Vector Fields for Path Following on Lie Groups with Application in Robot Control
arXiv:2602.21450v2 Announce Type: replace Abstract: Many robotic systems allow independent control of position and orientation (pose), including omnidirectional aerial vehicles, underwater robots, and manipulator end-effectors. In many applications, these systems must follow a continuous sequence of poses, leading to either trajectory-tracking or path following formulations. Compared to trajectory-tracking, path following offers important practical advantages. In particular, we focus on the problem of path following on Lie groups. Considering the robots as rigid bodies moving in the 3D space, this path-following problem can be posed as a problem of designing guiding vector fields on the matrix Lie group SE(3). In this paper, we develop a general vector-field framework for path following on connected matrix Lie groups, of which SE(3) is a prominent special case. The proposed vector field guarantees convergence to a desired parametric curve from almost all initial conditions while ensuri