The 5th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI 2008)

Dynamic Adaptation of Global Path for Safe Navigation of Mobile Robot Jae-Yeong Lee Kyuseo Han Wonpil Yu U-Robot Research Division, Electronics and Telecommunications Research Institute Daejeon, Korea email: {jylee, kyuseo, ywp}@etri.re.kr

Abstract - Obstacle avoidance or local path planning aims to arrive a goal position safely without colliding with obstacles. However, many local path planning approaches are easy to be stuck at local minima. This paper presents a method that generates safe path based on global path planning. The method does not require complex processing or parameter tuning, which is frequently required with conventional local planning approaches. Effectiveness of the method is shown with computer simulations. Keywords - Path Planning, Safe Path, Navigation, Mobile Robot, Obstacle Avoidance

1. Introduction Path planning or obstacle avoidance is one of the key technologies for the successful navigation of a mobile robot. Many researchers have studied methods to find a good path, which can guide a mobile robot to a destination as fast and safe as possible. The meaning or definition of a good path can vary depending on applications. Paths which minimize total traveling time or traveling distance can be preferred for some applications. However, safe path that has low probability of collision is usually more important for robotics applications. Ideally the best path would be a path that satisfies both safeness and shortest traveling time criterion. Global path planning approaches try to find an optimal or feasible path on a given knowledge of the world. A* search [1] and Dijkstra's search [2] are well-known path planning algorithms based on a graphical representations of the world. However, global approaches generally lack of safety term. Local path planning approaches cope with this problem by replanning the path adaptively based on local sensory information [3-8]. Dynamic window approach [5] or VHF+ [7] belongs to this category. Although local approaches find safe path, it is well known problem that they are easy to be stuck at local minima. In addition, most local approaches require complex parameter tuning and the optimal parameter varies depending on the structure of the environment. For the shake of finding safe path without being stuck at local minima, some researchers combined local planning and global planning [9-12]. Global dynamic window approach [11] determines goal direction based on navigation gradient which is computed by using a

wave-propagation technique. VHF* [10] extends VHF+ [7] such that candidate directions are pre-verified by expanding a search tree up to predefined depth based on A* search. However, VHF* does not solve the problem of local minima completely and it requires complex parameter tuning. Zelek and Levine [12] proposed a method of concurrent planning of local and global path, in which global path guides local path planning as a local goal. Recently Kristijan Macet et al. [9] propose a method that avoids local minima by determining goal alignment of the objective function based on the alignment score of A* generated geometric path and the dynamic window generated trajectory. In this paper we propose a path planning method which preserves both local clearance and global minimization of path length. The key idea of our method is to adapt global path dynamically based on the local clearance. Different from the previous local-global approaches our approach introduces only one adjustable parameter, which controls the trade off between the local safety and the global optimality in a very intuitive way. Our approach is free to local minima and finds a safe and possibly shortest path to a goal position where safeness of a path is intuitively represented by minimum distance to the obstacles along the path. The paper is organized as follows. In Sect. 2 we describe our global path planner which finds a shortest path to a goal position in a dynamic environment. The local path planner which modifies the global path based on local safety is presented in Sect. 3. We show experimental results from computer simulation in Sect. 4 and conclude the paper in Sect. 5.

2. Dynamic Global Planning Global path planning is to find an optimal or feasible path from starting configuration to a goal configuration based on the prior knowledge of the environment. In our approach the world is represented by an occupancy grid map, where the value of each cell represents the occupancy probability of the region. Our global planner is based on A* search and sensory data of range sensor is combined with the map before global search in order to cope with dynamic obstacles. The pose of a robot is assumed to be given in real time from external localization system.

The 5th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI 2008)

Although the global planner described above finds optimal path avoiding dynamic obstacles, it lacks concept of safety. Safe path is often more important than shortest path especially for robotics applications. Figure 1 shows typical A* path from a start position S to a destination point G on a sample grid map. While the path is optimal in a sense of path length, there is high possibility of collision during navigation especially around the corner point C. In the next section we will describe the method that adjusts the path to satisfy local safety.

3. Local Adaptation of Global Path

Fig. 1. A Sample A* path

Fig. 2. Dynamic adaptation of control point based on local clearance

The idea of combining sensor data with information extracted from a map of the environment was firstly introduced by Fox et al. [6] in a purpose of resolving sensory problems such as specular reflection in sonar sensor and improving accuracy. In our approach the sensor data is used to reflect dynamic obstacles into the environment map, and then the global path is replanned on the updated map. However, frequent replanning of global path could be computationally expensive for a large map and also make the motion of mobile robot unstable as the path changes. To cope with this problem, we use the strategy of updating the global path only when the initial path is invalidated by dynamic obstacles. Our global planning briefly operates as follows: 1) Find initial global path by using A* search. 2) Follows current path for a servo tick time of the control loop. 3) Update the map locally based on sensor data. 4) Investigate whether or not the current path is invalidated by obstacles. If it is invalidated, replan a new global path based on current updated map. 5) Repeat step 2 ~ step 4 until the robot reaches a destination.

Conventional local path planning approaches firstly compute local clearance based on periodic sensory data. The direction of the next movement of the robot is then determined by considering both local clearance and goal direction. Current robot velocity and pose information also can be considered. Final robot heading is determined based on weighted sum of these terms. However, if the clearance term is highly weighted, a robot can be stuck at local minima. In other case, the safety of a robot can be spoiled if the path is highly goal-oriented. Local approaches thus have intrinsic problem of parameter tuning and the optimal parameter can vary depending on the environment. In the previous section we have presented a method generating an obstacle-free global path. Before describing our path adaptation method we first introduce a concept of control point. Control point is a temporal goal position which determines the moving direction of a robot at the current control loop of robot motion. Let p = p0p1...pn be the global path to be tracked by a mobile robot at current step of control loop, where p0 is current robot position and pn is goal position. The control point is set to one of the path points on the path. Here we rather set the next control point to pk than p1 for a predetermined constant k (k≥1). Setting the control point some steps ahead has an effect of path smoothing and makes the robot motion more natural. Our path adaptation method is to adjust the control point considering clearance of the map. Clearance is computed along a line segment of length 2d + 1 grid cells which is perpendicular to the direction of global path at the control point pk., where d is an adjustable parameter that controls the degree of safety. The direction of global path at pk is computed by the direction of path segment pk-1pk. Since the path consists of grid cells, direction of perpendicular line segment can be four orientations of vertical, horizontal, left diagonal, and right diagonal. Here we define two marginal points PL and PR on the line segment. PL is the furthest unoccupied grid point from pk along the left side of the line segment. Similarly PR is defined as the furthest unoccupied grid point along the right side of the line segment. The control point pk is then adjusted to the middle point of PL and PR. The adjusted safe control point pk* is given by

pk* ( x, y ) = (

xL + xR y L + y R , ), 2 2

(1)

where PL = (xL, yL) and PR = (xR, yR). The safe control point is updated iteratively at every step of the control loop.

The 5th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI 2008)

Fig. 3. Path adjustment near a narrow passage

Figure 2 illustrates the procedure of determining the safe control point pk*. As shown in Fig. 2, the left marginal point PL does not span to the left end of the line segment due to the obstacles (left wall). Therefore, the new control point pk* is positioned to have more distance from obstacles. The parameter d controls the trade off between the safety and the path optimality. If we use large value of d, the robot trajectory will be more distanced from obstacles, slightly sacrificing path optimality (travelling time). In case of narrow passage such as door entrances, the safe control point is located at the center point of free space as shown in Fig. 3.

Fig. 4. Simulation result with d = 2

4. Experimental Results The experiment was performed by computer simulation. We implemented a software robot which models the motion of the Pioneer 3 DX mobile robot manufactured by ActiveMedia Robotics. We also modeled a virtual laser range sensor with viewing angle of 120 degree and angular resolution of 5 degree, which is mounted at the front of the robot. The laser range sensor senses obstacles within a range of 2 meters at a rate of 10Hz. The robot velocity was set to be 4.0meter/sec. The global map is assumed to be given. The simulation results are shown in Fig. 4 and Fig. 5, where the trajectories of the virtual robot are depicted with red dots. In the experiment, the initial control point set to be p8 and the length of the line segment d was set to be 2 for Fig. 4 and 10 for Fig. 5. In Fig. 4, we can see that the robot moves following the global shortest path as the safety parameter d was set to be very small value. The green circle represents a dynamic obstacle which is not known in advance. As shown in Fig. 4, the trajectory of the robot is not safe especially near the corner points or dynamic obstacles although it is obstacle-free shortest path. This problem of unsafe navigation can be easily solved by simply enlarging the safety parameter d. Figure 5 shows the simulation result with d = 10. We can see that the trajectory is adjusted to form a safer one.

Fig. 5. Simulation result with d = 10

The 5th International Conference on Ubiquitous Robots and Ambient Intelligence (URAI 2008)

5. Concluding Remarks In this paper we have presented global-local path planning scheme and dynamic path adaptation method. The presented global-local scheme gives an obstacle-free (static or dynamic) global shortest path. And our path adaptation method enables safe navigation of a mobile robot with minimal modification of the global path, which implies significant benefits. Firstly our method is not stuck at local minima with any value of parameter d as the path is based on a global path. Secondly it has a trade off with only path optimality (path length or traveling time), and therefore we don't need to adjust it according to the environment. Our future work is to extend the path modification method such that it can be applied for unknown environment.

Acknowledgement This work was supported by the IT R&D program of MKE and IITA [2008-S-031-01, Development of Hybrid u-Robot Service System Technology for u-City].

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