Solving the problem of stabilizing a given position and programmed motion of an anthropomorphic robotic arm
Received: 2026-10-13
Published: 2026-09-30
Abstract
stabilizing a given position and a programmed motion are solved under the condition that only the joint angles are measured. For position
stabilization, a nonlinear PI controller with feedback on the signs of half the error angles is proposed. Using Lyapunov functions, explicit
conditions on the gains and the damping coefficient are obtained under which the position is stabilized for any initial deviations. For
piecewise-constant sampled-data control, a bound on the admissible sampling period is found. For tracking a programmed motion, a
control law with a dynamic filter replacing velocity measurement is constructed. It is proved that, under the conditions found, the tracking
error tends to zero modulo 2???? for any initial conditions. The results are confirmed by numerical simulation.
Keywords
List of references
-
Kelly R, Santib´a˜nez V, Loria A. Control of Robot Manipulators in Joint Space. Springer; 2005.
-
Yurevich EI. Osnovy robototehniki: uchebnoe posobie [Fundamentals of robotics: a textbook]. 4th ed. BHV-Peterburg; 2018. (In Russian).
-
Alonge F, D’Ippolito F, Raimondi FM. An adaptive control law for robotic manipulators without velocity feedback. Control Eng Pract. 2003;11(7):999–1005. https://doi.org/10.1016/S0967-0661(02)00195-8.
-
Moreno-Valenzuela J, Camarillo K, Campa R, Santib´a˜nez V. A practical PID regulator with bounded torques for robot manipulators. Int J Control Autom Syst. 2010;8(3):544–555. https://doi.org/10.1007/s12555-010-0307-4.
-
Yarza A, Santib´a˜nez V, Moreno-Valenzuela J. An adaptive output feedback motion tracking controller for robot manipulators: uniform global asymptotic stability and experimentation. Int J Appl Math Comput Sci. 2013;23(3):599–611. https://doi.org/10.2478/amcs-2013-0045.
-
Kelly R. A simple set-point robot controller by using only position measurements. In: Proceedings of the 12th IFAC World Congress;
-
1993:173–176. 18–23 July 1993. https://doi.org/10.1016/S1474-6670(17)48783-0.
-
Berghuis H, Nijmeijer H. A passivity approach to controller-observer design for robots. IEEE Trans Robot Autom. 1993;9(6):740–754.
-
Zhang H, Zhao Y, Wang Y, Liu L. Adaptive neural network control of robotic manipulators with input constraints and without velocity
-
measurements. IET Control Theory Appl. 2024;18(10):1232–1247. https://doi.org/10.1049/cth2.12660.
-
Noghreian E, Koofigar HR. Robust tracking control of robot manipulators with friction and variable loads without velocity measurement: a switched control strategy. Proc Inst Mech Eng Part I J Syst Control Eng. 2021;235(4):532–539. https://doi.org/10.1177/0959651820947944.
-
Andreev AS, Peregudova OA. Trajectory tracking control for robot manipulators using only position measurements. Int J Control.
-
2019;92(7):1490–1496. https://doi.org/10.1080/00207179.2017.1397755.
-
Andreev A, Peregudova O, Sutyrkina K. Trajectory tracking control of robot manipulators with revolute joints using only position
-
measurements. In: Proceedings of the 18th International Conference on Mechatronics – Mechatronika (ME). IEEE; 2018:1–6.
-
Peregudova O. Robust trajectory tracking control for robot manipulators without velocity measurements. In: Proceedings of the 14th International Conference Stability and Oscillations of Nonlinear Control Systems (Pyatnitskiy’s Conference). IEEE; 2018. https://doi.org/10.1109/STAB.2018.8408385.
-
Akhmatov A, Buranov J, Khusanov J, Peregudova O. On semi-global output position feedback trajectory tracking control of a multi-link
-
revolute joined robotic manipulator. In: Proceedings of the 25th International Conference on System Theory, Control and Computing
-
(ICSTCC). IEEE; 2021:290–295.
-
Akhmatov AA. Stabilizaciˆa ustanovivˇsihsˆa dviˇzenij mehaniˇceskih sistem s cikliˇceskimi koordinatami diskretnym upravleniem bez
-
izmereniˆa skorostej [Stabilization of steady motions of mechanical systems with cyclic coordinates by sampled-data control without
-
velocity measurements]. Ilm sarchashmalari ilmiy-nazariy, metodik jurnal. 2025;(10.1):39–43. (In Russian).
-
Akhmatov AA. Diskretnaˆa stabilizaciˆa mehaniˇceskih sistem bez izmereniˆa skorostej [Sampled-data stabilization of mechanical systems
-
without velocity measurements]. Ilm sarchashmalari ilmiy-nazariy, metodik jurnal. 2026;(11):45–49. (In Russian).
-
Chang L, Fu C, Zhang H. Global sampled-data output feedback stabilization for nonlinear systems via intermittent hold. IEEE/CAA J Autom Sin. 2025;12(8):1586–1593. https://doi.org/10.1109/JAS.2024.125019.
-
Khalil HK. Nonlinear Systems. 3rd ed. Prentice Hall; 2002.
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