Motion Feasibility Conditions for Multi-Agent Control Systems on Lie Groups

TL;DR

This paper develops conditions for the feasibility of multi-agent motions on Lie groups, incorporating collision avoidance, for both kinematic and dynamical control systems using geometric and variational methods.

Contribution

It introduces a unified framework for analyzing motion feasibility on Lie groups for multi-agent systems with collision constraints, covering both kinematic and dynamical models.

Findings

Feasibility conditions derived for kinematic control systems.

Variational calculus applied to dynamical systems for feasibility analysis.

Linear control input combinations that satisfy collision avoidance constraints.

Abstract

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.