Consensus on a sphere for a 3-dimensional speeding up and slowing down strategy

We extend the Speeding Up and Slowing Down (SUSD) strategy for distributed source seeking from a three agent group to a swarm of any number of agents without communicating frame coordinates or gradient estimates among agents. We integrate a nonlinear time varying consensus-on-a-sphere control law with the SUSD strategy in a leader-follower frame-work, which is inspired by source seeking behavior of certain fish species. We provide Lyapunov-based convergence analysis for the leader-follower SUSD strategy integrated with the consensus law. We demonstrate the efficiency of the proposed method through simulated source seeking behavior in three dimensional scalar fields.