论文标题
使用多项式消除的集成商链动力学的有效在线轨迹计划
Efficient Online Trajectory Planning for Integrator Chain Dynamics using Polynomial Elimination
论文作者
论文摘要
提供平滑的参考轨迹可以有效地提高跟踪控制应用的性能和准确性，而过冲和不需要的振动会减少。通常，可以使用反馈线性化，差异平面度或控制器规范形式将系统动力学转换为脱钩的集成器链来显着简化轨迹计划计算。我们提出了一种有效的方法，以计划受衍生结合约束的积分链的时间最佳轨迹。因此，代数的预启用算法以一组多项式系统的形式制定了必要的时间最佳条件，然后使用gröbner碱基进行符号多项式消除。然后，快速在线算法通过计算分解多项式系统的根来计划轨迹。这些根描述了输入信号的切换时间瞬间，并且完整的轨迹仅通过多个集成而遵循。此方法提出了一种系统的方法，可以通过代数计算准确地计算时间最佳轨迹，而无需数字近似迭代。它应用于具有不同的连续性顺序，不对称衍生界限以及非时髦初始和最终状态的各种轨迹类型。
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 Gröbner 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.
