  We propose coordinating guiding vector fields to achieve two tasks
simultaneously with a team of robots: first, the guidance and navigation of
multiple robots to possibly different paths or surfaces typically embedded in
2D or 3D; second, their motion coordination while tracking their prescribed
paths or surfaces. The motion coordination is defined by desired parametric
displacements between robots on the path or surface. Such a desired
displacement is achieved by controlling the virtual coordinates, which
correspond to the path or surface's parameters, between guiding vector fields.
  Rigorous mathematical guarantees underpinned by dynamical systems theory and
Lyapunov theory are provided for the effective distributed motion coordination
and navigation of robots on paths or surfaces from all initial positions. As an
example for practical robotic applications, we derive a control algorithm from
the proposed coordinating guiding vector fields for a Dubins-car-like model
with actuation saturation.
  Our proposed algorithm is distributed and scalable to an arbitrary number of
robots. Furthermore, extensive illustrative simulations and fixed-wing aircraft
outdoor experiments validate the effectiveness and robustness of our algorithm.
