経路積分法による軌道最適化のサンプリング複雑性
Sampling Complexity of Path Integral Methods for Trajectory Optimization
経路積分法というサンプリングベース制御法について、所定の誤差とリスク確率を満たすのに必要なサンプル数を理論的に導出し、線形時変系などに適用した。
著者: Hyung-Jin Yoon, Chuyuan Tao, Hunmin Kim, Naira Hovakimyan, Petros Voulgaris
分類: cs.RO, cs.SY, eess.SY
原文アブストラクト
The use of random sampling in decision-making and control has become popular with the ease of access to graphic processing units that can generate and calculate multiple random trajectories for real-time robotic applications. In contrast to sequential optimization, the sampling-based method can take advantage of parallel computing to maintain constant control loop frequencies. Inspired by its wide applicability in robotic applications, we calculate a sampling complexity result applicable to general nonlinear systems considered in the path integral method, which is a sampling-based method. The result determines the required number of samples to satisfy the given error bounds of the estimated control signal from the optimal value with the predefined risk probability. The sampling complexity result shows that the variance of the estimated control value is upper-bounded in terms of the expectation of the cost. Then we apply the result to a linear time-varying dynamical system with quadratic cost and an indicator function cost to avoid constraint sets.
