COMPARISON OF ROBOT NAVIGATION METHODS USING PERFORMANCE METRICS

COMPARISON OF ROBOT NAVIGATION METHODS USING PERFORMANCE METRICS Adriano Flores Dantas, Rodrigo Porfírio da Silva Sacchi, Valguima V. V. A. Odakura Faculdade de Ciências Exatas e Tecnologia (FACET) Universidade Federal da Grande Dourados (UFGD) Dourados, Mato Grosso do Sul, Brasil Emails: adriano.dnt@gmail.com, rodrigosacchi@ufgd.edu.br, valguimaodakura@ufgd.edu.br Abstract Techniques to compute a path from an initial position to a goal position avoiding obstacles are crucial for robot navigation. When the robot trajectory is generated directly from sensor information, the techniques are called collision avoidance. Two interesting collision avoidance methods are Nearness Diagram (ND) and Vector Field Histogram (VFH). Besides both methods present some similarities, they differ specially in the performance in very cluttered environments. In order to compare and analyze the performance navigation of ND and VFH, some quality metrics were chosen, such as path length and smoothness of the trajectory. In this paper, ND and VFH are simulated in different environments, with different goal positions. The results are then compared and the analyses are presented. Keywords Mobile robot navigation, performance metrics, Nearness Diagram, Vector Field Histogram. 1 Introduction In navigation task, a mobile robot should be able to reach a goal position from its initial position given a partial knowledge of the environment and sensor measurements. Two important competences required for robot navigation are path planning and collision avoidance. Path planning involves generate a trajectory from initial position to a goal position while avoiding obstacles, using a map of environment. When the environment is dynamic, the trajectory generated becomes inaccurate and it is needed to replan continuously in order to reach the goal. In this situation, path planning is too time consuming to avoid collision. Collision avoidance approaches generate the motion commands that drive the robot towards the goal directly from sensory information. These approaches are well suited for situations when the environment is unknown and dynamic. However, it is based on local information, being unable to generate optimal solutions. Among the collision avoidance approaches there are two very interesting, Nearness Diagram (ND) and Vector Field Histogram (VFH), that are main subject of this paper. This paper is organized as follows. In Section 2, the collision avoidance approaches are presented. The proposed comparison methods for the navigation task are described in Section 3. Experiments are conducted in simulated environments and the results are shown in Section 4. Finally, in Section 5, our conclusions are derived and future works are presented. 2 Navigation methods Navigation task can be accomplished using collision avoidance approaches, which are useful specially in dynamic or unknown environment. The ND and VFH are two methods for collision avoidance. The ND (Minguez and Montano, 2000), (Minguez and Montano, 2004) is a collision avoidance algorithm that extracts a description of environment regions that are free from obstacles, choose one of these regions, and evaluate the robot security. Based on the security information evaluated, the algorithm generates motion commands. The VFH (Borenstein and Koren, 1991) creates local map of the environment around the robot. This map is represented as a small occupancy grid, populated by recent sensor range readings. VFH generates a polar histogram, where the x-axis represents the angle at which the obstacle was found and the y-axis represents the probability that there really is an obstacle in that direction based on the occupancy grid cell values. From this histogram a steering direction is calculated. The VFH+ (Ulrich and Borenstein, 1998) is the result of several improvements over the original VFH method. The robot trajectory becomes smoother and more reliable, it explicitly takes into account the robot width, and therefore this method can easily be implemented on robots of different sizes. Siegwart and Nourbakhsh (Siegwart and Nourbakhsh, 2004) present a comparison table for some collision avoidance approaches. This table is presented here with some adaptations, in table 1. In the table it is possible to notice that both techniques have several similarities, as circular shape, local view and local minima. However, in this paper we aim to investigate the differences between these techniques. Some performance metrics to ISSN: 2175-8905 - Vol. X 1132

Table 1: Obstacle avoidance algorithms. ND VFH shape circular circle kinematics holonomic basic view local local local map - histogram grid sensor 180 FOV SICK sonars laser scanner tested robot holonomic nonholomic (circular) (Guide Cane) remarks local minima local minima compare both techniques are presented in next section. 3 Performance metrics The analysis of the performance of mobile robot navigation method for the execution of a trajectory from an initial to a goal position is important to find out how to improve performance for a specific method or to compare similar methods. Some of quality metrics generally used are the time needed to reach the goal and the length of the path. However, there is no consensus on how to measure the performance. Some works as (Ceballos et al., 2007) and (Selekwa et al., 2004) present two performance metrics described in this section: length and smoothness of trajectory. It is considered that the optimal trajectory, when possible, is a line between initial and goal position. However, for most environments, the straight line is not a trajectory possible. In this case, the metric used can be the length of trajectory covered. Considering that the trajectory is composed by n points, and assuming that the initial point is (x 1, y 1 ) and the final point is (x n, y n ), the length trajectory is: n 1 L = ((xi+1 x i ) 2 + (y i+1 y i ) 2 ). (1) i=1 Another metric is the smoothness of a trajectory. A smooth trajectory is desired once it is beneficial to mechanical structure of the robot and it shows the ability to anticipate and to respond to events with sufficient speed. The smoothness is a measure of the energy and time requirements for the movement. For curves in x-y plane, the curvature at any point (x i, y i ) is given by: k(x i, y i ) = y i (1 + (y i, (2) )2 ) 3/2 where k(x i, y i ) is the curvature at each point of the robot trajectory. The bending energy B E is a function of the curvature k and can be calculated as: B E = 1 n 1 k 2 (x i, y i ). (3) n i=1 Less bending energy indicates that the motion is smooth while higher values indicate sharp motions. We argue that the length and smoothness of trajectory, time to complete the path and some observations about the environment are good metrics for measuring navigation performance. These metrics are used in this paper to compare ND and VFH in different environments, as shown in the next section. 4 Experimental results The experiments for comparing ND and VFH are conducted in the Player/Stage software. The Player/Stage project, released under the GNU General Public License, creates free software that enables research in robot and sensor systems. Player is a network server for robot control, it provides interface to the robot s sensors and actuators over the IP network. Stage simulates a population of mobile robots, sensors and objects in a two-dimensional environment (The Player Project - Free Software tools for robot and sensor applications, 2010). The Player provides the implementation of ND and VFH through drivers. The VFH driver implements the VFH+ navigation method, as a goal-seeking obstacle avoidance algorithm. The ND driver is a goal-seeking obstacle-avoidance, specially suited for tight spaces. The simulated robot is a pioneer 2DX, a nonholonomic robot, equipped with laser and odometry sensors. Four different environments are used to test ND and VFH. Two environments are more round, it means, the obstacle borders are not sharp and the other two environments present straight lines obstacles, similar to the walls in internal environments. One of the environments with straight lines obstacles presents narrow passages between obstacles. The first experiment is shown in Figure 1, the trajectories for ND and VFH can be seen in Figures 1 and 1, respectively. The visual inspection of the trajectories show that VFH trajectory is smoother than ND, and it seems shorter too. The second experiment is shown in Figure 2, and the visual inspection of the trajectories show the same results of the first experiment, the VFH results in smoother and shorter trajectory. Both experiments are similar in the shape of obstacles, that are round. Using the performance metrics presented in section 3 it is possible to confirm the visual inspection, as is shown in tables 2 and 3. The lines for scenarios 1 and 2, present shorter ISSN: 2175-8905 - Vol. X 1133

Figure 1: Scenario 1 ND. VFH. Figure 2: Scenario 2 ND. VFH. ISSN: 2175-8905 - Vol. X 1134

Figure 3: Scenario 3 ND. VFH. Figure 4: Scenario 4 ND. VFH. ISSN: 2175-8905 - Vol. X 1135

Table 2: Simulation performance results for path length. Optimal Path Length Scenario trajectory ND VFH 1 10.07 22.40 21.65 2 14.57 19.74 19.16 3 15.35 17.90 18.40 4 11.92 13.79 31.75 Table 3: Simulation performance results for bending energy and time. Bending Energy Time Scenario ND VFH ND VFH 1 0.39 0.06 56 57 2 0.10 0.05 60 66 3 0.18 0.06 48 53 4 0.03 5.90 43 154 path length and bending energy, however, the time consuming is shorter for ND in both experiments. The third and forth experiments are shown in Figures 3 and 4, respectively. Both experiments are similar in the shape of obstacles, that are straight lines, similar to internal environments. Using the performance metrics presented in section 3 to analyze the trajectories, as is shown in tables 2 and 3, in the lines for scenarios 3 and 4, it is possible to note that the path length is shorter and it is faster for ND in both experiments. However, for bending energy criteria, the trajectory is smoother for VFH in scenario 3, and for ND in scenario 4, the one with the narrow passages. It is worth to note that in experiment 4, the ND trajectory is shorter and faster than VFH one, once ND is well suited in tight spaces. Analyzing all the results is possible to confirm that the ND is faster for all scenarios, path length is shorter for ND trajectories in round environments, and the trajectory is smoother for all scenarios, excepted the narrow passages ones. These results are preliminary, but they are useful to guide the decision of the collision avoidance methods, considering the characteristics of the environment and the most important criteria. 5 Conclusions and future work In this paper we present a comparison of two important collision avoidance methods: Nearness Diagram and Vector Field Histogram. For comparing collision avoidance methods it is used some performance metrics: path length, bending energy, time consuming and shape of obstacles. Experimental results have shown some differences between the two methods. We have shown that using performance metrics, any navigation method can be compared with others. The results are important to guide a decision about the method that should be chosen considering the environment characteristics and which metric is more important to optimize. Finally, as part of our future work, we plan to investigate other metrics, more related to the characteristics of environment, as the form of and distance from obstacles. References Borenstein, J. and Koren, Y. (1991). The vector field histogram - fast obstacle avoidance for mobile robots, IEEE Journal of Robotics and Automation 7: 278 288. Ceballos, N. D. M., Valencia, J. A. and Ospina, N. L. (2007). Performance metrics for robot navigation, Congress of Eletronics, Robotics and Automotive Mechanics - CERMA, pp. 518 523. Minguez, J. and Montano, L. (2000). Nearness Diagram Navigation (ND): A new real time collision avoidance approach, Proceedings of the IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 00), pp. 2094 2100. Minguez, J. and Montano, L. (2004). Nearness Diagram (ND) navigation: collision avoidance in troublesome scenarios, IEEE Transactions on Robotics and Automation 20: 45 59. Selekwa, M. F., Collins, E. G. and Combey, J. Q. (2004). Multivalued versus univalued reactive fuzzy behavior systems for navigation control of autonomous ground vehicle, Proceedings of 17th Annual Florida Conference on Recent Advances in Robotics. Siegwart, R. and Nourbakhsh, I. R. (2004). Introduction to autonomous mobile robots, MIT Press. The Player Project - Free Software tools for robot and sensor applications (2010). Available: http://playerstage.sourceforge.net/ Accessed: 18/06/2010. Ulrich, I. and Borenstein, J. (1998). Vfh+: reliable obstacle avoidance for fast mobile robots, IEEE International Conference on Robotics and Automation, pp. 1572 1577. ISSN: 2175-8905 - Vol. X 1136