The distinctive feature of a polynomial parametric speed let polynomial Pythagorean-hodograph (PH) curves be attractive for the design of accurate and efficient application algorithms. We propose a robust path following scheme for the construction of smooth spatial motions by exploiting PH spline curves. In order to cover a general configuration setting, we present a guidance law which is suitable both for fully-actuated and (more common) under-actuated vehicles, which cannot control all the degrees of freedom. The robustness of the guidance law is enhanced by also taking into account the influence of wind or currents into the equations of motion. A selection of numerical experiments validates the effectiveness of the control strategy when $C^1$ spatial PH quintic interpolants are suitably considered for both kinematic and dynamic simulations.

翻译：多项式参数化速度的独特特性使得多项式毕达哥拉斯速端曲线在设计与实现精确高效的应用算法方面具有显著优势。本文提出一种鲁棒的路径跟踪方案，通过利用PH样条曲线构建平滑的空间运动轨迹。为适应一般构型设置，我们提出一种导引律，该律既适用于全驱动车辆，也适用于（更常见的）欠驱动车辆——后者无法控制全部自由度。通过将风或水流的影响纳入运动方程，进一步增强了导引律的鲁棒性。数值实验验证了当在运动学与动力学仿真中合理采用$C^1$连续空间五次PH插值曲线时，该控制策略的有效性。