# Real-Time Indoor Mapping for Mobile Robots with Limited Sensing

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2 (a) Hallway snapshot (b) Hallway floor plan Fig. 1. An example of the indoor environment: hallways in an office building (a) Robot trajectory from odometry (b) An outline obtained from mapping Fig. 2. Raw trajectory data (a) and a resulting map (b) by wall-following the hallway environment in Fig. 1. Note that although it appears in (a) that the odometry error may have a constant bias, it actually varies quickly and randomly upon closer inspection (and further experimentation). mapping algorithm where direction classification depends not only on the current odometry angle, but also on its past history. This state-based approach adds stability to the mapping algorithm, and can work successfully around obstacles. The probabilistic approach simultaneously maintains up to N hypotheses (N = 100 in our experiment), each of which is a candidate map. Hypotheses consistent with the input data are given high probabilities. The algorithm of segmentation and rectification are performed on-line during the wall-following exploration, and the hypothesis with the highest probability is the most probable map, hence chosen as the mapping output. In our approach, a map is represented as a planar polyline, i.e, a collection of line segments living in a 2-D plane (floor plane). Each line segment is represented as (l i, θ i ), where l i is the length, and θ i is its direction. This polyline representation is especially suitable for indoor environments since walls are straight. In other mapping work such as SLAM, occupancy maps are often represented as grids, but the polyline representation can offer many advantages, such as in [10]. For wall-following robot with short range sensors, the polyline representation is more efficient for computation and storage, as well as capable of representing non-discretized distances, hence we use polyline maps here. A polyline map is a connected sequence of lines. There is a 1-D mapping from the distance d traveled from the starting point of the polyline to the direction of travel θ. Figure 3 shows a polyline map (a) and its traveled distance vs. travel direction graph (b). The horizontal axis is d, and the vertical axis is θ. In our indoor mapping setting, θ is a multiple of π/2 due to the rectilinear assumption. We introduce the term Accumulated Turn Counts (ATC): let a left turn be 1 and a right turn be -1, ATC is the sum of all turns up to the current distance; θ = AT C pi 2. High positive or low negative ATCs indicate loops. ATC is used to (1) find similarity between maps such that exploration maps from two different robots can be merged, and (2) find repetition in the map from a robot, so that looping behavior can be detected on-line. If a loop is identified, loop closure is performed. The resulting map shows a complete enclosed outline of the environment (such as Fig. 2 (b)). The system has been tested extensively in hallway environments in two office buildings. C. Related Work Most existing work on SLAM relies on a long ranging device, such as a laser scanner or a camera [5], [7]. Most of these algorithms are based on probabilistic reasoning with data fusion from multiple sources. There has been related work on mapping and localization for low-cost robots in indoor office-

4 Inputs: odometry and sensor measurements {(x k, y k, bl k, wr k )} Outputs: line segments {(l i, θ i, t i )} Initialization: with the first two points l =p(x 2 x 1 ) 2 + (y 2 y 1 ) 2 θ = arctan(y 2 y 1, x 2 x 1 ) t = STRAIGHT record segment beginning: (x b, y b ) = (x 1, y 1 ) Parameters: κ: threshold for line fitting distance L: minimum length for line segments 0. while there is an input (x k, y k, bl k, wr k ): 0.a compute (l, θ ) for line (x b, y b ) (x k, y k ) 1. if bl k == 1 and bl k 1 == 0 then 1.a output segment (l, θ, t) 1.b create new segment (x b, y b ) = (x k, y k ), l = 0 1.c t = LEFT 2. else if wr k == 0 and wr k 1 == 1 then 2.a output segment (l, θ, t) 2.b create new segment (x b, y b ) = (x k, y k ), l = 0 2.c t = RIGHT 3. else 4a. d = cos(θ)(y k y b ) sin(θ)(x k x b ) 4b. d =p(x k x k 1 ) 2 + (y k y k 1 ) 2 5. if d > κ d and l > L then % create a new segment 5.a output current segment (l, θ, t) 5.b create new segment (x b, y b ) = (x k 1, y k 1 ), l = d 5.c t = STRAIGHT 6. else % extend current segment 6.a θ = θ, l = l 6.b end if 7. end if 8. end while TABLE I TRACE SEGMENTATION FROM WALL-FOLLOWING TRAJECTORY {x k, y k, bl k, wr k } k=1,2,,k. Here (x k, y k ) is the location coordinate, bl k and wr k are the readings of the left side bumper and the right side wall sensor, respectively. The algorithm clusters points into segments, each segment represented by (l, θ, t) where l and θ are the length and orientation of the segment respectively, and t indicates that the segment has turned LEFT, RIGHT, or STRAIGHT. The algorithm grows the current line segment as long as possible until there is a turn which is big enough for a new segment. To detect a possible turn, one of the following conditions is true for the k-th point: the left bumper sensor fired: (bl k = 1 and bl k 1 = 0): it is likely to be the left turning point, i.e., t for the new segment will be LEFT. the right wall sensor reset: (wr k = 0 and wr k 1 = 1): it is likely to be the right turning point, i.e., t for the new segment will be RIGHT. detection of turn in odometry: two measurements are compared: (1) the distance from the point to the current segment, and (2) the distance between the current and previous points. In particular, for any new point (x k, y k ), we compute its distance to the current line segment by d k = cos(θ)(y k y b ) sin(θ)(x k x b ), where (x b, y b ) is the beginning point of the current segment, and θ is its orientation. The distance from the current point (x k, y k ) to the previous point is d = (x k x k 1 ) 2 + (y k y k 1 ) 2. A turn is detected if a point deviates too much from the current segment, i.e., d k κ d, where 0 < κ < 1 is a constant which is a threshold setting the minimum turning angle between segments. The pseudo code of trace segmentation is in Table I. In addition to κ, parameter L sets the minimum segment length. We used κ = 0.1 and L = 0.7 meters in our experiments. IV. MAP RECTIFICATION Trace segmentation produces line segments that fit to the trajectory of wall-following. Due to odometry errors, trajectories are deformed due to measurement noise (Fig. 2 (a)). However, most indoor floor plans have perpendicular wall segments; indoor environments are often rectilinear. Using that assumption, we apply the rectification process to the line segments to make line segments either parallel or perpendicular to each other. The input of the rectification is a sequence of line segments (l, θ, t), and the output is a new sequence of line segments (l, s) where s is the rectified angle, with the constraint that two neighboring segments have to be aligned or rectilinear, i.e., s i+1 s i can only be multiples of π/2. One straight-forward idea is to examine the turning angle between two neighboring segments and classify it into discrete angles: 0, 90, and so on. A turning angle smaller than a threshold, e.g., 45, is classified as 0 (going straight); otherwise classified as a rectilinear turn. But this classification algorithm could easily fail. For instance, consider the case of four line segments, with direction θ i = 0, 30, 60, 90, respectively. The turning angle between any two segments is only 30, hence the straight-forward classification algorithm will classify as 0. However, it is apparent that the robot has finished a turn. This can be fixed by extending the classification from stateless classification of instantaneous turning angles to a state-based classification with turning angle history. We use a history horizon: for the classification of any segment i, we not only consider the turning angle of segment i, but also the history {i 1, i 2,, i H} where H is the horizon length. The horizon length could be defined as physical distance, e.g., any linear segment within a 5-meter distance are included in the horizon, or it could be defined as the number of segments. We use the former in this paper. Segments within the horizon are collectively considered to rectify the current linear segment and hence avoid the pathological case above. Furthermore, it is able to map in the presence of obstacles as long as the obstacles are small in size compared to the history horizon. This is because the segments before and after the obstacle are both used for rectification. We use an approximate sequential Bayesian filtering method, recursively updating an estimate of the posterior of underlying state s i+1 with observation sequences z i+1 = {z 0, z 1,..., z i+1 } as: p(s i+1 z i+1 ) p o (z i+1 s i+1 ) p d (s i+1 s i ) p(s i z i ) ds i. S (1)

5 Equation (1) is sequential: the belief p(s i+1 z i+1 ) is computed from the belief p(s i z i ) from the previous time i at every step. The integral makes a single step of prediction bringing the previous state up the the current time and then applying a new external measurement to modify the state. The prediction is then multiplied by a likelihood, reflecting the contribution of observation z i+1, using an observation model p o (z i+1 s i+1 ). The two components that are essential in the sequential Bayesian filtering approach are: Dynamics model p d (s i+1 s i ). This describes the evolution or drifting of the underlying state. Here s i is the traveling directions {s i, s i 1,, s i H }. Since we make the assumption that walls are rectilinear, i.e., walls intersect each other at perpendicular angles. Therefore we have the following model: s i p S = 0.5; % straight s s i+1 = i + π p U = 0.1; % U-turn s i π (2) 2 p L = 0.2; % right turn s i + π 2 p R = 0.2; % left turn Although we have used one particular probability distribution in our model, we have noticed that the result shows low sensitivity to different distributions. This model can be extended, e.g. to eight directions instead of four if the environment has a lot of 45 angles. Observation model p o (z s) describes the relationship between the underlying states and measurement observations. Here the measurement from odometry is z = {θ i, θ i 1 θ i H }, i.e., all measurements within the history horizon. We assume the measured turning angle is the true turning angle contaminated with noise, i.e., θ i+1 θ i j = s i s i j + n j, where j indicates the j-th previous segment and n j is noise. We assume a generalized Gaussian distribution (GGD) [4] for noise. GGD is parametrized by a shape parameter r and a standard deviation σ. GGD includes Gaussian distributions as a special case, when r = 2, but is more flexible because the shape parameter r can be varied to describe noise with heavy tails (when r < 2). This is necessary for modeling angle noise because the odometry data are quite noisy, especially when the line segment length is short. Hence we choose GGD for its increased flexibility. In our test, we use a shape parameter r = 0.5 and a standard deviation of 10 for n 1 and (H 1) 20 for n j where 1 < j H. The parameters are chosen by experimental data from real trajectories that result in best performance. Another observation available is the turn information t = {STRIGHT, LEFT, RIGHT}, obtained from trace segmentation. For this observation, we use a simple likelihood function: p(t s) = 1 if the turn state in the hypothesis agrees with the turn observation t, and p(t s) = 0.5 if the two do not agree. This discounts hypotheses which conflict with sensor observations. The observation likelihood is multiplied to that of the odometry data, assuming that the different sensing modalities are independent. The rectification process takes the line segment inputs over time and maintains up to N (100 in experiment) most probable state sequences and their respective probabilities p n. Whenever a new segment (l, θ, t) comes, each existing state sequence (s 0, s 1, s i ) forks into four possibilities, with the new traveling direction s i+1 being straight, a left or right, or U-turn. Probabilities of the new state sequences are updated using the dynamics model and observation model as illustrated above. State sequences with low probabilities (p n < 1/N) are discarded, and up to N most probable state sequences are kept, their probabilities re-normalized to sum up to 1. That brings us to the next update. The final mapping result is the most probable state sequence. This method does not only build the map but also localize the robot within the map, where the location of the robot is represented by the distance traveled along the outline map from its start position. This method is one-dimensional SLAM since both the map and the location is represented by one degree of freedom. V. EXPERIMENTS AND RESULTS Our map construction algorithms have been implemented both in Matlab and in C++ on the Gumstix, a PXA MHz computer. We have tested the system using a Create doing wall-following in hallways in two office buildings. The system works reliably even with noisy odometry and with obstacles and/or furniture along the walls. Fig. 1 and Fig. 2 illustrate the capability of our mapping system to create an outline map of an enclosed environment by following the hallway wall along its right side. Fig. 4 demonstrates an outline mapping of an island with nonrectilinear edges. Fig. 4 (a) is the floor plan of the area the robot travels around (dashed line indicating the path of the robot), with an open lounge at a corner. Fig. 4 (b) shows the scene in the lounge with three garbage cans (one of which is a cylinder) and the kitchen counter with 45 angles. Fig. 4 (c) displays raw trajectory data from odometry, which is clearly deformed due to noise and can be hardly recognized as a closed loop of the trajectory. Fig. 5 shows the result of mapping. We see that although the raw trajectory from odometry is very noisy, our algorithm successfully creates an outline of the area. From the ATC plot, we can clearly identify the matching points, that indicating a loop. So far our experiments are mostly done in hallways of office buildings where most segments follow the rectilinear assumptions. The system will not work well if most segments do not satisfy this assumption. Occasional obstacles along the walls can be handled, as we have demonstrated. Too many obstacles may introduce error in rectification that may cause the failure of loop detection by proximity measurements. VI. CONCLUSIONS AND FUTURE WORK We have presented a real-time floor map construction method for cheap and small robots without long-range perceptive sensing, using the wall-following motion strategy. We have shown by experiments using irobot Creates that the

6 (a) Floor plan (b) Open lounge in hallway (c) Raw trajectory Fig. 4. Trajectory resulting from looping around an island with an open lounge. (a) Rectified segments (b) Outline map (c) ATC sequence Fig. 5. The result of mapping from trajectory in Fig. 4 (c) method is robust to odometry noise and occasional obstacles along the walls. Such a method can be very useful for indoor robotic applications with limited sensing. The advantages of such a method are that it is extremely efficient, and the information extracted from the raw trajectories and short-range sensors is useful for many applications in surveillance and networking. Note that our probabilistic mapping does not use particle filters as most other mapping algorithms do. Rather, we choose to update probability for each possible case at every cycle. Particle filters are much less efficient since it needs a lot of particles ( 100) to keep low probability cases in consideration. We have developed algorithms for map merging, loop detection and loop closure. Due to space limitations, we will present them in other papers. We will also investigate the integration of other information from the environment, such as radio signal strengths from stationary known or unknown locations, for map merging and loop detection. Furthermore, we will extend our methods to non-rectilinear environments, e.g. with circular curves or diagonal edges. We will develop mapbuilding capability with navigation and exploration strategies in unknown environments, and multi-robot coordination for efficient sensing coverage and networking. ACKNOWLEDGMENT This work was sponsored by the Defense Advanced Project Research Agency (DARPA) contract #FA C-7814, LANdroids. REFERENCES [1] G. Dedeoglu and G. S. Sukhatme, Landmark-based matching algorithm for cooperative mapping by autonomous robots, in Distributed Autonomous Robotics Systems. Springer-Verlag, 2000, pp [2] A. Howard, G. S. Sukhatme, and M. J. Matarić, Multi-robot mapping using manifold representations, Proceedings of the IEEE - Special Issue on Multi-robot Systems, vol. 94, no. 9, pp , Jul [Online]. Available: pub details.pl?pubid=445 [3] M. Lopez-Sanchez, F. Esteva, R. L. de Mantaras, C. Sierra, and J. Amat, Map generation by cooperative low-cost robots in structured unknown environment, vol. 5, March [4] J. H. Miller and J. B. Thomas, Detectors for discretetime signals in non-gaussian noise, IEEE Trans. Information Theory, vol. IT-18, no. 2, p , [5] M. Montemerlo and S. Thrun, The FastSLAM Algortihm for Simultaneous Localization and Mapping. Springer Tracts in Advanced Robotics, [6] E. Olson, J. Leonard, and S. Teller, Fast iterative optimization of pose graphs with poor initial estmates, in Proceedings of the IEEE International Conference on Robotics & Automation, [7] S. Thrun, Learning metric-topological maps for indoor mobile robot navigation, Artificial Intelligence, vol. 99, no. 1, pp , [8] S. Thrun, W. Burgard, and D. Fox, Probabilistic Robotics. Cambridge, MA: MIT Press, [9] R. T. Vaughan, K. Stoy, G. S. Sukhatme, and M. J. Matarić, Lost: Localization-space trails for robot teams, IEEE Transactions on Robotics and Automation, Special Issue on Multi-Robot Systems, vol. 18, no. 5, pp , Oct [Online]. Available: pub details.pl?pubid=46 [10] M. Veeck and W. Burgard, Learning polyline maps from range scan data, in IEEE/RSJ Int. Conf. on Intelligent Robotics and Syst., [11] D. F. Wolf and G. S. Sukhatme, Mobile robot simultaneous localization and mapping in dynamic environments, Autonomous Robots, vol. 19, no. 1, pp , Jul [Online]. Available: pub details.pl?pubid=392

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