CBUG: A Quadratically Competitive Mobile Robot Navigation Algorithm

Gabriely, Y.; Rimon, Elon

doi:10.1109/robot.2005.1570409

Cited by 8 publications

(15 citation statements)

References 25 publications

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“…The environment is built from radial corridors which have the width of the robots, D, and one circular corridor containing the target with only one entrance. According to the construction of the environment [11], the area of the obstacles equals one third of the environment's area (Fig. 2b).…”

Section: A Universal Lower Bound For a Known Targetmentioning

confidence: 99%

“…The configuration space (or C-space) of a disc shaped robot is IR 2 , and the C-space obstacle CB i consist of all robot configurations where it intersects the obstacle B i . [11]) Let CB i be the C-space obstacle induced by an obstacle B i for a disc robot of size D. The traceable obstacle induced by B i , denoted B i , is obtained by filling any internal holes in CB i and then shrinking CB i inward by a distance of D/2. Note that the regions swept during tracing of the individual boundaries may overlap, so that in general the sum z i=1 q i may be larger than A(C).…”

Section: Competitive Complexity Analysis Of Mrbugmentioning

confidence: 99%

“…SAD1 assigns a search disc to the robot, which is doubled at each step, if the target is not found. MRBUG is based on growing bounding ellipses used in the CBUG algorithm for one robot [11] to restrict the search for the path to a target whose position is known in an unknown environment.…”

Section: Introductionmentioning

confidence: 99%

“…Gabriely and Rimon[11]) Let a planar environment contain z disjoint traceable obstacles B i , i = 1, . .…”

mentioning

confidence: 99%

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Classifying the multi robot path finding problem into a quadratic competitive complexity class

Sarid

Shapiro

2008

Ann Math Artif Intell

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We explore two motion planning problems where a group of mobile robots has to reach a target located in an a priori unknown environment while on-line planning the next step. In the first problem the target position is unknown and should be found by the robots, while in the second problem the target position is known and only a path to it should be found. We focus on optimizing the cost of the task in terms of motion time, which, under the assumption of uniform velocity of all the robots, correlates to the path length passed by the robot which reaches the target. The performance of an on-line algorithm is usually expressed in terms of Competitiveness, the constant ratio between the on-line and the optimal off-line solutions. Specifically, the ratio between the lengths of the actual path made by the robot which reached the target to the shortest path to the target. We use generalized competitiveness, i.e., the ratio is not necessarily constant, but could be any function. Classification of a motion planning task in the sense of performance is done by finding an upper and a lower bounds on the competitiveness of all algorithms solving that task. If the two bounds belong to the same functional class this is the Competitive Complexity Class of the task. We find the two bounds for the aforementioned common on-line motion planning problems, and classify them into competitive classes. It is shown that in general any on-line motion planning algorithm that tries to solve these problems must have at least a quadratic competitive performance. This is a lower bound of 170 S. Sarid, A. Shapiro the problems. This paper describes two new on-line navigation algorithm which solve the problems under discussion. The first is called MRSAM, short for MultiRobot Search Area Multiplication, and the second is called MRBUG, short for MultiRobot BUG which extends Lumelsky famous BUG algorithm. Both algorithms have quadratic upper bounds, which prove that the problems they solve have quadratic upper bounds. Thus it is shown that navigation in an unknown environment by a group of robots belongs to a quadratic competitive class. MRSAM and MRBUG have a quadratic competitive performance and thus have optimal competitiveness. The algorithms' performance is simulated in office-like environments.

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Section: A Universal Lower Bound For a Known Targetmentioning

confidence: 99%

Section: Competitive Complexity Analysis Of Mrbugmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Gabriely and Rimon[11]) Let a planar environment contain z disjoint traceable obstacles B i , i = 1, . .…”

mentioning

confidence: 99%

See 2 more Smart Citations

Classifying the multi robot path finding problem into a quadratic competitive complexity class

Sarid

Shapiro

2008

Ann Math Artif Intell

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“…These paper focuses on developing systematic exploration strategies for robots moving in unknown environments [4], [9], [10]. This is inspired from the lost-cow problem, in which a cow moves along a fence trying to find a gate to access a pasture.…”

Section: Introductionmentioning

confidence: 99%

Searching and mapping among indistinguishable convex obstacles

Tovar

LaValle

2010

2010 IEEE International Conference on Robotics and Automation

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Abstract-We present exploration and mapping strategies for a mobile robot moving among a finite collection of convex obstacles in the plane. The obstacles are unknown to the robot, which does not have access to coordinates and cannot measure distances or angles. The robot has a unique sensor, called the gap sensor, that tracks the direction of the depth discontinuities in the robot's visibility region. Furthermore, the robot can only move towards depth discontinuities. As the robot moves, the depth discontinuities split and merge, and these changes are encoded in a Gap Navigation Tree. We present a strategy for this robot that is guaranteed to explore the whole environment, but that cannot decide whether the exploration has been completed. If in addition it is assumed that the robot has access to a pebble, which is an identifiable point that the robot can manipulate, then we prove that the robot can decide (in polynomial time in the number of obstacles) whether the environment has been completely explored. For this, the robot is able to distinguish every obstacle using only the gap sensor and a single pebble. These results are a continuation of our previous work on gap sensing for multiply connected environments [24], in which we reduce the sensing requirements for the robot by constraining the shape of the obstacles.

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Competitive Disconnection Detection in On-Line Mobile Robot Navigation

Gabriely

Rimon

Springer Tracts in Advanced Robotics

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CBUG: A Quadratically Competitive Mobile Robot Navigation Algorithm

Cited by 8 publications

References 25 publications

Classifying the multi robot path finding problem into a quadratic competitive complexity class

Classifying the multi robot path finding problem into a quadratic competitive complexity class

Searching and mapping among indistinguishable convex obstacles

Competitive Disconnection Detection in On-Line Mobile Robot Navigation

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