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.

中文翻译：

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李群上多智能体控制系统的运动可行性条件

我们研究了具有避免碰撞约束的李群上的多智能体控制系统的运动可行性问题。我们首先考虑运动学上的不变式控制系统，然后考虑由左平凡的拉格朗日函数给出的动态控制系统的问题。运动学问题的解决方案引起线性子空间中控制输入的线性组合，从而消除了避免碰撞的约束。在动力学问题中，使用矢量流中的一组方程，通过使用流形上的变分演算技术来获得运动可行性条件，拉格朗日乘子消除了约束力，该约束力可防止解从约束子流形偏离。