TY - JOUR

T1 - Path following control in 3D using a vector field

AU - Yao, Weijia

AU - Cao, Ming

PY - 2020/7

Y1 - 2020/7

N2 - Using a designed vector field to control a mobile robot to follow a given desired path has found a range of practical applications, and it is in great need to further build a rigorous theory to guide its implementation. In this paper, we study the properties of a general 3D vector field for robotic path following. We stipulate and investigate assumptions that turn out to be crucial for this method, although they are rarely explicitly stated in the existing related works. We derive conditions under which the local path-following error vanishes exponentially in a sufficiently small neighborhood of the desired path, which is key to show the local input-to-state stability (local ISS) property of the path-following error dynamics. The local ISS property then justifies the control algorithm design for a fixed-wing aircraft model. Our approach is effective for any sufficiently smooth desired path in 3D, bounded or unbounded; the results are particularly relevant since unbounded desired paths have not been sufficiently discussed in the literature. Simulations are conducted to verify the theoretical results.

AB - Using a designed vector field to control a mobile robot to follow a given desired path has found a range of practical applications, and it is in great need to further build a rigorous theory to guide its implementation. In this paper, we study the properties of a general 3D vector field for robotic path following. We stipulate and investigate assumptions that turn out to be crucial for this method, although they are rarely explicitly stated in the existing related works. We derive conditions under which the local path-following error vanishes exponentially in a sufficiently small neighborhood of the desired path, which is key to show the local input-to-state stability (local ISS) property of the path-following error dynamics. The local ISS property then justifies the control algorithm design for a fixed-wing aircraft model. Our approach is effective for any sufficiently smooth desired path in 3D, bounded or unbounded; the results are particularly relevant since unbounded desired paths have not been sufficiently discussed in the literature. Simulations are conducted to verify the theoretical results.

KW - Path following

KW - Vector field

KW - Autonomous mobile robots

KW - Nonlinear systems

KW - Nonholonomic models

U2 - 10.1016/j.automatica.2020.108957

DO - 10.1016/j.automatica.2020.108957

M3 - Article

VL - 117

JO - Automatica

JF - Automatica

SN - 1873-2836

M1 - 108957

ER -