T-S Fuzzy H∞ Tracking Control of Input Delayed Robotic Manipulators

Time delays are often encountered by practical control systems while they are acquiring, processing, communicating, and sending signals. Time delays may affect the system stability and degrade the control system performance if they are not properly dealt with. Taking the classical robot control problem as an example, the significant effect of time delay on the closed-loop system stability has been highlighted in the bilateral teleoperation, where the communication delay transmitted through a network medium has been received widespread attention and different approaches have been proposed to address this problem (Hokayem and Spong, 2006). In addition, examples like processing delays in visual systems and communication delay between different computers on a single humanoid robot are also main sources that may cause time delays in a robotic control system (Chopra, 2009), and the issue of time delay for robotic systems has been studied through the passivity property. For systems with time delays, both delay dependent and delay independent control strategies have been extensively studied in recent years, see for example (Xu and Lam, 2008) and references therein. For the control of nonlinear time delay systems, model based Takagi- Sugeno (T-S) fuzzy control (Tanaka and Wang, 2001; Feng, 2006; Lin et al., 2007) is regarded as one of the most effective approach because some of linear control theory can be applied directly. Conditions for designing such kinds of controllers are generally expressed as linear matrix inequalities (LMIs) which can be efficiently solved by using most available software like Matlab LMI Toolbox, or bilinear matrix inequalities (BMIs) which could be transferred to LMIs by using algorithms like iteration algorithm or cone complementary linearisation algorithm. From the theoretical point of view, one of the current focus on the control of time delay systems is to develop less conservative approaches so that the controller can stabilise the systems or can achieve the defined control performance under bigger time delay

PDC Control for Mobile Robot Formations with Virtual Reference Based on Separation-Bearing

This paper presents a development of leader-follower formation control using separation-bearing control (SBC) and Parallel Distribution Compensation (PDC) control. The formation control involves tracking of each desired trajectory by leader and follower robots. The follower trajectory is generated using SBC approach with respect to predefined trajectory of the leader. This design is used to improve formation control when initial error is given to leader. In order to maintain the formation and avoid internal collision, the error tracking of each robot must be kept near zero. Each robot is controlled by kinematic and dynamics controller which is designed using PDC and PID. The velocity reference for dynamic robots is limited. The simulation result shows the tracking errors for position and orientation with initial lateral error set at 0.5 m are less than 0.5 m and 1.2 rad which then converges to the desired value. Thus, the good trajectory formation tracking is achieved

Models, Methods, and Applications of Dynamics and Control in Engineering Sciences: State of the Art

Guest editor, numero speciale di Mathematical Problems in Engineerin

Supervision and fault tolerance for assistive robotics

In this Master Thesis, the supervision and control problem of service robots in unknown anthropic domains has been addressed from the Fault Detection and Diagnosis (FDD) framework, presenting a complete Fault-Tolerant scheme able to detect, isolate and compensate the effects of an exogenous force acting on a robotic manipulator. Therefore, a systematic approach has been presented, applied to the TIAGo head subsystem, to obtain a Takagi-Sugeno representation suitable for a Parallel Distributed Controller, with the main advantage of defining the complete behaviour of the system using only its representation at the operational limits. Additionally, the Robust Unknown Input Observer for Takagi-Sugeno Models has been implemented for an incomplete information model scenario, which allows decoupling the given estimation from the effect of exogenous faults, disregarding its behaviour nor eventuality. Finally, a characterization of the real robot actuators has been performed, in order to design the suitable mechanisms for their implementation into the complete Fault-Tolerant scheme

BIBO stabilisation of continuous time takagi sugeno systems under persistent perturbations and input saturation

[EN] This paper presents a novel approach to the design of fuzzy state feedback controllers for continuous-time non-linear systems with input saturation under persistent perturbations. It is assumed that all the states of the Takagi¿Sugeno (TS) fuzzy model representing a non-linear system are measurable. Such controllers achieve bounded input bounded output (BIBO) stabilisation in closed loop based on the computation of inescapable ellipsoids. These ellipsoids are computed with linear matrix inequalities (LMIs) that guarantee stabilisation with input saturation and persistent perturbations. In particular, two kinds of inescapable ellipsoids are computed when solving a multiobjective optimization problem: the maximum volume inescapable ellipsoids contained inside the validity domain of the TS fuzzy model and the smallest inescapable ellipsoids which guarantee a minimum *-norm (upper bound of the 1-norm) of the perturbed system. For every initial point contained in the maximum volume ellipsoid, the closed loop will enter the minimum *-norm ellipsoid after a finite time, and it will remain inside afterwards. Consequently, the designed controllers have a large domain of validity and ensure a small value for the 1-norm of closed loop.The authors wish to thank the Editor-in-Chief and the anonymous reviewers for their valuable comments and suggestions. This work has been funded by Ministerio de Economia y Competitividad (Spain) through the research project DPI2015-71443-R and by Generalitat Valenciana (Valencia, Spain) through the research project GV/2017/029.Salcedo-Romero-De-Ávila, J.; Martínez Iranzo, MA.; Garcia-Nieto, S.; Hilario Caballero, A. (2018). BIBO stabilisation of continuous time takagi sugeno systems under persistent perturbations and input saturation. International Journal of Applied Mathematics and Computer Science (Online). 28(3):457-472. https://doi.org/10.2478/amcs-2018-0035S45747228

T-S Fuzzy Bibo Stabilisation of Non-Linear Systems Under Persistent Perturbations Using Fuzzy Lyapunov Functions and Non-PDC Control Laws

[EN] This paper develops an innovative approach for designing non-parallel distributed fuzzy controllers for continuous-time non-linear systems under persistent perturbations. Non-linear systems are represented using Takagi-Sugeno fuzzy models. These non-PDC controllers guarantee bounded input bounded output stabilisation in closed-loop throughout the computation of generalised inescapable ellipsoids. These controllers are computed with linear matrix inequalities using fuzzy Lyapunov functions and integral delayed Lyapunov functions. LMI conditions developed in this paper provide non-PDC controllers with a minimum *-norm (upper bound of the 1-norm) for the T-S fuzzy system under persistent perturbations. The results presented in this paper can be classified into two categories: local methods based on fuzzy Lyapunov functions with guaranteed bounds on the first derivatives of membership functions and global methods based on integral-delayed Lyapunov functions which are independent of the first derivatives of membership functions. The benefits of the proposed results are shown through some illustrative examples.This work has been funded by Ministerio de Economia y Competitividad, Spain (research project RTI2018-096904-B-I00) and Conselleria de Educacion, Cultura y Deporte-Generalitat Valenciana, Spain (research project AICO/2019/055).Salcedo-Romero-De-Ávila, J.; Martínez Iranzo, MA.; Garcia-Nieto, S.; Hilario Caballero, A. (2020). T-S Fuzzy Bibo Stabilisation of Non-Linear Systems Under Persistent Perturbations Using Fuzzy Lyapunov Functions and Non-PDC Control Laws. International Journal of Applied Mathematics and Computer Science (Online). 30(3):529-550. https://doi.org/10.34768/amcs-2020-0039S52955030