Distributed Formation Control of the Special Euclidean Group and Its Applications

Abstract

In this thesis, distributed formation control problems of the special Euclidean group are studied. The objective of the distributed formation control of the special Euclidean group is to control both orientation and formation of agents by using relative information with regard to each agent's local reference frame. It shows that the agents can achieve the desired formation shape in the fully distributed environment when agents' orientations are rotated to point toward their target orientations. The agents are characterized in the special Euclidean group, where the special Euclidean group denotes the orientation and the position of the agents.

In the fully distributed environment, each agent only measures the displacement with regard to each agent's local reference frame. The agents can estimate or control their orientations with regard to a global(common) reference frame by using the displacement with regard to the local reference frame under a given interaction topology. It implies the displacement can be analyzed with regard to a global(common) reference frame. In this thesis, each agent estimates its own orientation with regard to a global reference frame by using the relative orientation. The estimated orientation is used to point the agent's orientation toward the prescribed desired orientation. It shows that the displacement with regard to the local reference frame can be analyzed with regard to a common reference frame by using desired orientation information. Thus, the distributed formation control of the special Euclidean group can be achieved via orientation control.

The distributed formation control of the special Euclidean group can be employed in various applications of multi-sensor networks. In this thesis, distributed object pose estimation problems over strongly connected networks are studied as applications of the formation control of the special Euclidean group. Consider a static object observed by a multi-agent system. Each agent measures the object pose, assumed to be Gaussian, with regard to a global(local) reference frame. Then, the optimal object pose is estimated based on the maximum likelihood computed in a distributed manner. To estimate the optimal object pose without a global reference frame, the agents' poses with regard to a common reference frame are estimated by using noiseless relative pose information.