多項式の二重記述を用いた大規模軌道の効率的生成
Generating Large-Scale Trajectories Efficiently using Double Descriptions of Polynomials
多項式軌道の係数表現と端点微分表現の変換構造を解析し、jerk/snap最小化と勾配評価を線形計算量で行う手法を提案。100万区間規模でも1区間あたり1μsでエネルギー最適軌道を生成できる。
著者: Zhepei Wang, Hongkai Ye, Chao Xu, Fei Gao
分類: cs.RO
原文アブストラクト
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 $\mu s$ 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.
