Configuring tasks as constraints for coordinated mechanical systems: A Udwadia–Kalaba theory based adaptive robust control

• Published in: Journal of the Franklin Institute Vol. 357; no. 6; pp. 3387 - 3418
• Main Authors: Sun, Hao, Chen, Ye-Hwa, Xiong, Yangshou, Zhao, Han
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.04.2020; Elsevier Science Ltd
• Subjects: Adaptive control; Control; Control tasks; Mechanical properties; Mechanical systems; Robot arms; Robotics; Robust control; Servocontrol; Subsystems; Uncertainty
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2019.12.030

•Uncertain coordinated mechanical systems are studied to follow a set of prescribed constraints.•A leakage-type and fraction-style adaptive robust control is designed.•Uniform boundedness and uniform ultimate boundedness can be guaranteed.•The proposed control approach is demonstrated by coordinated robotic manipulators. In this paper, we deal with the control problem of coordinated mechanical systems by configuring the control tasks as servo constraints. For the nominal systems, a Udwadia–Kalaba control scheme is implemented. In the presence of system uncertainties and initial condition deviations from the servo constraints, an adaptive robust control scheme is designed and proved to be able to guarantee the deterministic performance: uniform boundedness and uniform ultimate boundedness. The leakage-type and performance-based adaptive law contains two specific terms, with the first term to compensate the uncertainty and the second term to prevent the control magnitude to be too excessive. The developed scheme is able to deal with both holonomic constraints and nonholonomic constraints, which makes it have a wide range of applications. An example of coordinated robotic manipulators with two individual subsystems is given to demonstrate effectiveness of the proposed adaptive robust control methodology.