Autonomous navigation of a non‐holonomic robot for 3D tracking unsteady environmental boundaries

Abstract

AbstractAn under‐actuated non‐holonomic robot moves in three dimensions with a constant surge speed and is actuated by upper bounded yawing and pitching rates. The 3D workspace hosts an unknown and time‐varying scalar field. The robot measures only its value at the current location and has no access to the field gradient. Starting from an occasional initial location, the robot should arrive at the level set (isosurface) where the field assumes a predefined value. After this, the robot should repeatedly sweep the entirety of this moving and deforming isosurface. We present a hybrid control law that solves this mission. This law switches among three discrete states, two of which are interchanged on a regular basis, and follows the sliding mode paradigm to drive the robot within a given discrete state. It does not visibly try to estimate the field gradient, is computationally inexpensive, and exhibits a regular, smooth motion. The proposed law is rigorously justified by a global convergence result. Its performance is demonstrated by computer simulation tests.