This work was sponsored by the Department of Energy Grant DEFGNE Page  Reprint of Proceedings of the  IEEE International Conference on Robotics and Automation  Cincinnati Ohio May   pp

This work was sponsored by the Department of Energy Grant DEFGNE Page Reprint of Proceedings of the IEEE International Conference on Robotics and Automation Cincinnati Ohio May pp - Description

572577 Realtime Obstacle Avoidance for Fast Mobile Robots in Cluttered Environments by J Borenstein and Y Koren Department of Mechanical Engineering and Applied Mechanics The University of Michigan Ann Arbor ABSTRACT new realtime obstacle avoidan ce ID: 28584 Download Pdf

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This work was sponsored by the Department of Energy Grant DEFGNE Page Reprint of Proceedings of the IEEE International Conference on Robotics and Automation Cincinnati Ohio May pp

572577 Realtime Obstacle Avoidance for Fast Mobile Robots in Cluttered Environments by J Borenstein and Y Koren Department of Mechanical Engineering and Applied Mechanics The University of Michigan Ann Arbor ABSTRACT new realtime obstacle avoidan ce

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This work was sponsored by the Department of Energy Grant DE-FG02-86NE37969 Page 572 Reprint of Proceedings of the 1990 IEEE International Conference on Robotics and Automation , Cincinnati, Ohio, May 13-18, 1990, pp. 572-577. Real-time Obstacle Avoidance for Fast Mobile Robots in Cluttered Environments by J. Borenstein and Y. Koren Department of Mechanical Engineering and Applied Mechanics The University of Michigan, Ann Arbor ABSTRACT new real-time obstacle avoidan ce method for mobile robots has been developed and implemented. This method, named e Vector Field Histogram

(VFH), permits the detection of unkn own obstacles and avoids collisions whil imultaneously steering the mob ile robot toward the target. A FH-controlled mobile robo t maneuvers quickly and without stopping among densely cluttered obstacles. The VFH method uses a two-dimensional Cartesia Histo gram Grid as a world model. This world model i update continuously and in real-time with range dat sa mpled by the onboard ultrasonic range sensors. Based o the accumulated environmental data, the VFH method then compu tes a one-dimensional Polar Histogram that i constructed around the robot's momentary

location. Eac sec tor in the Polar Histogram holds the polar obstacl den sity in that direction. Finally, the algorithm selects th ost suitable sector f rom among all Polar Histogram sectors with low obstacle density, and the steering of the robot i aligned with that direction. Experimental results from obile robot traversin g a densely cluttered obstacle course at an average speed of 0.7 m/sec demonstrate the power of the VFH method. 1. Introduction n our p revious research, we developed a real-time obstacle- avoidance algorithm for fast mobile robots, entitled th Vi rtual Force Field (VFF)

method (Borenstein and Koren 1988, 1989). This method used a force-field approach i hich ob stacles applied virtual repulsive forces to the robot, hile the target applied a vir tual attractive force. Force-field- based obstacle avoidance had been suggested by Khati (1985) Krogh (1984), and Krogh and Thorpe (1986) The VFH method uses a two-dimensional Cartesian His although these methods were not used for real-tim navigation. y contrast, Brooks (1986) and Arkin (1989) use force-field me thods on experimental mobile robots (equipped wit ltrasonic sensors). However, in Broo ks' implementation

only the current set of range readings is used to compute th resultant repulsive force. This way, erroneous and "good readings receive the same weight, making the algorith ore prone to sensor errors. Arkin's robot employs a similar method; his robot was able to traverse an obstacle course at 0.12 cm/sec (0.4 feet/sec). e found, however, that the force-field approach has several sev ere limitations (Borenstein and Koren, 1990). Fo example, force-based obstacle-avoidance methods do no allow the robot to pass through narrow passages. Anothe pro blem is the instability of motion when traveling

withi narrow corridors; limitations that were also observed b Arkin (1989) and Tilove (1989). This paper introduces our new Vector Field Histogra (VFH method, a real-time obstacle-avoidance method fo fas t-running vehicles that constitutes a significant im rovement over the Virtual Force F ield method. VFH control results in smooth motion of the controlled vehicle amon de nsely cluttered and unexpected obstacles. A VF controlled vehicle can easily enter narrow passages and can tra vel in narrow corridors at high speeds and withou oscillations. These features are made possible through number of

novel ideas that we have implemented as fas computer algorithms. 2. he Histogram Grid for Sensor-Based World Modeling togram Grid for the representation of obstacles. This rep
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Page 573 Figure 1 a. Only one cell is incremented for each range reading. b. Histogramic probability distribution is obtained by continuous and rapid sampling while the vehicle is moving. resent ation is derived from the certainty grid concep eveloped by Morave c and Elfes (1985) and Moravec (1988) at Ca rnegie Mellon University (CMU). Like the certaint rid, each cell in the Hi stogram Grid holds a

certainty value, CV, that represents the confidence of the algorithm in th xistence of an obstacle at that location. The Histogram Grid differ from the certainty grid in the way it is built an updated: CMU's method projects a probability profile ont those ce lls that are affected by a range reading. Thi procedure is computationally intensive and would impose a he avy time-penalty if real-time execution on an onboar computer was attempted. Our method, on the other hand, creates a probabilit distribution with only little computational overhead. Thi effect is obtained by incrementing only one

cell in th His togram Grid for each range reading. For ultrasoni ensors, this cell corr esponds to the measured distance d (see ig. 1a) and lies on the acoustic a xis of the sensor. While this approach may seem to be an oversimplification, robabilistic distributio n is actually obtained by continuously and rapidly sampling each sensor while the vehicle i mo ving. Thus, the same cell and its neighboring cells ar epea tedly incremented, as shown in Fig. 1b. This results in histogramic probability distribution , in which high CVs are is an integer (e.g., =5 and =72). Each sector obtained in cells

close to the actual location of the obstacle. orres ponds to a discrete angle quantized to multiples of Ou experiments show that actual rapid sampling from th such that = 0, , 2 ... 360- . A transformatio moving robot is more accurate than methods using an as umed prob ability function (Raschke and Borenstein, 1990). 3. The Vector Field Histogram Method The VF H method employs a two-stage data reductio echnique, in which three lev els of data representation can be distinguished. a. The highest level holds the detailed description of th ro bot's environment. In this level, the two-dimensiona

Cart esian Histogram Grid is continuously updated i real-time with range data sampled by the onboard range se nsors. The Histogram Grid is absolute and does no change with the robot's momentary location. However along with the vehicle moves a notional window of siz overlaying a square region of . We will call this regi on the " active region " (denoted *), and cells tha moment arily belong to the active region will be calle act ive cells " (denoted ). In our curren i,j im plementation, the size of the active region is 33 cells. As will be discussed in Sect. 3.1, only active cells have

immediate influence on the robot control. b. At the intermediate level, a Polar Histogram is con structed around the robot's momentary center. com prises angular sectors of width (see Fig. 2). ay be cho sen arbitrarily but must be such that =360/ describe d in Sect. 3.1, below) maps * into resulting in each sector holding a value which represents the polar obstacle density in the direction . c. he lowest level of data representa tion is the output of the VFH algorithm: the reference values for the drive an steer controllers of the vehicle. 3.1 First Data Reduction: Creation of the Polar

Histogram The first data reduction stage maps the active region of the Histogr am Grid * into the Polar Histogram . For thi purpos e, we will now treat the certainty value of all activ cells as an obstacle vector , the direction of which i i,j determ ined by the direction from the cell to the Vehicl i,j Center Point (VCP) . Note that for our symetrically shaped mobile robot, the VCP is easily defined as the geometric center of the robot. For rectangular shaped mobile robots, it is possible to chose two VCPs, e.g., each one at the center-point of the front and rear axles.
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574 Figure 2 : Mapping active cells into sectors of the Polar Histogram active cells can be related to a sector by means of equations = tg ))) (1) i,j -1 and the magnitude is given by = ( [ a - b d (2) i,j i,j i,j where a,b Positive constants. Distance between active cell ( i,j ) and the VCP. i,j Certainty value of active cell ( i,j ). i,j Magnitude of the obstacle vector at cell ( i,j ). i,j , Present coordinates of the VCP. , Coordinates of active cell ( i,j ). Direction from active cell ( i,j ) to the VCP. i,j ote that is proportional to - . Therefore, occupied cells i,j prod uce large

vector magnitudes when they are in th mmediat e vicinity of the robot, and smaller ones when they are further away. Specifically, and are chosen such that a-bd = 0, where = ( -1)/2 is the distance between max max he f arthest active cell and the VCP. This way =0 for the i,j farthest active cell and increases linearly for closer cells. Correspondence between and sector is establishe i,j through = INT( (3) or e ach sector , the polar obstacle density is calculated by = (4) i,j i,j Fig. 2 sh ows graphically the mapping from * into . Al (1) and (3). In Fig. 2 all active cells related to sector

have been high lighted. Note that the sector width in Fig. 2 i =10 (not =5 , as in the actual algorithm), to clarify th drawing. Notice that a. i n Eq. (2) is proportional to ( . This expresse i,j i,j our confidence that recurring range reading represen actua obstacles, as opposed to single occurrences o range readings, which may be caused by noise. b. in Eq. (2) is proportional to - . Therefore, occupie i,j cells produce large vector magnitudes when they are i the im mediate vicinity of the robot, and smaller one when they are further away. Becau se of the discrete nature of the histogram

grid , th esult of the mappin g may appear ragged and cause errors in he selection of the steering direct ion (as explained in Section .2). Therefore, a smoothing function is applied to , which is defined by +2 +...+ lh +...+2 k-l k-l +1 k+l -1 k+l h' = )))))))))))))))))))))))))))))))) (5) +1 In our current implementation, =5 yields satisfactor smoothing results. Fig. 3a shows a typical obstacle setup in our lab. Note tha the gap between obstacles B and C is only 1.2 m and that A is a thin pole 3/4" in diameter. The actual Histogram Gri obtained after partially traversing this obstacle course

i hown in Fig. 3b. The Polar Histo gram , corresponding to the momentary position of the robot O is shown in Fig. 3c. The irections (in de grees) in the Polar Histogram correspond to direc tions measured counterclockwise from the positive x axis of the Histogram Grid . The peaks A, B, and C in th olar Histogram resul t from obstacle clusters A, B, and C in the Histogram Grid 3.2 Second Data Reduction: Computation of Steering Control Th second data reduction stage computes the require steer ing direction. We will call this direction , and th free corresponding sector in , . Thi s section

explains how the free required steering direction (in terms of ) is computed. free As can be seen in Fig. 3c, a Polar Histogram typically has pea ks (sectors with high obstacle density), and valley sectors w ith low obstacle density). Any valley with obstacle densities below threshold is a candidate for travel. Sinc there are usually several candidate-valleys, the algorith
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Page 575 Figure 3 a. Experimental lab setup b. Histogram representation of experimental lab setup c: Polar histogram of obstacles, as seen from position 'O'. elects the o ne that most closely matches the

direction to the target (or ). targ targ hen the mobile rob ot approaches or travels between two or more closely spaced obstacles, only a very narrow valley i availa ble for travel. In this case, is chosen to be in th free en ter of the valley, in order to maintain equal clearance on ach side of the robot. If the se lected valley is very wide (e.g., when only one obstacle is close to the robot) the algorith ch ooses several sectors "deep" into the valley, but no free necessarily in its center). 3.3 Speed Control he robot's maximum s peed , can be set at the beginning max f a run. The robot

tries to maintai n this speed during the run nless forced by the VFH algorithm to a lower instantaneous peed . is determined in each samp ling interval as follows: he smoothed polar obst acle density in the current direction of travel will be denoted h' . >0 indicates that an obstacl ies ahead of the robot, requiring a reduction in speed. Large values of h' mean that a lar ge obstacle lies ahead of the robot, r an obstacle is very close to the robot. Either case is likely to require a drastic change in direction and a reduction i speed i s necessary to allow for the steering wheels to tur into

the new direction. This reduction in speed i implemented by the following function: ' = (1 - h'' (6) max where h'' = min( h' , (7) is an empirically determined constant that causes sufficient reduction in speed. Note that Eq. (7) guarantees 0, since h'' While E qs. (6) and (7) reduce the speed of the robot i an ticipation of a steering maneuver, speed can be furthe reduced proportionally to the actual steering rate = '(1- (9) max where is the maximal allowable steering rate for th max mobile robot.
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Page 576 Figure 4 : Histogram Grid representation of a test run through a field

of densely spaced, thin vertical poles. 4. Experimental Results We implemented and tested the VFH method on a com merc ially available mobile platform (Cybermation, 1987) his platform has a maximum travel s peed S of 0.78 m/sec max and weighs about 125 kg. The Cybermation platform has uniq ue three-wheel drive (synchro-drive) that permit omnidirectional steering. e equipped this vehicle wi th a ring of 24 ultrasonic sensors (Polar oid, 1989). The sensor ring has a diameter of 0.8m nd objects must be at least 0.27m away from the sensors to be d etected. Therefore, the theoretical minimum width

fo safe travel in a narrow corridor is W = 0.8 + 2 0.27 min 1.34m. wo computers were adde d to the platform: a PC-compatible single-board computer to control the sensors, and a 20Mhz, 80386-based AT-compatible that runs the VFH algorithm. In extensive tests we run the VFH-controlled platfor thr ough difficult obstacle courses. The obstacles wer unmarked, commonplace objects such as chairs, partitions nd bookshelves. In mo st experiments, the vehicle runs at its maximum speed (0.78 m/sec). This speed was only reduced hen an obsta cle was approached frontally or if required for dynamic reasons.

Fig. 4 s hows the Histogram Grid after a run through articularly challen ging obstacle course that comprised 3/4" thin vertical poles spaced at a distance of about 1.4m fro each other. The approximate original location of the rods is dicated with (+) symbols in Fig. 4. It should be noted that non of the obstacle locations were known to the robot i dva nce: the obstacle locations in Fig. 4 gradually appeared on the operator's screen while the robot was moving. ach dot in Fig. 4 repr esents one cell in the Histogram Grid n our curren t implementation, certainty values (CVs) range from 0 to 5. CV

= 0 means no sensor reading has bee rojected into the cell during the run (i.e., no dot). CV = 1 (to 4) indicates that one (to four) readings have been projecte nto t he cell; this is shown in Fig. 4 with dots comprising of ne pixel (or more). CV = 5 means th at five or more readings have been projected into the same cell, and which i represented by a 9-pixel dot in Fig. 4. The robot traverse this obstacle course at an average speed of 0.58 m/sec without stopping in front of obstacles. An indi cation for the real-time performance of the VF lgori thm is the sampling time (i.e., the rate at

which the steer and speed commands for the low-level controller ar issued). On an Intel 80386-based PC-compatible compute run ning at 20Mhz, = 27msec. The following steps occu during a. Read sonar information, b. update the Histogram Grid c. create the Polar Histogram d. determine the free sector and steering direction, e. calculate the speed command, f. omm unicate with the low-level motion controller (send speed and steer command and receive position update). 5. Conclusions This paper presents a new obstacle-avoidance method fo ast-running vehicles. This method, called the VFH method, has

been developed and successfully tested on a expe rimental mobile robot. The VFH algorithm is com utationally efficient, ver y robust, insensitive to misreadings, and al lows continuous and fast motion of the mobile robo without stopping in front of obstacles. The VFH method is based on the following principles: a. two-dimensio nal Cartesian Histogram Grid is updated ontinuously and in real-tim e with range data sampled by the onboard range sensors. b. The data in the Histogram Grid is reduced to a one imensi onal Polar Histogram that is constructed around
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Page 577 the r obot's

momentary location. This Polar Histogra rogh, B. H., 1984, "A Generalized Poten tial Field Approach represents the polar obstacle density around the robot. to Obstacle Avoidance Control." International Robotic c. sect or with low obstacle density which is close to th tar get direction is selected, and the robot's steering i Krog h, B. H. and Thorpe, C. E., 1986, "Integrated Pat aligned with that direction. Pl anning and Dynamic Steering Control for Autonomou he strength of the VFH method lies in its ability to maintain Con ference on Robotics and Automation , San Francisco statistical obstacle

representation at both the world-model California, April 7-10, pp. 1664-1669. level and the intermediate data-level. Therefore, the VFH ontrolled vehicle responds to clusters of high likelihood for orave c, H. P. and Elfes, A., 1985, "High Resolution Maps the existence of an obstacle, while ignoring single (possibly rom Wide Angle Sonar." EEE Conference on Robotics and rroneous) data points. Also, since information about narrow Automation assages i s still available at the intermediate data level ( free valleys the vehicle is able to navigate through narro oravec, H. P., 1988, "Sensor Fusion

in Certainty Grids for passages (e.g., doorways) or negotiate narrow corridor Mobile Robots." AI Magazine , Summer 1988, pp. 61-74. without oscillations. 7. References Ark in, R. C., "Motor Schema-Based Mobile Robo Na vigation." The International Journal of Robotic Research , August 1989, pp. 92-112. Borenstein, J. and Koren, Y., 1988, "High-speed Obstacl Av oidance for Mobile Robots." Proceedings of the IEE Symp osium on Intelligent Control , Arlington, Virginia August 24-26, 1988, pp. 382-384. Borenstein, J. and Koren, Y., 1989, "Real-time Obstacl Avoidance for Fast Mobile Robots." IEEE

Transactions o Systems, Man, and Cybernetics , Vol. 19, pp. 1179-1187. Borenstein, J. and Koren, Y., 1990, "Critical Analysis o Po tential Field Methods for Mobile Robot Obstacl Avoidance." Submitted for publication in the IEEE Journal of Robotics and Automation , February. rooks , R. A., 1986, "A Robust Layered Control System for Mobile Robot." IEEE Jo urnal of Robotics and Automation Vol. RA-2, No. 1, pp. 14-23. Cybermation, 1987, "K2A Mobile Platform." Commercia Offer , 5457 JAE Valley Road, Roanoke, Virginia 24014. Khatib, O., 1985, "Real-Time Obstacle Avoidance fo anipulator s and Mobile

Robots." 1985 IEEE International Conference on Robotics and Automation , March 25-28, St. Louis, pp. 500-505. Koren, Y. and Borenstein, J, 1989, "Analysis of Mobile obot/Environment Interaction" The University of Michigan, Technical Report No. UM-MEAM-89-1 , January 1989. Research Conference , Bethlehem, Pennsylvania, August. Vehic les." Proceedings of the 1986 IEEE Internationa POLA ROID Corporation, 1989, Ultrasonic Component Group, 119 Windsor Street, Cambridge, MA, 02139. aschke, U. and Borenstein, J., " A Comparisson of Grid-type Map-building Techniques by Index of Performance." 199 EEE

International Conference on Robotics and Automation Cincinnati, Ohio, May 13-18, 1990. Tilov e, R. B., 1990, "Local Obstacle Avoidance for Mobil Robots Based on the Method of Artificial Potentials." To be presen ted at the 1990 IEEE International Conference o Rob otics and Automation , Cincinnati, Ohio, May 13-18 1990.