论文标题
使用多项式的双重描述有效地生成大规模轨迹
Generating Large-Scale Trajectories Efficiently using Double Descriptions of Polynomials
论文作者
论文摘要
对于四轨道轨迹计划，通过系数和最终衍生品描述多项式轨迹，都在能量最小化方面享有自己的便利性。我们将它们命名为多项式轨迹的双重描述。本文正式分析了它们之间的转换，从而导致大多数效率和不稳定。利用其分析结构，我们设计了一个线性复杂方案，以最小化和参数梯度评估，该方案具有效率，稳定性，灵活性和可扩展性。在我们的计划的帮助下，产生一种能量最佳（最小扣）轨迹的轨迹仅需1 $μs$，每块最高1,000,000件。此外，针对常规方法，还可以加速产生大规模的能源最佳轨迹。
For quadrotor trajectory planning, describing a polynomial trajectory through coefficients and end-derivatives both enjoy their own convenience in energy minimization. We name them double descriptions of polynomial trajectories. The transformation between them, causing most of the inefficiency and instability, is formally analyzed in this paper. Leveraging its analytic structure, we design a linear-complexity scheme for both jerk/snap minimization and parameter gradient evaluation, which possesses efficiency, stability, flexibility, and scalability. With the help of our scheme, generating an energy optimal (minimum snap) trajectory only costs 1 $μs$ per piece at the scale up to 1,000,000 pieces. Moreover, generating large-scale energy-time optimal trajectories is also accelerated by an order of magnitude against conventional methods.
