Yoav Gabriely

Spanning-tree based coverage of continuous areas by a mobile robot

This paper considers the problem of covering a continuous planar area by a square-shaped tool attached to a mobile robot. Using a tool-based approximation of the work-area, we present an algorithm that covers every point of the approximate area for tasks such as floor cleaning, lawn mowing, and field demining. The algorithm, called Spanning Tree Covering (STC), subdivides the work-area into disjoint cells corresponding to the square-shaped tool, then follows a spanning tree of the graph induced by the cells, while covering every point precisely once. We present and analyze three versions of the STC algorithm. The first version is off-line, where the robot has perfect apriori knowledge of its environment. The off-line STC algorithm computes an optimal covering path in linear time O(N), where N is the number of cells comprising the approximate area. The second version of STC is on-line, where the robot uses its sensors to detect obstacles and construct a spanning tree of the environment while covering the work-area. The on-line STC algorithm completes an optimal covering path in time O(N), but requires O(N) memory for its implementation. The third version of STC is “ant”-like. In this version, too, the robot has no apriori knowledge of the environment, but it may leave pheromone-like markers during the coverage process. The ant-like STC algorithm runs in time O(N), and requires only O(1) memory. Finally we present simulation results of the three STC algorithms, demonstrating their effectiveness in cases where the tool size is significantly smaller than the work-area characteristic dimension.

Competitive on-line coverage of grid environments by a mobile robot

We describe in this paper two on-line algorithms for covering planar areas by a square-shaped tool attached to a mobile robot. Let D be the tool size. The algorithms, called Spanning Tree Covering (STC) algorithms, incrementally subdivide the planar area into a grid of D-size cells, while following a spanning tree of a grid graph whose nodes are 2D-size cells. The two STC algorithms cover general planar grids. The first, Spiral-STC, employs uniform weights on the grid-graph edges and generates spiral-like covering patterns. The second, Scan-STC , assigns lower weights to edges aligned with a particular direction and generates scan-like covering patterns along this direction. Both algorithms cover any planar grid using a path whose length is at most (n + m)D, where n is the total number of D-size cells and m ≤ n is the number of boundary cells, defined as cells that share at least one point with the grid boundary. We also demonstrate that any on-line coverage algorithm generates a covering path whose length is at least (2 - e)lopt in worst case, where lopt is the length of the optimal off-line covering path. Since (n + m)D ≤ 2lopt, the bound is tight and the STC algorithms are worst-case optimal. Moreover, in practical environments m || n, and the STC algorithms generate close-to-optimal covering paths in such environments.

Spiral-STC: an on-line coverage algorithm of grid environments by a mobile robot

We describe an on-line sensor based algorithm for covering planar areas by a square-shaped tool attached to a mobile robot. Let D be the tool size. The algorithm, called Spiral-STC, incrementally subdivides the planar work-area into disjoint D-size cells, while following a spanning tree of the resulting grid. The algorithm covers general grid environments using a path whose length is at most (n + m)D, where n is the number of D-size cells and m /spl les/ n is the number of boundary cells, defined as cells that share at least one point with the grid boundary. We also report that any on-line coverage algorithm generates a covering path whose length is at least (2 - /spl epsiv/)l/sub opt/ in the worst case, where l/sub opt/ is the length of the optimal covering path. Since (n + m)D /spl les/ 2l/sub opt/, Spiral-STC is worst-case optimal. Moreover, m << n in practical environments, and the algorithm generates close-to-optimal covering paths in such environments. Simulation results demonstrate the spiral-like covering patterns typical to the algorithm.

CBUG: A Quadratically Competitive Mobile Robot Navigation Algorithm

This paper is concerned with online navigation of a size D mobile robot in an unknown planar environment. A formal means for assessing algorithms for online tasks is competitiveness. For the navigation task, competitiveness measures the algorithms path length relative to the optimal offline path length. While competitiveness usually means constant relative performance, it is measured in this paper in terms of a quadratic relationship between online performance and optimal offline solution. An online navigation algorithm for a size D robot called CBUG is described. The competitiveness of CBUG is analyzed and shown to be quadratic in the length of the shortest offline path. Moreover, it is shown that, in general, quadratic competitiveness is the best achievable performance over all online navigation algorithms. Thus, up to constants, CBUG achieves optimal competitiveness. The algorithm is improved with some practical speedups, and the usefulness of its competitiveness in terms of path stability is illustrated in office-like environments.

COMPETITIVE COMPLEXITY OF MOBILE ROBOT ON-LINE MOTION PLANNING PROBLEMS

This paper classifies common mobile robot on-line motion planning problems according to their competitive complexity. The competitiveness of an on-line algorithm measures its worst case performance...

MRBUG: A Competitive Multi-Robot Path Finding Algorithm

We explore an on-line problem where a group of robots has to reach a target whose position is known in an unknown planar environment whose geometry is acquired by the robots during task execution. The critical parameter in such a problem is the physical motion time, which, under the assumption of uniform velocity of all the robots, corresponds to length or cost of the path traveled by the robot which reached the target. The Competitiveness of an on-line algorithm measures its performance relative to the optimal off-line solution to the problem. While competitiveness usually means constant relative performance, this paper uses generalized competitiveness, i.e. any functional relationship between online performance and optimal off-line solution. Given an online task, its competitive complexity class is a pair of lower and upper bounds on the competitive performance of all online algorithms for the task, such that the two bounds satisfy the same functional relationship. We prove that in general any on-line navigation algorithm must have at least a quadratic competitive performance. This paper describes a new on-line navigation algorithm, called MRBUG (short for Multi-Robot BUG), which requires constant memory and has a quadratic competitive performance. Thus, the above mentioned problem is classified into a quadratic competitive class. Moreover, since MRBUG achieves the quadratic lower bound, it has optimal competitiveness. The algorithm performance is illustrated in office-like environments

MRSAM: a quadratically competitive multi-robot online navigation algorithm

We explore an online problem where a group of robots has to find a target whose position is unknown in an unknown planar environment whose geometry is acquired by the robots during task execution. The critical parameter in such a problem is the physical motion time, which, under the assumption of uniform velocity of all the robots, corresponds to length or cost of the path traveled by the robot which finds the target. The competitiveness of an online algorithm measures its performance relative to the optimal offline solution to the problem. While competitiveness usually means constant relative performance, this paper uses generalized competitiveness, i.e. any functional relationship between online performance and optimal offline solution. Given an online task, its competitive complexity class is a pair of lower and upper bounds on the competitive performance of all online algorithms for the task, such that the two bounds satisfy the same functional relationship. We classify a common online motion planning problem into competitive class. In particular, it is shown that group of robots navigation to a target whose position is recognized only upon arrival belongs to a quadratic competitive class. This paper describes a new online navigation algorithm, called MRSAM (short for multi-robot search area multiplication), which requires linear memory and has a quadratic competitive performance. Moreover, it is shown that in general any online navigation algorithm must have at least a quadratic competitive performance. The MRSAM algorithm achieves the quadratic lower bound and thus has optimal competitiveness. The algorithms performance is illustrated in an office-like environments

Competitive Disconnection Detection in On-Line Mobile Robot Navigation

This paper concerns target unreachability detection during on-line mobile robot navigation in an unknown planar environment. Traditionally, competitiveness characterizes an on-line navigation algorithm in cases where the target is reachable from the robot’s start position. This paper introduces a complementary notion of competitiveness which characterizes an on-line navigation algorithm in cases where the target is unreachable. The disconnection competitiveness of an on-line navigation algorithm measures the path length it generates in order to conclude target unreachability relative to the shortest off-line path that proves target unreachability from the same start position. It is shown that only competitive navigation algorithms can possess disconnection competitiveness. A competitive on-line navigation algorithm for a disc-shaped mobile robot, called CBUG, is described. This algorithm has a quadratic competitive performance, which is also the best achievable performance over all on-line navigation algorithms. The disconnection competitiveness of CBUG is analyzed and shown to be quadratic in the length of the shortest off-line disconnection path. Moreover, it is shown that quadratic disconnection competitiveness is the best achievable performance over all on-line navigation algorithms. Thus CBUG achieves optimal competitiveness both in terms of connection and disconnection paths. Examples illustrate the usefulness of connection-and-disconnection competitiveness in terms of path stability.

C-space characterization of contact preserving paths with application to tactile-sensor based mobile robot navigation

This paper considers the navigation of a three degrees-of-freedom mobile robot equipped with position and tactile sensors in an unknown planar environment. The paper focuses on the contact preserving segments of the robots path. Any contact preserving path can trace a single or two simultaneous contacts. The paper establishes that motions involving two contacts induce two types of configuration-space curves: contractible loops representing passable gaps, and non- contractible loops representing impassable gaps. The paper identifies a generic class of contact preserving paths which requires only single-contact tracings with efficient transitions at double-contact configurations involving impassable gaps, and at triple-contact configurations involving both passable and impassable gaps. A preliminary tactile-sensor navigation algorithm based on these paths is illustrated with an example.

Online Scan Coverage of Grid Environments by a Mobile Robot

We describe an on-line sensor based algorithm for covering planar areas with a uniform scan pattern, where the covering is executed by a D×D square-shaped tool attached to a mobile robot. The algorithm, called Scan-STC, incrementally subdivides the planar area into a grid of D-size cells, while following a spanning tree of a graph whose nodes are 2D-size cells. The algorithm covers any planar grid with a scan path whose total length is at most (n + m)D, where n is the number of D-size cells and m ≤ n is the number of boundary cells, defined as cells that share at least one point with the grid boundary. Scan-STC additionally strives to minimize the total length of path segments orthogonal to the scan direction, and we report a preliminary bound on the length of these segments. We also demonstrate that any on-line coverage algorithm generates a covering path whose length is at least (2 − e)l opt in worst case, where l opt is the length of the optimal off-line covering path. Since (n+m)D ≤ 2l opt , the bound is tight and Scan-STC is worst-case optimal. Moreover, in practical environments m << n, and Scan-STC generates close-to-optimal covering paths in such environments.