  In this paper, we develop a hybrid distance-angle rigidity theory that
involves heterogeneous distances (or unsigned angles) and signed constraints
for a framework in the 2-D and 3-D space. The new rigidity theory determines a
(locally) unique formation shape up to a translation and a rotation by a set of
distance and signed constraints, or up to a translation, a rotation and
additionally a scaling factor by a set of unsigned angle and signed
constraints. Under this new rigidity theory, we have a clue to resolve the flip
(or reflection) and flex ambiguity for a target formation with hybrid
distance-angle constraints. In particular, we can completely eliminate the
ambiguity issues if formations are under a specific construction which is
called \myemph{signed Henneberg construction} in this paper. We then apply the
rigidity theory to formation shape control and develop a gradient-based control
system that guarantees an exponential convergence close to a desired formation
by inter-neighbor measurements. Several numerical simulations on formation
shape control with hybrid distance-angle constraints are provided to validate
the theoretical results.
