  We present a Cucker-Smale (C-S) type flocking model on a sphere. We study
velocity alignment on a sphere and prove the emergence of flocking for the
proposed model. Our model includes three new terms: a centripetal force,
multi-agent interactions on a sphere and inter-particle bonding forces. To
compare velocity vectors on different tangent spaces, we introduce a rotation
operator in our new interaction term. Due to the geometric restriction, the
rotation operator is singular at antipodal points and the relative velocity
between two agents located at these points is not well-defined. Based on an
energy dissipation property of our model and a variation of Barbalat's lemma,
we show the alignment of velocities for an admissible class of communication
weight functions. In addition, for sufficiently large bonding forces we prove
time-asymptotic flocking which includes the avoidance of antipodal points.
