Udwadia–Kalaba constraint-based tracking control for artificial swarm mechanical systems: dynamic approach

• Published in: Nonlinear dynamics Vol. 100; no. 3; pp. 2381 - 2399
• Main Authors: Zhao, Ruiying, Li, Meng, Niu, Qian, Chen, Ye-Hwa
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.05.2020; Springer Nature B.V
• Subjects: Automotive Engineering; Classical Mechanics; Computer simulation; Constraint modelling; Control; Control systems; Dynamic control; Dynamical Systems; Engineering; Kinematics; Mechanical Engineering; Mechanical systems; Moving targets; Original Paper; Tracking; Tracking control; Vibration; Udwadia–Kalaba constraints; Artificial swarm; Swarm tracking; Mechanical systems
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-020-05613-7

A novel swarm tracking control for artificial swarm mechanical systems consisting of multiple mechanical agents is proposed. In this paper, the agents could not only perform some biological swarm behaviors, such as the repulsion and attraction between agents, but also track the moving target or desired trajectory together. Based on the artificial potential functions, the kinematic modeling of each agent is constructed. The kinematic performance of the swarm system is analyzed, which includes convergence, tracking, aggregation and formation. Inspired by Udwadia–Kalaba constraints, the kinematic modeling of the swarm system is treated as servo constraints and formulated in the second-order form. With the second-order constraints, the explicit servo constraint forces are derived. In virtue of the constraint forces in the closed form, we creatively design a dynamic control for each agent which guarantees the controlled swarm system to obey the required motion. The proposed control scheme is proved by a series of theorems and illustrated by the simulation of multiple nonholonomic mobile robots.