Robust Noncolocated µ-Tip Rate Control of Flexible Robotic Manipulators with Uncertain Dynamics

• Published in: 2023 IEEE Conference on Control Technology and Applications (CCTA) pp. 327 - 332
• Main Authors: Halverson, Robert D., Kwan Cheah, Sze, Caverly, Ryan J.
• Format: Conference Proceeding
• Language: English
• Published: IEEE 16.08.2023
• Subjects: Computational modeling; Convex functions; Design methodology; Linear systems; Robustness; Systematics; Uncertainty
• ISSN: 2768-0770
• DOI: 10.1109/CCTA54093.2023.10253148

This paper introduces a systematic approach to determine the parameter µ ∗ that is central to the design of passivity-based µ-tip controllers for flexible robotic manipulators. The importance of this parameter lies in the fact that implementing µ-tip control with a value of µ larger than µ ∗ will lead to a passivity violation and potential instability of the closed-loop system. In the literature, µ ∗ has been solved for analytically when dealing with very simple systems, while intuition is relied upon for more realistic systems. The µ-tip formulations presented in this paper systematically solve for µ ∗ using convex optimization techniques. A robust formulation of the proposed method is presented, which can explicitly account for model uncertainty and nonlinearity through the use of integral quadratic constraints (IQCs). A numerical example of a single-link flexible-joint manipulator is included that demonstrates the capabilities of the proposed design methods and the importance of considering robustness in the computation of µ ∗ .