Non-singular Cooperative Guiding Vector Field Under a Homotopy Equivalence Transformation

The present article advances the concept of a non-singular cooperative guiding vector field under a homotopy equivalence transformation. Firstly, the derivation of a guiding vector field, based on a non-singular vector field, is elaborated to navigate a transformed path from another frame. The existence of such vector fields is also deliberated herein. Subsequently, a coordination vector field derived from the guiding vector field is presented, incorporating an in-depth analysis concerning the impact of the vector field parameters. Lastly, the practical implementation of this novel vector field is demonstrated by its applications to 2-D and 3-D cooperative moving path following issues, establishing its efficacy.Comment: 12 pages, 12 figures, submitting to TAC at presen

A Frequency-Domain Path-Following Method for Discrete Data-Based Paths

This paper presents a novel frequency-domain approach for path following problem, specifically designed to handle paths described by discrete data. The proposed algorithm utilizes the fast Fourier Transform (FFT) to process the discrete path data, enabling the construction of a non-singular guiding vector field. This vector field serves as a reference direction for the controlled robot, offering the ability to adapt to different levels of precision. Additionally, the frequency-domain nature of the vector field allows for the reduction of computational complexity and effective noise suppression. The efficacy of the proposed approach is demonstrated through a numerical simulation, and theoretical analysis provides an upper bound for the ultimate mean-square path-following error

Direct-PoseNet: Absolute Pose Regression with Photometric Consistency

We present a relocalization pipeline, which combines an absolute pose regression (APR) network with a novel view synthesis based direct matching module, offering superior accuracy while maintaining low inference time. Our contribution is twofold: i) we design a direct matching module that supplies a photometric supervision signal to refine the pose regression network via differentiable rendering; ii) we modify the rotation representation from the classical quaternion to SO(3) in pose regression, removing the need for balancing rotation and translation loss terms. As a result, our network Direct-PoseNet achieves state-of-the-art performance among all other single-image APR methods on the 7-Scenes benchmark and the LLFF dataset