Sampling Complexity of Path Integral Methods for Trajectory Optimization
Sampling Complexity of Path Integral Methods for Trajectory Optimization
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DOI：
10.23919/acc53348.2022.9867607
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发表时间：
2022-03
期刊：
影响因子：
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通讯作者：
Hyung-Jin Yoon;Chuyuan Tao;Hunmin Kim;N. Hovakimyan;P. Voulgaris
中科院分区：
文献类型：
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作者：
Hyung-Jin Yoon;Chuyuan Tao;Hunmin Kim;N. Hovakimyan;P. Voulgaris
在决策和控制中使用随机采样已经变得流行，因为可以轻松访问图形处理单元，该图形处理单元可以为实时机器人应用生成和计算多个随机轨迹。与顺序优化相比，基于采样的方法可以利用并行计算来保持恒定的控制回路频率。受其在机器人应用中的广泛适用性的启发，我们计算了适用于一般非线性系统的采样复杂性结果，考虑基于采样的路径积分方法。结果确定所需的样本数量，以满足估计的控制信号的给定的误差范围，从最佳值与预定义的风险概率。抽样复杂性结果表明，估计的控制值的方差是上界的期望的成本。然后，我们将结果应用到一个线性时变动力系统的二次成本与二次加指标成本函数。
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 sampling based path integral 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 with a quadratic plus indicator cost function.