3 research outputs found
Integrated Path Following and Collision Avoidance Using a Composite Vector Field
Path following and collision avoidance are two important functionalities for mobile robots, but there are only a few approaches dealing with both. In this paper, we propose an integrated path following and collision avoidance method using a composite vector field. The vector field for path following is integrated with that for collision avoidance via bump functions, which reduce significantly the overlapping effect. Our method is general and flexible since the desired path and the contours of the obstacles, which are described by the zero-level sets of sufficiently smooth functions, are only required to be homeomorphic to a circle or the real line, and the derivation of the vector field does not involve specific geometric constraints. In addition, the collision avoidance behaviour is reactive; thus, real-time performance is possible. We show analytically the collision avoidance and path following capabilities, and use numerical simulations to illustrate the effectiveness of the theory
Singularity-free Guiding Vector Field for Robot Navigation
Most of the existing path-following navigation algorithms cannot guarantee
global convergence to desired paths or enable following self-intersected
desired paths due to the existence of singular points where navigation
algorithms return unreliable or even no solutions. One typical example arises
in vector-field guided path-following (VF-PF) navigation algorithms. These
algorithms are based on a vector field, and the singular points are exactly
where the vector field diminishes. In this paper, we show that it is
mathematically impossible for conventional VF-PF algorithms to achieve global
convergence to desired paths that are self-intersected or even just simple
closed (precisely, homeomorphic to the unit circle). Motivated by this new
impossibility result, we propose a novel method to transform self-intersected
or simple closed desired paths to non-self-intersected and unbounded
(precisely, homeomorphic to the real line) counterparts in a higher-dimensional
space. Corresponding to this new desired path, we construct a singularity-free
guiding vector field on a higher-dimensional space. The integral curves of this
new guiding vector field is thus exploited to enable global convergence to the
higher-dimensional desired path, and therefore the projection of the integral
curves on a lower-dimensional subspace converge to the physical
(lower-dimensional) desired path. Rigorous theoretical analysis is carried out
for the theoretical results using dynamical systems theory. In addition, we
show both by theoretical analysis and numerical simulations that our proposed
method is an extension combining conventional VF-PF algorithms and trajectory
tracking algorithms. Finally, to show the practical value of our proposed
approach for complex engineering systems, we conduct outdoor experiments with a
fixed-wing airplane in windy environment to follow both 2D and 3D desired
paths.Comment: Accepted for publication in IEEE Trransactions on Robotics (T-RO