  We study the problem of motion feasibility for multiagent control systems on
Lie groups with collision avoidance constraints. We first consider the problem
for kinematic left invariant control systems and next, for dynamical control
systems given by a left-trivialized Lagrangian function. Solutions of the
kinematic problem give rise to linear combinations of the control inputs in a
linear subspace annihilating the collision avoidance constraints. In the
dynamical problem, motion feasibility conditions are obtained by using
techniques from variational calculus on manifolds, given by a set of equations
in a vector space, and Lagrange multipliers annihilating the constraint force
that prevents deviation of solutions from a constraint submanifold.
