Real-time Optimization of Trajectories that Guarantee the Rendezvous of Mobile Robots

Since the 1960s, consensus problems have puzzled the minds of many researchers in fields ranging from computer science to information aggregation. In this work, although specifically addressing the rendezvous problem for a team of robots, we develop a methodology that can also be applied to other consensus problems, where optimality is important and where non-holonomicity characterizes the system at hand. In particular, we consider a group of differential-wheeled robots endowed with noisy relative positioning capabilities. We develop a distributed, real-time optimization method based on a receding horizon controller that minimizes a user-defined cost whilst guaranteeing the rendezvous. Finally, we perform experiments on real robots to confirm the validity of our approach.