非定常环境边界监测导航算法的技术效果证明
Proofs of Technical Results Justifying and Illustrating an Algorithm of Navigation for Monitoring Unsteady Environmental Boundaries
摘要：
本文考虑一个非完整Dubins类机器人在先验未知的非稳态平面环境中以恒定纵向速度运动。机器人应该检测、定位和跟踪动态环境标量场的边界。该场由机载传感器在机器人的位置以逐点方式测量。重点是不稳定的边界，随着时间的推移，在任意的方式，包括变形，即演变，形状和大小的变化。我们提出了一种滑模控制方法定位和跟踪这样的边界：机器人被引导到边界和循环在其附近之后。所提出的控制算法不需要估计场的空间梯度，并且对于计算和运动都是无要求的。本文提供了所需的技术事实的证明，严格的理由所提出的控制律的非局部收敛，以及在特定的情况下，其性能的理论说明。
英文摘要：
We consider a single non-holonomic Dubins-like robot traveling with a constant longitudinal speed in an a priori unknown and unsteady planar environment. The robot should detect, locate, and track the boundary of a dynamic environmental scalar field. The field is measured by an on-board sensor in a point-wise fashion at the robot's location. The focus is on unsteady boundaries that evolve over time in an arbitrary fashion, including deformations, i.e., changes of shapes and sizes. We present a sliding mode control method for localizing and tracking such boundaries: the robot is steered to the boundary and circulates in its close proximity afterwards. The proposed control algorithm does not require estimation of the spatial gradient of the field and is non-demanding with respect to both computation and motion. The paper offers the proofs of technical facts required for rigorous justification of non-local convergence of the proposed control law, as well as theoretical illustrations of its performance in specific scenarios.
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