  We consider the problem of cooperative motion coordination for multiple
heterogeneous mobile vehicles subject to various constraints. These include
nonholonomic motion constraints, constant speed constraints, holonomic
coordination constraints, and equality/inequality geometric constraints. We
develop a general framework involving differential-algebraic equations and
viability theory to determine coordination feasibility for a coordinated motion
control under heterogeneous vehicle dynamics and different types of
coordination task constraints. If a coordinated motion solution exists for the
derived differential-algebraic equations and/or inequalities, a constructive
algorithm is proposed to derive an equivalent dynamical system that generates a
set of feasible coordinated motions for each individual vehicle. In case
studies on coordinating two vehicles, we derive analytical solutions to motion
generation for two-vehicle groups consisting of car-like vehicles, unicycle
vehicles, or vehicles with constant speeds, which serve as benchmark
coordination tasks for more complex vehicle groups. The motion generation
algorithm is well-backed by simulation data for a wide variety of coordination
situations involving heterogeneous vehicles. We then extend the vehicle control
framework to deal with the cooperative coordination problem with time-varying
coordination tasks and leader-follower structure. We show several simulation
experiments on multi-vehicle coordination under various constraints to validate
the theory and the effectiveness of the proposed schemes.
