SUMMARYThis paper deals with motion planning and control problems for a class of partially differentially flat systems. They possess a feature that the derivative of the fiber variable can be represented purely by the base variable and its derivatives. Based on this feature, a Beta function-based motion planning algorithm is proposed with less computational cost compared with the optimal control formulation while providing similar system performance. Then, an adaptive controller is constructed through a function approximation technique-based approach. Finally, the feasibility of the proposed motion planning and control algorithms is verified by simulations.

中文翻译：

---

偏微分平面系统的运动规划与控制

摘要本文处理一类部分微分平面系统的运动规划和控制问题。它们具有纤维变量的导数可以完全由基变量及其导数表示的特征。基于这一特点，提出了一种基于Beta函数的运动规划算法，与最优控制公式相比，计算成本更低，同时提供相似的系统性能。然后，通过基于函数逼近技术的方法构建自适应控制器。最后，通过仿真验证了所提出的运动规划和控制算法的可行性。