Consensus on SO(3) with piecewise-continuous sinusoids

We present and analyze feedback control algorithms for multi-agent orientation consensus on SO(3), where each agent's angular-velocity control is restricted to be a piecewise-continuous sinusoid. The main results are three algorithms for orientation consensus using piecewise-continuous sinusoidal controls. Each algorithm can either include or not include a leader, which can be either stationary or rotating. The first algorithm achieves almost global orientation consensus for the case where each agent uses absolute-orientation feedback of its neighbor agents. The second algorithm achieves local orientation consensus for the case where each agent uses relative-orientation feedback of its neighbor agents. The third algorithm achieves local reduced-orientation (i.e., pointing-direction) consensus for the case where each agent uses pointing-direction feedback of its neighbor agents. We also present numerical simulations to demonstrate these algorithms.