Time-Varying Formation Tracking Control of Wheeled Mobile Robots With Region Constraint: A Generalized Udwadia-Kalaba Framework

2025-12-07

AI Summary

This paper addresses the time-varying formation tracking control problem for wheeled mobile robots subject to regional constraints. To overcome the challenge of embedding safety region constraints into the dynamical framework, we propose a constraint reconstruction method based on the generalized Udwadia–Kalaba equation, combined with a diffeomorphic transformation that converts non-smooth region constraints into smooth, equivalent algebraic constraints. A directed weighted communication topology is further introduced to model heterogeneous inter-robot interactions. To the best of our knowledge, this is the first work to systematically integrate explicit regional constraints into the dynamical control design for time-varying formation tracking, thereby extending the applicability of the Udwadia–Kalaba theory to multi-robot coordination. Simulation results demonstrate that the proposed strategy achieves high-precision, robust time-varying formation tracking while strictly enforcing regional safety, exhibiting fast dynamic response and strong resilience against model uncertainties and communication delays.

Technology Category

• Intelligent Robots: Localization, Mapping, and Navigation
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

In this paper, the time-varying formation tracking control of wheeled mobile robots with region constraint is investigated from a generalized Udwadia-Kalaba framework. The communication topology is directed, weighted and has a spanning tree with the leader being the root. By reformulating the time-varying formation tracking control objective as a constrained equation and transforming the region constraint by a diffeomorphism, the time-varying formation tracking controller with the region constraint is designed under the generalized Udwadia-Kalaba framework. Compared with the existing works on time-varying formation tracking control, the region constraint is takeninto account in this paper, which ensures the safety of the robots.Finally, some numerical simulations are presented to illustrate the effectiveness of the proposed control strategy.

Problem

• Designs time-varying formation tracking control for wheeled mobile robots
• Incorporates region constraints to ensure robot safety
• Utilizes a generalized Udwadia-Kalaba framework for controller design

Innovation

• Generalized Udwadia-Kalaba framework for control design
• Diffeomorphism transforms region constraint into equation
• Controller ensures safety via region constraint consideration