Safe consensus tracking with guaranteed full state and input constraints: A control barrier function based approach

• Published in: IEEE transactions on automatic control Vol. 68; no. 12; pp. 1 - 8
• Main Authors: Fu, Junjie, Wen, Guanghui, Yu, Xinghuo
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.12.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: control barrier function; input saturation; Liapunov functions; Lyapunov methods; multi-agent system; Multi-agent systems; Multiagent systems; Nonlinear systems; Quadratic programming; Safe consensus tracking; Safety; Stability analysis; state constraint; Target tracking; Tracking problem; Trajectory; Upper bound
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2023.3283697

In this paper, we consider the safe consensus tracking problem for uncertain second-order nonlinear multi-agent systems subject to both position, velocity and input constraints. The agents are required to cooperatively track a desired leader's trajectory while always satisfying their local state and input constraints. Therefore, conflicting objectives may exist for an agent when the desired trajectory violates its local constraints. We propose to solve this problem using a control barrier function based (CBF-based) approach. The cooperative tracking objective is encoded by a novel control Lyapunov function based (CLF-based) condition while the state and input constraints are handled by CBF-based constraints. For the relative degree two position constraint, two classes of CBF-based conditions are proposed based on high-order CBFs and a modified CBF design, respectively. It is proven that, with the modified CBF, there always exist feasible control inputs which satisfy all the CBF-based constraints. Then, unified quadratic programming (QP) based controllers are formulated and the performances are analyzed. Simulation examples are provided to verify the obtained results.