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1 Combined Map-Based and Case-Based Path Planning for Mobile Robot Navigation Maarja Kruusmaa and Bertil Svensson Chalmers University of Technology, Department of Computer Engineering, S Gothenburg, Sweden fmaarja, Abstract This paper presents an integrated approach to mobile robot path planning by combining grid-map based and case-based methods. The map-based path planner is used to suggest new innovative solutions for a particular path planning problem. A probabilistic path transform method is introduced for grid-map based path planning which proposes several alternative solutions for a single path planning problem. The casebase is used to store the paths and evaluate their traversability. Using the casebase allows the robot to benet from its former experiences while planning a new route. As the dynamic properties of the environment may change the exploration as well as the evaluation of the paths will allow the system to self-organize by forming a set of paths that will be safest to follow. 1 Introduction In recent years, much progress has been made in robot navigation in dynamic environments. Robots with ability to navigate in changing environment are starting to appear in industry and take the place of AGVs (Automated Guided Vehicles) whose motion is restricted to certain predened paths [1]. Still, the main task of these robots is the transport of parts and sub-assemblies between manufacturing cells, which, to a great extent, means following one and the same path in the majority of cases. There is a good evidence that animals seem to prefer well dened and constant paths, even if it means longer travel distances [2]. The knowledge of these paths seems to be acquired in some cases (e.g. bees), in others they must be genetically preprogrammed (e.g. juvenile terns). The reason for preferring already known paths is obvious. Once the path is safely passed it is natural to expect that taking the same path next time will lead to the same positive result. The more times the path is successfully followed the less reason there is to explore a new path through unfamiliar and, thus, possibly dangerous environment. However, if the usual path is blocked or appears to be very risky to traverse due the changes in environmental conditions, a new route has to be found. The approach presented in this paper uses case-based reasoning to learn from past experiences. The robot will save the paths that it has followed in a casebase, and next time it has to go from the same starting point to the same goal it simply triggers that case from the casebase. However, if no corresponding case exists, or the case is not good enough, the robot has to use the help of a map-based path planner or let the human operator suggest a path. 2 Case-Based Reasoning Case-based reasoning solves new problems by adapting previously successful solutions to similar problems. The past experiences are stored in a casebase which is managed by applying database techniques. To facilitate the case retrieval the cases in a casebase are indexed. When a new problem occurs the indices are extracted from its features and used to nd matching cases in a casebase. If more than one matching case is found the candidate cases are evaluated to nd the most suitable one. Unless the retrieved case is a close match the solution will probably have to be modied before using it for problem solving. If the modied case is found to be successful, it produces a new case which is stored in a casebase. Thus, in case-based reasoning, learning is through accumulation of new cases. 1
2 Case-based reasoning seems to oer solutions to many problems in knowledge engineering such as knowledge elicitation, encoding and maintenance and is often viewed as low risk technology [3]. The ability to learn from past experience makes case-based systems suitable for use in changing environments. At the same time, the knowledge in a casebase can be stored explicitly making it possible for human operators to author new cases themselves and to easily understand how decisions are reached. 3 Map-Based Path Planning Two dierent approaches are used for environment modelling in mobile robot navigation: topological maps and grid-based maps. Both approaches have their own merits and demerits. While grid-based maps are easy to build and permit computation of shortest path, topological maps facilitate more ecient planning and, as they determine the robot position relative to the landmarks, localization is easier. Recently some attempts have been made to overcome the weaknesses of both of the methods by combining them together. An example of this kind of work is presented in [4] where a topological map is extracted from an occupancy grid map with the help of Voronoi diagrams and the topological map is then used for ecient path planning. Among path planning methods that use grid-based maps we nd the distance transform method [5], the path transform [6] and path planning based on virtual diusion process [7]. All these methods are able to nd a path if one exists and do not require expensive computations. The distance transform method works by propagating distances from the goal through free space and the path is planned by following the cells with lowest values. The path transform method is an extension of the distance transform that overcomes the main disadvantage of the result of the distance transform, namely of moving too near to the obstacles. When the distance transform method assumes that the \best" path is the shortest path, the path transform assumes that the \best" path is the shortest safe path. Path planning based on virtual diusion process assumes the goal cell to be the source of a gaseous substance. In a steady state the concentration distribution of a gas shows monotonously decreasing concentration along a path connecting the goal point to the arbitrary starting point. As, in reality, the environments are almost always dynamic, it is essential to consider the uncertainty while solving the path planning problem. The problem of uncertainty is most often tackled with local navigation methods by introducing the reexive obstacle avoidance behaviour (see [8] for a survey). On the global level the concept of occupancy grids is used, where each grid cell has assigned to it a value of probability of it being occupied. However, the occupancy grid does not reect the statistical properties of a particular cell. The changing environmental conditions may cause problems in map updating. If, in the case of a grid-based map, a cell is occupied, a high occupancy value is assigned to it, and, while planning a path the planner will naturally try to avoid that particular cell. As the robot now does not traverse that cell any more it can not know when the obstacle is removed and the cell is passable again. In order to update all cells, a wandering behaviour might be invoked but if large real-world maps are considered a wandering would be time-consuming as well as risky. In addition, the diculties in robot localization may lead to a very ambiguous updated map. An interesting approach is taken in [9] to cope with dynamic obstacles. In order to get statistical data cameras are mounted to the ceiling and information from these is incorporated into the grid-map. Our approach is to not update the map at all but use a casebase to reect the dynamic changes in the environment. The paths are planned using a grid-map based method and then, while following the paths, the occupancy of the whole path is evaluated rather than that of every particular grid cell. The paths once planned are stored in a casebase together with the statistical information about their traversability. While planning the path the casebase is searched rst. If no matching cases are found or the cases are not good enough, the map-based path planning method is used for path planning. Our system divides the robot control architecture into two levels (Fig.1): global planner and local planner. The task of the global planner is to nd a collision free path from start to goal. It poses tasks to the local planner as a sequence of sub-goals. The local reactive planner is then responsible for reaching to every sub-goal while avoiding the unknown obstacles. If the local planner fails to reach a subgoal, the path has to be re-planned by the global planner. The navigation unit is responsible for localization. It uses the information of dead-reckoning, sensors and from recognized landmarks and determines the position of the robot. The global planner is accessible via a user interface allowing a human operator to monitor the path-planning process or make its own suggestions, thus forcing the robot to follow some particular path. The global planner uses two complementary methods for path-planning: map-based and case-based. 2
3 Map User Interface Global planner Casebase Navigation and localization unit Local planner actuators sensors Figure 1: System Architecture 4 The Probabilistic Path Transform Method The map represents the environment in a 2D regular grid. It is not updated and contains unremovable objects and areas where the robot is not allowed to enter (e.g. for the sake of safety). The map-based path planner uses a probabilistic path transform method which is an extension of the distance transform method of Jarvis [5] and the path transform method of Zelinsky [6]. While distance transform and path transform methods assume that the environment is static, the probabilistic path transform method assumes that the environment contains dynamic obstacles and therefore the best path to the goal is not necessarily the shortest. As the presence and density of dynamic obstacles may be unknown, the probabilistic path transform uses a probabilistic mechanism to nd several alternative solutions to the path planning problem. Let P denote the set of all possible paths on the grid. The probabilistic path transform plans a path P (c s ; c g ) 2 P from the start cell c s to the goal cell c g. A path P (c s ; c g ) is specied as an ordered set of grid cells c i P (c s ; c g ) = fc s ; ; c i ; ; c g g The neighbourhood N(c i ) of the cell c i is the set of all cells closer to the cell c i than a certain distance ". The probabilistic path transform method works by propagating cell values along the map. The map may contain xed obstacles. Each cell, which does not contain a xed obstacle, gets a value which is a combination of the distance from the goal, the measure of the discomfort moving near obstacles and a parameter with a random value: P T (c) = min (length(p (c; c g )) + P (c;c g)2p(c;c g) X c i2p (c;c g) obstacle(c i ) + X c i2p (c;c g) grow(c i )) (1) where P(c; c g ) is a set of all possible paths from the cell c to the goal. The function length(p (c; c g )) is the length of the path to the goal. The function obstacle(c) represents the discomfort the nearest xed obstacle exerts on the cell c. The parameter 0 determines how strongly the path transform will avoid obstacles. The function grow(c i ) is dened as follows: grow(c i ) = C if ci 2 N(c k ) 0 otherwize where parameter C is a random positive constant, N(c k ) is a neighbourhood of a randomly chosen cell c k with a random width ". The third term in (1) then represents a disturbance of the path transform in the form of higher cell values in N(c k ) so that new paths are created. Once the values of all grid cells are calculated, the path is found by tracing the path of the steepest descent from start to goal. Because the probabilistic distance transform determines the costs of all paths to the goal from each cell, it does not contain local minima and if there exists a path from the given start to the given goal, it is guaranteed to be found. The method does not need particularly time-consuming computations and can be used as a real-time path planning algorithm. 3
4 5 Case-Based Path Planning Each path that the robot has traversed is stored as a case in the casebase indexed by the start and goal cells. The casebase serves two purposes: (1) to accelerate the path planning process and (2) to gather statistical information about paths. To characterize the traversability of every particular path P there is dened a cost function (P ). The value of this function is stored together with the path P. The cost of the path P is determined as follows: (P ) = f(l; r; I ) The parameter l is the length of the path. The parameter r characterizes the risk (or diculty) of following the path and is calculated by gathering information during the path following process (e.g. based on the control signals that the local planner gives to the actuators, such as average speed or the number of turns the robot makes in order to avoid unknown obstacles, etc.). In order to normalize the costs, the cost of every path (P ) is calculated with respect to an ideal cost I, the cost of the shortest and easily traversable path from start to goal. Several dierent paths may exist between two specic points in the casebase; therefore, when retrieving a case, each of these paths is selected with the probability inversely proportional to its cost. The cost is thus used to force the robot to take the same route the more certainly the more successfully it has been followed. If the casebase does not contain a case, which is needed, a case adaptation procedure can be used to retrieve the most similar case and adapt it to the current one. As the knowledge about paths in the casebase is stored explicitly, it is possible for human operators to author new cases themselves and to easily understand how decisions are reached. 6 The Global Planner The global planner of the robot is responsible for choosing either the casebase or the map. The global planner (or the human operator) will decide how strongly the system is biased to exploration. Using the probabilistic mechanism of the map-based path planner, on one hand, encourages the exploration in search for the best possible solution. The casebase, on the other hand, allows the usage of the suciently good solutions already found and therefore avoids taking additional risks while exploring the unknown environment. The global planner will also be responsible for casebase management. Determination and deletion of irrelevant and useless cases is important to keep the size of the casebase small enough to be managed in real-time. 7 The Experiments Computer experiments in a simulated environment show that the system is able to adapt to use the paths that are less probably occupied by obstacles. In Fig.2 the simulated environment is presented. The colour of a cell shows its probability of being occupied by dynamic obstacles. The darker the colour of a cell is, the higher is the probability that it is occupied. This map is not known to the robot but only used to evaluate the paths planned by the map-based path planner. The map of the robot is shown in Fig.3 together with the xed obstacles the robot is aware of. In this gure also the shortest paths between four start and goal cells are represented. These paths are the optimal ones in terms of length and distance from the xed obstacles but they do not consider the presence and density of dynamic obstacles. To test the performance of the system a sequence of tasks is presented to the global planner. Fullling a task means planning a path from a given start cell to a given goal cell (using either the casebase or the map), evaluating its traversability and updating the casebase. In the experiments below the number of tasks is 300 and the casebase can contain maximum 30 cases. Two dierent cost functions are used to evaluate the system. In the experiment in Fig. 4 the cost is based on both the length and the clearance (traversability) of the path. Therefore the best paths found sofar cut the corners of the risky regions (dark area in Fig.2 ). In the experiment in Fig.5 only the traversability of the paths is considered when calculating the cost. The best, and therefore the most often chosen paths are presented. 4
5 Figure 2: The map of probabilities. Figure 3: The map of the robot with the shortest paths. The crosses mark the start and goal cells. Figure 4: The best paths. Both the length and the clearance of the paths is considered. Figure 5: The best paths. Only the clearance of the paths is considered. 5
6 8 Conclusions and Future Work In this article we have presented a path planning method that combines map-based and case-based path planning. The probabilistic path transform method uses a grid-map and allows computing of paths without particularly time-consuming computations. The casebase adds new features by incorporating path evaluation and making the whole system able to adapt in a dynamic environment. The computer experiments in a simulated environment show that the system is able to adapt to use the paths that, according to its experiences, are least risky to follow. While the performance of the probabilistic path transform is tested rather carefully, the casebase performance and management are still to be investigated and evaluated. In order to use case-based reasoning in an eective way, several problems need to be addressed, e.g., how does the size of the casebase inuence the performance, how to adapt cases, which similarity measure to use in case adaptation, which cases are worth remembering and how to choose a forgetting criterion. References [1] Automated Guided Vehicle Systems. R.H.Hollier ed. IFS Publications Ltd. Springer-Verlag, [2] U.Nehmzow. Animal and Robot Navigation. In The Biology and Technology of Intelligent Autonomous Agents. NATO/ASI series NATO , Springer-Verlag, [3] I.Watson, F.Marir. Case-Based Reasoning: A Review. In The Knowledge Engineering Review. Vol.9 No.4, [4] S.Thrun, A.B}ucken. Integrating Grid-Based and Topological Maps for Mobile Robot Navigation. In Proc. of the Thirteenth National Conference on Articial Intelligence AAAI, Portland, Oregon, August [5] R.Jarvis, K.Kang. A New Approach to Robot Collision-Free Path Planning. In Robots in Australia's Future Conference, pp.71-79, [6] A.Zelinsky. Using Path Transforms to Guide the Search for Findpath in 2D. In The International Journal of Robotics Research, Vol.13, No.4, August 1994, pp [7] K.Azarm, G.Schmidt. Integrated Mobile Robot Motion Planning and Execution in Changing Indoor Environments. In Proc. of the IEEE International Conference of Intelligent Robots and Systems (IROS'94), Sept , Vol.1, pp [8] R.C.Arkin. Reactive Robotic Systems. In Handbook of Brain Theory and Neural Networks, ed. M.Arbib, MIT Press, pp , [9] R.Gutche, C.Laloni, M.Wahl. Path Planning for Mobile Vehicles within Dynamic Worlds Using Statistical Data. In Proc. of the IEEE International Conference of Intelligent Robots and Systems (IROS'94),Sept , 1994, pp
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