  This letter studies a distributed collision avoidance control problem for a
group of rigid bodies on a sphere. A rigid body network, consisting of multiple
rigid bodies constrained to a spherical surface and an interconnection
topology, is first formulated. In this formulation, it is shown that motion
coordination on a sphere is equivalent to attitude coordination on the
3-dimensional Special Orthogonal group. Then, an angle-based control barrier
function that can handle a geodesic distance constraint on a spherical surface
is presented. The proposed control barrier function is then extended to a
relative motion case and applied to a collision avoidance problem for a rigid
body network operating on a sphere. Each rigid body chooses its control input
by solving a distributed optimization problem to achieve a nominal distributed
motion coordination strategy while satisfying constraints for collision
avoidance. The proposed collision-free motion coordination law is validated via
simulation.
