Time-Delay Based Controller for Independent Joint Control of Robot Manipulators

Resumen: A well-known strategy for the control of robot manipulators consists in independently controlling each joint. In this paper, we propose a class of time-delay based controllers under this scheme, which ensures practical stability of the tracking position error dynamics corresponding to each joint. In order to tune the controller, a simple methodology based on the feasibility of a Linear Matrix Inequality derived from a proposed Lyapunov-Krasovskii functional is provided. In contrast to classical control algorithms, the presented scheme does not require estimators nor velocity measures but only measures of position at the present and a given delayed time. Numerical simulations show the potential advantages of the proposed class of controllers when position measures are corrupted by noise.

¿Cómo citar?

Marco A. Gomez. Time-Delay Based Controller for Independent Joint Control of Robot Manipulators. Memorias del Congreso Nacional de Control Automático, pp. 27-32, 2021.

Palabras clave

control of robot manipulators; time-delay based controllers; time-delay systems

• Armstrong, B., Khatib, O., and Burdick, J. (1986). The explicit dynamic model and inertial parameters of the PUMA 560 arm. In Proceedings of the 1986 IEEE International Conference on Robotics and Automation, volume 3, 510–518. IEEE.
• Corke, P.I. and Armstrong-Helouvry, B. (1994). A search for consensus among model parameters reported for the PUMA 560 robot. In Proceedings of the 1994 IEEE International Conference on Robotics and Automation, 1608–1613. IEEE.
• Fridman, E. and Shaikhet, L. (2017). Stabilization by using artificial delays: An LMI approach. Automatica, 81, 429–437. Gomez, M.A., Cruz-Ancona, C.D., and Fridman, L. (2021). Lyapunov redesign for a class of uncertain systems with delays. Nonlinear Analysis: Hybrid Systems (Accepted).
• Gomez, M.A., Michiels, W., and Mondie, S. (2019). Design of delay-based output-feedback controllers optimizing a quadratic cost function via the delay Lyapunov matrix. Automatica, 107, 146–153.
• Kelly, R. and Santibáñez, V. (2003). Control de movimiento de robots manipuladores. Pearson educación.
• Lewis, F.L., Dawson, D.M., and Abdallah, C.T. (2003). Robot manipulator control: theory and practice. CRC Press.
• Niculescu, S.I. and Michiels, W. (2004). Stabilizing a chain of integrators using multiple delays. IEEE Transactions on Automatic Control, 49(5), 802–807.
• Niculescu, S.I. (2001). Delay effects on stability: a robust control approach, volume 269. Springer Science & Business Media.
• Ochoa-Ortega, G., Villafuerte-Segura, R., Ramirez-Neria, M., and Vite-Hernández, L. (2019). σ-stabilization of a flexible joint robotic arm via delayed controllers. Complexity, Article ID 7289689, 12 pages.
• Ramírez, A., Mondie, S., Garrido, R., and Sipahi, R. (2015). Design of proportional-integral-retarded (PIR) controllers for second-order LTI systems. IEEE Transactions on Automatic Control, 61(6), 1688–1693.
• Sipahi, R., Niculescu, S.I., Abdallah, C.T., Michiels, W., and Gu, K. (2011). Stability and stabilization of systems with time delay. IEEE Control Systems Magazine, 31(1), 38–65.
• Solomon, O. and Fridman, E. (2013). New stability conditions for systems with distributed delays. Automatica, 49(11), 3467–3475.
• Spong, M.W., Hutchinson, S., and Vidyasagar, M. (2006). Robot modeling and control. Wiley, 2nd edition.
• Suh, I. and Bien, Z. (1979). Proportional minus delay controller. IEEE Transactions on Automatic Control, 24(2), 370–372.
• Villafuerte, R., Mondie, S., and A., P. (2011). Practical stability of time-delay ssystem: LMI’s approach. European Journal of Control, 2011(2), 127–138.
• Villafuerte, R., Mondie, S., and Garrido, R. (2012). Tuning of proportional retarded controllers: theory and experiments. IEEE Transactions on Control Systems Technology, 21(3), 983–990.