Abstract-This paper presents an approach for automatically synthesizing and re-synthesizing a hybrid controller that guarantees a robot will exhibit a user-defined high-level behavior while exploring a partially known workspace (map).The approach includes dynamically adjusting the discrete abstraction of the workspace as new regions are detected by the robot's sensors, automatically rewriting the specification (formally defined using Linear Temporal Logic) and re-synthesizing the control while preserving the robot state and its history of task completion. The approach is implemented within the LTLMoP toolkit and is demonstrated using a Pioneer 3-DX in the lab.

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 algorithm's performance is illustrated in an office-like environments.

Abstract-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.

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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