Competitive Complexity of Mobile Robot On Line Motion Planning Problems

Gabriely, Y.; Rimon, Elon

doi:10.1007/10991541_12

Cited by 11 publications

(18 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Definition 1 (Generalized Competitiveness [10]) An on-line algorithm solving a task P is f (l opt )-competitive when l is bounded from above by a scalable function f (l opt ) over all instances of P. In particular, l ≤ c 1 l opt + c 0 is the traditional linear competitiveness, while l ≤ c 2 l 2 opt + c 1 l opt + c 0 is a quadratic competitiveness, where the c i 's are positive constant coefficients that depend on the robot size D, the number of robots and the geometry of the environment.…”

Section: Basic Setup and Definition Of Competitivenessmentioning

confidence: 99%

“…Definition 2 (Competitive Complexity Class [10]) A universal lower bound on the competitiveness of a task P is a lower bound l ≥ g(l opt ) over all on-line algorithms for P at worst case conditions. If a competitive upper bound f (l opt ) and a universal lower bound g(l opt ) for P are the same function up to constant coefficients, this function is the competitive complexity class of P.…”

Section: Basic Setup and Definition Of Competitivenessmentioning

confidence: 99%

“…In particular, an algorithm for a task P is said to be competitive if its solution to every instance of P is bounded by a constant times l opt [17]. Generalized Competitive Complexity and Competitive Complexity Classes are introduced and discussed in [10]; however, most research dealing with competitiveness strive to identify specific classes of environments in which constant competitiveness can be achieved. In contrast, our objective is to identify the competitive relationship governing the fully general on-line navigation problem for multiple robots.…”

Section: Introductionmentioning

confidence: 99%

“…Optimality is proved by showing that the problems themselves belong to the quadratic competitive complexity class and that the performance of MRSAM and MRBUG belongs to that class too. MRSAM is based on the area doubling strategy of SAD1 algorithm introduced in [10], which launches one robot to search for a target whose position is unknown in an unknown environment. SAD1 assigns a search disc to the robot, which is doubled at each step, if the target is not found.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Sarid

Shapiro

2008

Ann Math Artif Intell

View full text Add to dashboard Cite

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.

show abstract

Section: Basic Setup and Definition Of Competitivenessmentioning

confidence: 99%

Section: Basic Setup and Definition Of Competitivenessmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

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

View full text Add to dashboard Cite

show abstract

“…To evaluate the quality of the paths generated by the presented inverse kinematics (IK) solutions, we study the set of reachable needle poses and competitivity (Icking & Klein 1995, Gabriely & Rimon 2005 of the computed solutions. Competitivity in this case refers to the path length of the computed solution; it has no relation to competitivity in the sense of computational speed (the IK algorithms run in constant time).…”

Section: Reachability and Competitivitymentioning

confidence: 99%

Three-dimensional Motion Planning Algorithms for Steerable Needles Using Inverse Kinematics

Duindam

Alterovitz

et al. 2009

The International Journal of Robotics Research

View full text Add to dashboard Cite

Abstract:-Steerable needles can be used in medical applications to reach targets behind sensitive or impenetrable areas. The kinematics of a steerable needle are nonholonomic and, in 2D, equivalent to a Dubins car with constant radius of curvature. In 3D, the needle can be interpreted as an airplane with constant speed and pitch rate, zero yaw, and controllable roll angle.We present a constant-time motion planning algorithm for steerable needles based on explicit geometric inverse kinematics similar to the classic Paden-Kahan subproblems. Reachability and path competitivity are analyzed using analytic comparisons with shortest path solutions for the Dubins car (for 2D) and numerical simulations (for 3D). We also present an algorithm for local path adaptation using null-space results from redundant manipulator theory. Finally, we discuss several ways to use and extend the inverse kinematics solution to generate needle paths that avoid obstacles.

show abstract

Competitive Disconnection Detection in On-Line Mobile Robot Navigation

Gabriely

Rimon

Springer Tracts in Advanced Robotics

View full text Add to dashboard Cite

Competitive Complexity of Mobile Robot On Line Motion Planning Problems

Cited by 11 publications

References 0 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

Three-dimensional Motion Planning Algorithms for Steerable Needles Using Inverse Kinematics

Competitive Disconnection Detection in On-Line Mobile Robot Navigation

Contact Info

Product

Resources

About