Motion Feasibility Conditions for Multiagent Control Systems on Lie Groups

摘要

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 the deviation of solutions from a constraint submanifold.