Coordinated Motion Control Of Multiple Mobile Robots Via Geometric Approach

With the development of artificial intelligence, embedded and communicationtechnologies, multiple mobile robots systems(MMRS) had a solid technicalfoundation in research and applications. The advantage of the robot system isobvious, a lot of robots which have the simple structure, limited sensing quantity,poor computing and communication ability, can achieve some functions or tasksthat one single complex robot can’t or difficult to complete. However, when thenumber of robots is growing, one important problem needed to be considered isthe coordination control of the robotic team.An important research direction of MMRS coordination control problem is thecoordinated motion. Most researches about this topic have been restricted onvector space framework. The drawback of this framework is lack of consideringpose control of robot, and possibly results in some singularity problems. Otherstudies concentrate on the models of some special robots, and then utilize theoptimization algorithms, artificial potential fields, or other methods to design thecontrol law. Different to these studies, this thesis will construct a generaldifferential geometric framework of modeling, analysis and control system designfor coordinated motion of MMRS.First of all, a general geometric framework of modeling of coordinated motionis established. Via definition of two kinds of relative position on Lie group by leftinvariance and right invariance, and then three forms of coordinated motion areobtained. Each type of them corresponds to the relations of robotic velocity.Therefore, the coordinated motion problem on lie group can turn into theconsensus problem on lie algebra. And the design of control law follows thegeneral method which is used to solve the consensus problem on vector space.Further, the mobile robots which configuration space is SE(3) group areresearched. In this paper a robot model base on steering control is established.Then, the control law for two types of communicate situation are designed, and theasymptotic stability of the system can be proved by using La Salle principle. Andlast, some simulations have been finished, and the results bring out that the robotsteam can eventually reach the left invariance coordinated motion.Finally, focus on the four wheel differential ground mobile robots, whichconfiguration space are SE(2) group. In this paper left-invariance andbi-invariance coordination are studied, the special robots model are set up bygeometric approach. Then, control laws by steering and non-steering controlmodel are designed. And last, simulation results can make out that the robots reach the coordinated motion under the control laws.