Formation control for multiple agents with local measurements: continuous-time and sampled-data-based cases

We study the formation control problem for a group of mobile agents in a plane, in which each agent is modeled as a kinematic point and can only use the local measurements in its local frame. The agents are required to maintain a geometric pattern while keeping a desired distance to a static/moving target. The prescribed formation is a general one which can be any geometric pattern, and the neighboring relationship of the N-agent system only has the requirement of containing a directed spanning tree. To solve the formation control problem, a distributed controller is proposed based on the idea of decoupled design. One merit of the controller is that it only uses each agent's local measurements in its local frame, so that a practical issue that the lack of a global coordinate frame or a common reference direction for real multi-robot systems is successfully solved. Considering another practical issue of real robotic applications that sampled data is desirable instead of continuous-time signals, the sampled-data based controller is developed. Theoretical analysis of the convergence to the desired formation is provided for the multi-agent system under both the continuous-time controller with a static/moving target and the sampled-data based one with a static target. Numerical simulations are given to show the effectiveness and performance of the controllers.