An Algorithm for Fast Rendezvous Seeking of Wireless Networked Robotic Systems

The recent development of wireless network architecture and distributed control algorithm allows the onset of large scale robotic application such as monitoring, formation control and flocking, coordination, exploration of unknown environments, and surveillance. In such applications there are many autonomous robots which have capabilities of sensing and acting on the environment and that can communicate with the other robot by wireless communication network defining a Wireless Networked Robotic Systems (in the follows briefly WNR). Usually a robot implements a cooperative algorithm to get some common WNR objective. A widely studied cooperative algorithm allows every robot automatically converge to a common position (consensus or rendezvous) using only local information received from its one hop neighboring robots. Therefore WNR brings together the cooperative control algorithm and the communication capabilities. Despite of a large body of research produced by robotics research community, it is a challenging problem to explore the analysis, the design and evaluation of cooperative algorithm in a more realistic scenario of wireless networked robotic application where the networking and protocol features might affect the overall closed loop WNR performance. In this direction the paper deals with the analysis and design of m-order cooperative control algorithm for fast rendezvous seeking over WNR. Specifically we give a sufficient stability condition of the control algorithm in the presence of heterogeneous time delays affecting the communication through the hops of the WNR. Moreover we analyze the effect of the packet collision phenomena and the presence of background disturbance traffic on the resulting WNR performance. The above sufficient stability condition and analysis, joining with the implementation issues can give a guideline about the design of the rendezvous control algorithm and wireless protocol parameters when we deal with a realistic network environment of WNR. Simulation experiments carried out by a realistic simulation confirm the theoretical findings.