具有非对称成形限制的左变量多机构系统最佳控制 (Optimal Control of Left-Invariant Multi-Agent Systems with Asymmetric Formation Constraints)

from arxiv, This work was supported by the Swedish Research Council (VR), Knut och Alice Wallenberg foundation (KAW), the H2020 Project Co4Robots and the H2020 ERC Starting Grant BUCOPHSYS. arXiv admin note: text overlap with arXiv:1808.04612

In this work, we study an optimal control problem for a multi-agent system modeled by an undirected formation graph with nodes describing the kinematics of each agent, given by a left-invariant control system on a Lie group. The agents should avoid collision between them in the workspace. Such a task is done by introducing some potential functions into the cost function for the optimal control problem, corresponding to fictitious forces, induced by the formation constraint among agents, that break the symmetry of the individual agents and the cost functions, and rendering the optimal control problem partially invariant by a Lie group of symmetries. Reduced necessary conditions for the existence of normal extremals are obtained using techniques of variational calculus on manifolds. As an application, we study an optimal control problem for multiple unicycles.

翻译：在这项工作中,我们研究一个多试剂系统的最佳控制问题,该多试剂系统是由一个无方向的成形图制成的,配有节点,描述每种物剂的动脉,由利伊集团的左变量控制系统提供。该物剂应避免在工作空间发生碰撞。完成这项任务的方法是,在最佳控制问题的成本功能中引入某些潜在功能,与因物剂的形成制约而引发的虚构力量相对应,这些力量打破了个别物剂的对称和成本功能,并使最佳控制问题部分由一个对称体的谎言组产生,使最佳控制问题部分不易变。利用在多管上变微量技术获得正常体存在必要的条件。作为一种应用,我们研究多环周期的最佳控制问题。