method for Autonomous Omni-directional Mobile Robot, Proc. of the 6th Int. Conf. on Informatics in Control, Automation and Robotics.