Min–Max Optimal Control of Robot Manipulators Affected by Sensor Faults
This paper is concerned with the control law synthesis for robot manipulators, which guarantees that the effect of the sensor faults is kept under a permissible level, and ensures the stability of the closed-loop system. Based on Lyapunov’s stability analysis, the conditions that enable the applicat...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-02-01
|
| Series: | Sensors |
| Subjects: | |
| Online Access: | https://www.mdpi.com/1424-8220/23/4/1952 |
| _version_ | 1827755529138601984 |
|---|---|
| author | Vladimir Milić Josip Kasać Marin Lukas |
| author_facet | Vladimir Milić Josip Kasać Marin Lukas |
| author_sort | Vladimir Milić |
| collection | DOAJ |
| description | This paper is concerned with the control law synthesis for robot manipulators, which guarantees that the effect of the sensor faults is kept under a permissible level, and ensures the stability of the closed-loop system. Based on Lyapunov’s stability analysis, the conditions that enable the application of the simple bisection method in the optimization procedure were derived. The control law, with certain properties that make the construction of the Lyapunov function much easier—and, thus, the determination of stability conditions—was considered. Furthermore, the optimization problem was formulated as a class of problem in which minimization and maximization of the same performance criterion were simultaneously carried out. The algorithm proposed to solve the related zero-sum differential game was based on Newton’s method with recursive matrix relations, in which the first- and second-order derivatives of the objective function are calculated using hyper-dual numbers. The results of this paper were evaluated in simulation on a robot manipulator with three degrees of freedom. |
| first_indexed | 2024-03-11T08:10:38Z |
| format | Article |
| id | doaj.art-38ad3aaa73c942bebc4fdbee89e62e04 |
| institution | Directory Open Access Journal |
| issn | 1424-8220 |
| language | English |
| last_indexed | 2024-03-11T08:10:38Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Sensors |
| spelling | doaj.art-38ad3aaa73c942bebc4fdbee89e62e042023-11-16T23:08:23ZengMDPI AGSensors1424-82202023-02-01234195210.3390/s23041952Min–Max Optimal Control of Robot Manipulators Affected by Sensor FaultsVladimir Milić0Josip Kasać1Marin Lukas2Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, HR-10000 Zagreb, CroatiaFaculty of Mechanical Engineering and Naval Architecture, University of Zagreb, HR-10000 Zagreb, CroatiaFaculty of Mechanical Engineering and Naval Architecture, University of Zagreb, HR-10000 Zagreb, CroatiaThis paper is concerned with the control law synthesis for robot manipulators, which guarantees that the effect of the sensor faults is kept under a permissible level, and ensures the stability of the closed-loop system. Based on Lyapunov’s stability analysis, the conditions that enable the application of the simple bisection method in the optimization procedure were derived. The control law, with certain properties that make the construction of the Lyapunov function much easier—and, thus, the determination of stability conditions—was considered. Furthermore, the optimization problem was formulated as a class of problem in which minimization and maximization of the same performance criterion were simultaneously carried out. The algorithm proposed to solve the related zero-sum differential game was based on Newton’s method with recursive matrix relations, in which the first- and second-order derivatives of the objective function are calculated using hyper-dual numbers. The results of this paper were evaluated in simulation on a robot manipulator with three degrees of freedom.https://www.mdpi.com/1424-8220/23/4/1952robot manipulatorssensor faultsℒ<sub>2</sub>-gainmin–max optimizationNewton-like algorithm |
| spellingShingle | Vladimir Milić Josip Kasać Marin Lukas Min–Max Optimal Control of Robot Manipulators Affected by Sensor Faults Sensors robot manipulators sensor faults ℒ<sub>2</sub>-gain min–max optimization Newton-like algorithm |
| title | Min–Max Optimal Control of Robot Manipulators Affected by Sensor Faults |
| title_full | Min–Max Optimal Control of Robot Manipulators Affected by Sensor Faults |
| title_fullStr | Min–Max Optimal Control of Robot Manipulators Affected by Sensor Faults |
| title_full_unstemmed | Min–Max Optimal Control of Robot Manipulators Affected by Sensor Faults |
| title_short | Min–Max Optimal Control of Robot Manipulators Affected by Sensor Faults |
| title_sort | min max optimal control of robot manipulators affected by sensor faults |
| topic | robot manipulators sensor faults ℒ<sub>2</sub>-gain min–max optimization Newton-like algorithm |
| url | https://www.mdpi.com/1424-8220/23/4/1952 |
| work_keys_str_mv | AT vladimirmilic minmaxoptimalcontrolofrobotmanipulatorsaffectedbysensorfaults AT josipkasac minmaxoptimalcontrolofrobotmanipulatorsaffectedbysensorfaults AT marinlukas minmaxoptimalcontrolofrobotmanipulatorsaffectedbysensorfaults |