Survey navigation for a mobile robot by using a hierarchical cognitive map

Transcription

1 Survey navigation for a mobile robot by using a hierarchical cognitive map E.J. Pérez, A. Poncela, C. Urdiales, A. Bandera and F. Sandoval Departamento de Tecnología Electrónica, E.T.S.I. Telecomunicación Universidad de Málaga, Campus de Teatinos, Málaga (Spain) Abstract This paper presents a survey navigation scheme for a mobile. One of the main features of these schemes is that they must support planning over unexplored areas. To this purpose, a new cognitive map construction technique using sonar sensors is proposed. This technique consists of building a hierarchical map where higher levels of the structure conforming the topological map are explicitly related to the lowest level of the structure, which is a metric map. Thus, geometrical information is preserved in the topological map and unexplored areas can also be represented. The proposed scheme has been successfully tested using a Nomad 200 robot equipped with a ring of 16 sonar sensors. 1. Introduction Navigation is traditionally defined as the process of determining and maintaining a trajectory to a goal location (Gallistel, 1990). Biological navigation behaviours have been an important source of inspiration for robotics in the past decade. According to Levitt and Lawton (Levitt and Lawton, 1990), navigation consists of answering three questions: (a) Where am I? ; (b) Where are other places with respect to me? ; and (c) How do I get to other places from here?. However, biological systems do not necessarily require all that knowledge to navigate, but they usually work on a how do I reach the goal? basis. Most systems typically deal with different degrees of knowledge depending on the circumstances. Much work on navigation classification schemes is available, but one of the most popular schemes is the navigation hierarchy one (Franz and Mallot, 2000) because: i) each level of the hierarchy can be tested experimentally; and ii) it is valid for biological and technical navigation. In this hierarchy, navigation behaviours are classified according to the complexity of the task they can perform. Local navigation behaviours, which require only recognition of the goal location, are divided into four levels: i) search; ii) direction following; iii) aiming; and iv) guidance. Way-finding behaviours, which require knowledge about several places as well as the relation between them, are divided into three levels: i) recognition-triggered response; ii) topological navigation; and iii) survey navigation. There are many examples of local navigation mechanisms, recognition triggered responses and topological navigation in the animal kingdom, but survey navigation may be limited to vertebrates. More information on these behaviours may be found in (Franz and Mallot, 2000). This paper focuses on survey navigation, which provides the capacity of planning on partially unknown environments. To this purpose and to increase the robot performance, a new cognitive map structure is proposed. This map presents a hierarchical structure that is especially suitable to work with the navigation hierarchy. Section 2 presents the way-finding problem. Section 3 presents the proposed hierarchical cognitive map. The map is constructed using a ring of sonar sensors, which are very popular in robot navigation because they are cheap, light and simple to process. Section 4 presents a survey navigation scheme based on the proposed map, plus some experiments using a Nomad 200 robot. Finally, section 5 presents conclusions.

2 2. The way-finding problem The way-finding problem involves the recognition of several places, which may be outside the current range, and a representation of relation between them. Consequently, the agent needs to store a representation of the environment that is known as cognitive map (Kuipers, 2000). Way-finding relies on local navigation skills to move from one place to another, but it allows the agent to find places that could not be reached by local navigation alone. Most literature on way-finding focuses on recognition-triggered response and topological navigation. Basically, the difference between all three way-finding schemes relies on the cognitive map they use. Recognition triggered responses (Gaussier and Zrehen, 1995) connect two locations by using a local navigation method. A pair <starting location, local navigation method> represents them. When a starting location is recognised, a local navigation method is triggered. There is no planning of a sequence of movements, but just a selection of the very next action. Hence, the scheme is not flexible to dynamic changes in the environment. This scheme is used to build routes as a concatenation of recognition triggered responses. These routes may connect places that could not be reached by local navigation alone. Topological navigation (Mataric, 1991) consists of generating a cognitive map of the environment where places are nodes. Typically, nodes are inserted in the graph when a distinctive sensory input is detected. Two nodes are connected if a feasible route between the places they represent has been tracked and the weight of the arc joining them is usually related to factors like the travelled distance. Hence, an agent is bound to follow the same path every time it wants to travel between two nodes. Topological maps do not preserve geometric relations. Hence, most topological navigation methods rely on disambiguation processes to optimise the acquired maps. The main advantage of topological navigation is that it supports deliberative planning. Finally, survey navigation requires embedding of all known places and their spatial relations into a common frame of reference so that the representation can be manipulated as a whole. It must be noted that topological navigation only requires spatial relations between connected places. Since every location is embedded into a common frame of reference in survey navigation, the agent may find novel paths over unknown terrain by inferring its spatial relation to the known places. There is not much work on survey navigation. In fact, existing approaches to planning in partially unknown environments rely on metric maps (Moravec, 1988), where geometric relations between places are explicitly represented in an analytical way. Metric maps are easy to build and fast to update. Their main disadvantages are that they are sensitive to all errors affecting metric information, namely robot slippage, and that they typically yield a very large data volume. Hence, planning over an average sized environment may be so constly that on-line operation is not possible. 3. A hierarchical cognitive map for survey navigation To benefit from the advantages of metric and topologic maps, we propose a new cognitive map calculation algorithm that combines both schemes. The proposed algorithm relies on building a hierarchical structure over an occupancy grid, which is constructed using a ring of sonar sensors as proposed in (Moravec, 1988). In these grids, each cell (x, y) in the map yields the occupancy probability of the corresponding region of the environment. The robot used metric in our research is the Nomad200 mobile robot, which is equipped with a ring of 16 equally spaced sonar sensors presenting an arc of uncertainty of approximately 25 degrees. To build the metric map,

3 cells are modelled in a sonar scan by using a very simple probability distribution. Then, sonar readings are integrated over time to yield a coherent map. The topological and metric map building procedures are described in more detail in (Bandera et al, 2001). It is important to note that the exactitude of the generated metric map depends on the correct alignment of the robot with its map. Hence, grid-based approach must be capable of identifying and correcting slippage and drifting. Currently, odometry and compass information are used to maintain a coherent correlation between the robot and its virtual image at the metric map. In order to improve this position estimation, the correlation of the sonar readings at current instant of time and the corresponding section of the global map (Schiele and Crowley, 1994) could be easily added. This correlation would give a second source of information for correcting the position of the robot. The cognitive map is built as follows: 1. Grid thresholding. First, the metric map is thresholded. Cells whose occupancy value is below threshold U 1 are considered free-space (P(x,y)=0). Cells whose occupancy values are above U 1 and below threshold U 2 are considered non-explored (P(x,y)=0.5). The rest of the cells are considered occupied (P(x,y)=1) (Fig. 1.a). 2. Hierarchical structure generation. The thresholded metric map becomes the base of a pyramidal structure. Each level l of the pyramid is a reduced map presenting 1/4 of the cells of the level immediately below. The following 5 parameters are associated to each pyramid node (x,y,l): Homogeneity, H(x,y,l). H(x,y,l) is set to 1 if the four cells immediately underneath (x,y,l) at level l-1 present the same occupancy probability and their homogeneity values are equal to 1. Otherwise, it is set to 0. Occupancy probability, P(x,y,l). If (x,y,l) is homogeneous, P(x,y,l) is equal to the occupancy probability value of any of the four nodes immediately underneath at level l-1. If (x,y,l) is not homogeneous, the value of P(x,y,l) is set to a fixed value. Area, A(x,y,l). It is equal to the addition of the areas of the four nodes immediately underneath (x,y,l) at level l-1. Parent link, (X,Y)(x,y,l). If (x,y,l) is homogeneous, the values of the parent link of the four cells immediately underneath (x,y,l) at level l-1 are set to (x,y). Otherwise, these four parent links are set to a null value. Centroid, C(x,y,l). It is the centre of mass of the region at the base level which is linked to node (x,y,l). When the structure is generated, cells at upper levels presenting a homogeneity value equal to 1 are linked to regular homogeneous regions at the metric map. These nodes may conform a topological map representing free, occupied and unexplored nodes. The map does not need disambiguation because metric relationships are preserved at the base of the structure. However, the map size depends on the layout of the obstacles and it is poorly optimised (Fig. 1.b). Hence, several additional steps are still necessary.

4 3. Linkage of unlinked nodes (Fig. 1.c). The goal of this step is to link nodes whose parent link values are null. Basically, a node (x,y,l) is linked to the parent of neighbour node, (x, y, l+1), if the following conditions are true: H(x,y,l)=1 and H(x,y,l+1)=1 P(x,y,l)=P(x,y,l+1) C(x,y,l)-C(x,y,l+1) 2 <DistMax, being DistMax a threshold that fixes the maximum dispersion of the regions at the base. 4. Fusion of homogeneous nodes. Two neighbour nodes, (x 1,y 1,l) and (x 2, y 2,l), are fused if the following conditions are true: (X,Y) (x 1,y 1,l)=NULL (X,Y) (x 2, y 2,l)=NULL H(x 1,y 1,l)=1 and H(x 2, y 2,l)=1 P(x 1,y 1,l)=P(x 2, y 2,l) C(x 1,y 1,l) -C(x 2, y 2,l) 2 <DistMax Fig. 1. Cognitive map construction in a real environment: a) occupancy grid; b) initial topological layout; c) topological layout after linkage of unlinked nodes; d) topological layout after fusion of homogeneous nodes. When these four steps are accomplished, each node of the resulting structure presenting an homogeneity value equal to 1 is linked to an homogeneous irregular region at the base. A node of the structure presenting an homogeneity value equal to 1 becomes a node of the topological map if it is not linked to a parent cell presenting an homogeneity value equal to 1 as well. This way, the resulting topological map presents the minimum possible number of nodes. An arc whose weight is equal to the distance between their centroids connects nodes linked to touching regions at the base. Arcs connected to nodes presenting an occupancy value equal to 1 yield an infinite weight. It must be noted that the nodes of the resulting topological map are spread all over the different levels of the structure (Fig. 1.d). The proposed algorithm abstracts the topological map from the metric representation on-line. This map building process is so fast that the robot may recalculate the topological map each time the metric map is significantly updated. It can be observed that this map preserves geometrical reference because nodes are linked to the original metric map. There are other approaches to topological-metric map building, which rely either on annotating a topological map with metric information to disambiguate it (Kuipers, 1993) or on abstracting a topological map from a metric one (Thrun et al, 1998). However, none is valid for on-line map acquisition in partially unknown environments.

5 4. Survey navigation After the proposed cognitive map is constructed, planning may be performed at topological level. Hence, once a departure and arrival points are available, the link structure indicates which nodes at topological level they are connected to. Then, a route between them can be calculated by using any path planning algorithm (i.e. the A* algorithm). Finally, the route is propagated and tracked at metric level by using the potential fields method. Fig. 2 presents a typical problem for way-finding schemes. The 1056 m 2 environment in Fig. 2.a is only partially explored by the robot. Fig. 2.b presents an occupancy grid yielding 256x256 cells where obstacles are black, free space is white and unexplored areas are grey. Initially, the north door is open so that the easiest way to go from point D (departure) to point A (arrival) is to cross that door. Then, we close the door. A recognition triggered response scheme would fail, because the response to the input sensory pattern at point D would always be to cross the door. A topological approach would find a route through the west side of the room, because no nodes nor arcs are available at the non-explored area. Fig. 2. Test environment: a) environment layout; b) partially explored evidence grid Fig. 3 presents the results of the proposed survey navigation scheme for the problem in Fig. 2. To prove the efficiency of the scheme, three different situations have been tested. Fig. 3.a shows the topological-metric initially estimated cognitive map, when the door is still open. Topological nodes are marked with circles. It must be noted that if there is an arc between two nodes, it means that there is a feasible path from one node to the other. However, that path is not a straight line. Thus, even though some arcs in the representation cross obstacles, it can be observed that there are free paths joining the regions they connect (i.e. the arc of the left extreme of the figure means that there is a path bordering the north wall to travel between the nodes it connects). It can also be observed that unexplored areas are also represented at topological level because their geometrical relations to the rest of the nodes can be extracted from the associated metric map. Hence, even though the robot has not travelled through the east side of the map, it is feasible that there might be a path from D to A crossing the unexplored area. Nevertheless, as long as the door is open, the shortest path from D to A runs through the door as expected. In Fig. 3.b the robot has navigated towards the formerly open door and it finds it closed. Hence, a new path is required to reach the goal. It can be noted that the metric map is updated to include the closed door. Consequently, the associated topological map is also modified and the path in Fig. 3.a is no longer feasible. It can be observed how the upper part of the topological graph is modified to represent this situation. Fig. 3.b shows the new route chosen by the robot to reach A. It can be

6 observed that the route crosses the unexplored area, because it would be more costly to border the north wall. Finally, Fig. 3.c presents a typical problem when travelling through unknown regions: there is an unexpected obstacle in the unexplored area that makes it impossible to track the path in Fig. 3.b, which was calculated when no information on that area was available. Since the cognitive map can be updated very fast and path planning over the topological map is fast as well, the robot may calculate a new route and still reach its goal in a more efficient way than if it had chosen to border the north wall. Fig. 3. Cognitive maps and resulting paths for: a) original situation with open door; b) situation a) with closed door; c) unexpected obstacle in unexplored regions. Tests were performed over a 700 MHz Pentium III with 164 Mb RAM. In all three cases, the topological map was generated in 0.17 seconds. Path planning took only 0.09 seconds. Consequently, each time a route is detected to be unfeasible, a new one is available after 0.26 seconds. For a robot moving in an indoor environment, this time is reduced enough to correct the trajectory before collision without stopping the robot. 5. Conclusions This paper has presented a survey navigation scheme based on a new cognitive map construction technique. In the proposed map, a topological representation is extracted from a metric one. The main advantage of this technique is that geometrical relations in the topological map are explicitly preserved by means of a link set connecting its nodes to the metric representation. Also, unexplored regions are included in the topological map so that they can be analysed for planning purposes. Because of the low planning time obtained by using approaches like the potential field one at metric maps, one might be inclined to think that metric maps are suficient for robot planning (Konolige, 2000). However, many of these approaches require time quadratic in the number of grid cells, imposing intrinsic scaling limitations that forbid eficient planning in large environments (Thrun, 1998). Due to their compactness, topological maps adjust much better to large environments. The map generation algorithm has been successfully tested using a Nomad 200 robot equipped with a ring of 16 sonar sensors. Acknowledgements This work has been partially supported by the spanish Ministerio de Ciencia y Tecnología (MCYT) and FEDER funds, project No. TIC

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