基于Lagrange乘子理论的轨迹跟踪和局部规划一体化

Unification of Trajectory Tracking and Local Path Planning Based on Lagrange Multiplier Theory

基于Ｌａｇｒａｎｇｅ 乘子理论，根据移动机器人自主行走的具体要求，提出完成轨迹跟踪、到达目标和避障的优化模型，实现了控制与规划的一体化。利用Ｌｙａｐｕｎｏｖ 稳定理论证明了系统的稳定性，讨论了Ｌａｇｒａｎｇｅ 乘子对系统响应的影响。

Based on Lagrange multiplier theory, an optimized model of a mobile robot for trajectory tracking, goal seeking and obstacle avoiding to meet the requirements of a mobile robot′s motion was presented. This unified path planning and control. The stability of the system was proved via Lyapunov function. Furthermore, the effects of Lagrange multiplier on the system response were discussed. Simulation results show that trajectory tracking and local path planning can be achieved simultaneously.