This paper discusses the adaptive sampling problem in a nonholonomic mobile robotic sensor network for efficiently monitoring a spatial field. It is proposed to employ Gaussian process to model a spatial phenomenon and predict it at unmeasured positions, which enables the sampling optimization problem to be formulated by the use of the log determinant of a predicted covariance matrix at next sampling locations. The control, movement and nonholonomic dynamics constraints of the mobile sensors are also considered in the adaptive sampling optimization problem. In order to tackle the nonlinearity and nonconvexity of the objective function in the optimization problem we first exploit the linearized alternating direction method of multipliers (L-ADMM) method that can effectively simplify the objective function, though it is computationally expensive since a nonconvex problem needs to be solved exactly in each iteration. We then propose a novel approach called the successive convexified ADMM (SC-ADMM) that sequentially convexify the nonlinear dynamic constraints so that the original optimization problem can be split into convex subproblems. It is noted that both the L-ADMM algorithm and our SC-ADMM approach can solve the sampling optimization problem in either a centralized or a distributed manner. We validated the proposed approaches in 1000 experiments in a synthetic environment with a real-world dataset, where the obtained results suggest that both the L-ADMM and SC- ADMM techniques can provide good accuracy for the monitoring purpose. However, our proposed SC-ADMM approach computationally outperforms the L-ADMM counterpart, demonstrating its better practicality.
翻译:本文讨论了在非单流式移动机器人传感器网络中的适应性抽样问题,以便有效监测空间场域。建议采用高斯进程,模拟空间现象,并在未测的位置上预测,这样就可以通过在下一个取样地点使用预测的共变矩阵的对数决定因素来制定抽样优化问题。在适应性取样优化问题中也考虑了移动传感器的控制、移动和非非单流式动态动态制约。为了解决优化问题中目标功能的非线性性和不兼容性,我们首先利用可有效简化目标功能的线性交替方向方法(L-ADMM),尽管计算成本很高,因为非电解问题需要在每个迭接点完全解决。然后,我们提出了一种新颖的方法,即连续的调和不线性ADMM(SC-AMM)的动态动态制约,从而将最初的优化方法分为一个直线性、不切换方向方法,从而可以演示正反向的乘数法方法。我们提出的LADMM-M-M-正(S-MM-MA-M-S-S-C-MLAD-C-MLML-MA-MLAD-MA-MA-ML-S-MA-MA-MA-MA-MA-MA-S-S-S-MLMLR-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-SA-SA-SA-SA-SA-SA-MA-MA-MA-MA-MA-MA-MA-MALLR-MA-MA-MA-MA-MA-SA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-MA-