Time-Varying Formation Tracking Control of Wheeled Mobile Robots With Region Constraint: A Generalized Udwadia-Kalaba Framework
Kang Yijie, Hao Yuqing, Wang Qingyun, Chen Guanrong
TL;DR
This work develops a generalized Udwadia-Kalaba framework to achieve time-varying formation tracking for networks of wheeled mobile robots with region constraints under directed, weighted connectivity having a leader-root spanning tree. By reformulating the tracking objective as an equality constraint and employing a diffeomorphism to handle region bounds, the authors derive both equality and inequality constraint forces, enabling safe, coordinated motion. Key contributions include extending formation tracking to dynamic, underactuated wheel models, integrating region safety via GUK, and providing stability conditions tied to graph eigenstructure. Numerical simulations demonstrate effective tracking and region safety, illustrating practical applicability in constrained environments. The approach offers a principled method to guarantee safety while maintaining cooperative formation in realistic multi-robot scenarios.
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.