论文标题
减少对称碰撞的对称性的最佳控制降低，避免了谎言组上多代理系统的障碍物
Reduction in optimal control with broken symmetry for collision and obstacle avoidance of multi-agent system on Lie groups
论文作者
论文摘要
我们研究了对称性的减少，以确保左旋仿射多代理控制系统的最佳控制问题中的最佳条件，并具有局部对称性破坏成本功能，用于连续时间和离散时间系统。我们将最佳控制问题重新阐述为一个约束的变异问题，其中局部对称性破坏了拉格朗日，并通过在两种设置，连续时间和离散时间中通过对称性减少技术从减少的变异原理中获得了降低的最佳条件。我们将结果应用于在存在静态障碍物的情况下在$ SE（2）上进化的多辆车的碰撞和避免障碍问题。
We study the reduction by symmetry for optimality conditions in optimal control problems of left-invariant affine multi-agent control systems, with partial symmetry breaking cost functions for continuous-time and discrete-time systems. We recast the optimal control problem as a constrained variational problem with a partial symmetry breaking Lagrangian and obtain the reduced optimality conditions from a reduced variational principle via symmetry reduction techniques in both settings, continuous-time, and discrete-time. We apply the results to a collision and obstacle avoidance problem for multiple vehicles evolving on $SE(2)$ in the presence of a static obstacle.
