  Motivated by the challenging formation stabilization problem for mobile
robotic teams when no distance or relative displacement measurements are
available and each robot can only measure some of those angles formed by rays
towards its neighbors, we develop the notion of ``angle rigidity" for a
multi-point framework, named ``angularity", consisting of a set of nodes
embedded in a Euclidean space and a set of angle constraints among them.
Different from bearings or angles defined with respect to a global axis, the
angles we use do not rely on the knowledge of a global coordinate system and
are signed according to the counter-clockwise direction. Here \emph{angle
rigidity} refers to the property specifying that under proper angle
constraints, the angularity can only translate, rotate or scale as a whole when
one or more of its nodes are perturbed locally. We first demonstrate that this
angle rigidity property, in sharp comparison to bearing rigidity or other
reported rigidity related to angles of frameworks in the literature, is
\emph{not} a global property since an angle rigid angularity may allow flex
ambiguity. We then construct necessary and sufficient conditions for
\emph{infinitesimal} angle rigidity by checking the rank of an angularity's
rigidity matrix. We develop a combinatorial necessary condition for
infinitesimal minimal angle rigidity. Using the developed theories, a formation
stabilization algorithm is designed for a robotic team to achieve a globally
angle rigid formation, in which only angle measurements are needed.
