Mobile manipulators typically encounter significant challenges in navigating narrow, cluttered environments due to their high-dimensional state spaces and complex kinematics. While reactive methods excel in dynamic settings, they struggle to efficiently incorporate complex, coupled constraints across the entire state space. In this work, we present a novel local reactive controller that reformulates the time-domain single-step problem into a multi-step optimization problem in the spatial domain, leveraging the propagation of a serial kinematic chain. This transformation facilitates the formulation of customized, decoupled link-specific constraints, which is further solved efficiently with augmented Lagrangian differential dynamic programming (AL-DDP). Our approach naturally absorbs spatial kinematic propagation in the forward pass and processes all link-specific constraints simultaneously during the backward pass, enhancing both constraint management and computational efficiency. Notably, in this framework, we formulate collision avoidance constraints for each link using accurate geometric models with extracted free regions, and this improves the maneuverability of the mobile manipulator in narrow, cluttered spaces. Experimental results showcase significant improvements in safety, efficiency, and task completion rates. These findings underscore the robustness of the proposed method, particularly in narrow, cluttered environments where conventional approaches could falter. The open-source project can be found at https://github.com/Chunx1nZHENG/MM-with-Whole-Body-Safety-Release.git.

In conclusion, for general QM problems, the traditional approach solves them by employing some numerical or iterative algorithms [4]. A message-passing scheme for solving QM problems is presented in [5] by Ruozzi and Tatikonda. In addition, Zhang et al. present a QM-based dual-arm cyclic-motion-generation manipulator control scheme and analyze its properties from the perspective of cybernetics [3]. It is worth noting that although considerable research has been devoted to solving conventional QM problems, studies aimed explicitly at the time-varying quadratic minimization (TVQM) problem are insufficient. Traditional solutions have serious lag errors when facing large-scale time-varying issues, resulting in inadequate solution accuracy and even the collapse of the solution system [6]. To break through the dilemma that traditional algorithms cannot effectively deal with time-varying problems, Zhang et al. design the original zeroing neural network (OZNN) model [7]. The OZNN model employs the derivative information of the time-varying problem to predict its evolution direction and continuously adjust the solution strategy of the solution system through a named evolution function [8].

Graph is powerful for representing various types of real-world data. The topology (edges' presence) and edges' features of a graph decides the message passing mechanism among vertices within the graph. While most existing approaches only manually define a single-value edge to describe the connectivity or strength of association between a pair of vertices, task-specific and crucial relationship cues may be disregarded by such manually defined topology and single-value edge features. In this paper, we propose the first general graph representation learning framework (called GRATIS) which can generate a strong graph representation with a task-specific topology and task-specific multi-dimensional edge features from any arbitrary input. To learn each edge's presence and multi-dimensional feature, our framework takes both of the corresponding vertices pair and their global contextual information into consideration, enabling the generated graph representation to have a globally optimal message passing mechanism for different down-stream tasks. The principled investigation results achieved for various graph analysis tasks on 11 graph and non-graph datasets show that our GRATIS can not only largely enhance pre-defined graphs but also learns a strong graph representation for non-graph data, with clear performance improvements on all tasks. In particular, the learned topology and multi-dimensional edge features provide complementary task-related cues for graph analysis tasks. Our framework is effective, robust and flexible, and is a plug-and-play module that can be combined with different backbones and Graph Neural Networks (GNNs) to generate a task-specific graph representation from various graph and non-graph data. Our code is made publicly available at https://github.com/SSYSteve/Learning-Graph-Representation-with-Task-specific-Topology-and-Multi-dimensional-Edge-Features.