The Pattern Formation Problem for Autonomous Mobile

Preface Given today's technological advances and decreasing manufacturing cost, mobile robots are expected to be utilized in the near future in a wide range of applications to assist humans , in places like factories, hospitals, museums and households. Since roughly speaking a robot, just like a computer, is hardware (wheels, motors, manipulators, sensors, etc.) controlled by software, a useful robot must have hardware capable of performing the required physical actions and software capable of analyzing the sensor output and determining a good course of action for achieving the given goal efficiently in a given (possibly unknown) environment. Consequently, there are two general aspects of robotics research, one on hardware and one on software. In this note we focus on the latter, and give a brief overview of a research topic in mobile robot algorithm design that has received considerable attention in recent years — formation of geometric patterns by autonomous mobile robots under distributed control. Motion coordination and self-organization of mobile robots under distributed control have been a common research area in automatic control, robotics and computer science. Engineering motivations for investigating self-organization arise in designing algorithms for distributed systems such as mobile sensor networks and autonomous robot teams, where mobile agents are deployed to perform search, monitoring, exploration, etc., adaptively in an unknown environment. To motivate the pattern formation problem, consider the following scenario. Suppose that a school teacher wants her 100 children in the playground to form a circle. She could use " centralized control " by drawing a circle on the ground as a guideline or even giving each child a specific position to move to. Alternatively, she could use " distributed control " and obtain a fairly good approximation of a circle by asking each child to move adaptively, based on the movement of other children and his/her knowledge of the shape of a circle. We wish to solve such pattern formation problems for autonomous mobile robots, using the latter distributed approach. To simplify the discussion, we model each robot as a mobile automaton that repeats a " Look-Compute-Move " cycle in discrete time steps indefinitely. The robots are anonymous (i.e., they have no ID's and use the same algorithm), and may even be oblivious (i.e., they have no memory to remember the past). They do not have a common x-y coordinate system. Given a group of n such robots and a target geometric pattern F …