Problem: Consensus of multiple robots

In the last chapter we will study control of robotic systems. One of the problems to be studied is cooperative control of multiple robots. As we know, individual animals routinely face decisions that are crucial to them. In social species, however, many of these decisions need to be made jointly with other group members because the group will be broken apart unless a consensus is reached.    

 

 For the control of multiple mobile robots, consensus reaching is also a basic problem studied. Let us consider a flock of N agents (think them as birds). Each bird flies with the same speed but with possibly different directions. Namely

vi=(vcosθi,vsinθi)^T

where θi is the heading of bird i.

Now suppose for each bird, it changes its heading by the following model:

dθi/dt=ui,

An interesting question is how each bird should update its heading so eventually we have

θ₁(t)=···=θ_N(t).

Here the assumption is that each bird knows only the relative heading of its neighbors. Thus the design of controller ui should be based only on such knowledge.