标题： 基于多项式消去的积分器链动力学高效在线轨迹规划 显示英文标题

标题： Efficient Online Trajectory Planning for Integrator Chain Dynamics using Polynomial Elimination

摘要： 提供平滑的参考轨迹可以有效提高跟踪控制应用的性能和准确性，同时减少超调和不必要的振动。 通过使用反馈线性化、微分平坦性或控制器规范形式等方法，将系统动力学转换为解耦的积分器链，可以显著简化轨迹规划计算。 我们提出了一种高效的方法，用于在导数边界约束下为积分器链规划时间最优轨迹。 因此，一种代数预计算算法以多项式系统的形式表述了时间最优性的必要条件，随后使用格罗布纳基进行符号多项式消去。 然后，一种快速的在线算法通过计算分解后的多项式系统的根来规划轨迹。 这些根描述了输入信号的切换时间点，完整的轨迹只需通过多次积分即可得到。 该方法通过代数计算精确地计算时间最优轨迹，而无需数值近似迭代。 它被应用于各种轨迹类型，包括不同连续阶数、非对称导数边界以及非静止初始和最终状态的情况。 显示英文摘要

摘要： Providing smooth reference trajectories can effectively increase performance and accuracy of tracking control applications while overshoot and unwanted vibrations are reduced. Trajectory planning computations can often be simplified significantly by transforming the system dynamics into decoupled integrator chains using methods such as feedback linearization, differential flatness or the controller canonical form. We present an efficient method to plan time optimal trajectories for integrator chains subject to derivative bound constraints. Therefore, an algebraic precomputation algorithm formulates the necessary conditions for time optimality in form of a set of polynomial systems, followed by a symbolic polynomial elimination using Gr\"obner bases. A fast online algorithm then plans the trajectories by calculating the roots of the decomposed polynomial systems. These roots describe the switching time instants of the input signal and the full trajectory simply follows by multiple integration. This method presents a systematic way to compute time optimal trajectories exactly via algebraic calculations without numerical approximation iterations. It is applied to various trajectory types with different continuity order, asymmetric derivative bounds and non-rest initial and final states.