Collision-Free Navigation of Wheeled Mobile Robots: An Integrated Path Planning and Tube-Following Control Approach

In this paper, an integrated path planning and tube-following control scheme is proposed for collision-free navigation of a wheeled mobile robot (WMR) in a compact convex workspace cluttered with sufficiently separated spherical obstacles. An analytical path planning algorithm is developed based on Bouligand's tangent cones and Nagumo's invariance theorem, which enables the WMR to navigate towards a designated goal location from almost all initial positions in the free space, without entering into augmented obstacle regions with safety margins. We further construct a virtual "safe tube" around the reference trajectory, ensuring that its radius does not exceed the size of the safety margin. Subsequently, a saturated adaptive controller is designed to achieve safe trajectory tracking in the presence of disturbances. It is shown that this tube-following controller guarantees that the WMR tracks the reference trajectory within the predefined tube, while achieving uniform ultimate boundedness of both the position tracking and parameter estimation errors. This indicates that the WMR will not collide with any obstacles along the way. Finally, we report simulation and experimental results to validate the effectiveness of the proposed method.

Unsupervised Manifold Alignment with Joint Multidimensional Scaling

We introduce Joint Multidimensional Scaling, a novel approach for unsupervised manifold alignment, which maps datasets from two different domains, without any known correspondences between data instances across the datasets, to a common low-dimensional Euclidean space. Our approach integrates Multidimensional Scaling (MDS) and Wasserstein Procrustes analysis into a joint optimization problem to simultaneously generate isometric embeddings of data and learn correspondences between instances from two different datasets, while only requiring intra-dataset pairwise dissimilarities as input. This unique characteristic makes our approach applicable to datasets without access to the input features, such as solving the inexact graph matching problem. We propose an alternating optimization scheme to solve the problem that can fully benefit from the optimization techniques for MDS and Wasserstein Procrustes. We demonstrate the effectiveness of our approach in several applications, including joint visualization of two datasets, unsupervised heterogeneous domain adaptation, graph matching, and protein structure alignment.