Small-Satellite Attitude Consensus on SO(3) Using Continuous but only Piecewise-Continuously Differentiable Sinusoidal Controls

We consider attitude consensus for small satellites, where each satellite has internal rotating-mass actuators that, unlike reaction wheels, cannot perform complete rotations. Instead, these actuators are limited to a radians of total rotation. We present and analyze two attitude-feedback consensus control algorithms, where the controls for each satellite are the angles of rotation of the actuators and these controls are continuous but only piecewise-continuously differentiable sinusoids. Each control algorithm can either include or not include a leader satellite, which can be either rotating or non-rotating. The first control algorithm achieves local attitude consensus for the case where each satellite uses relative-attitude feedback of its neighbors. The second control algorithm achieves almost global attitude consensus for the case where each satellite uses absolute-attitude feedback of its neighbors.