Laurent Vermeiren

LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno's form

This paper presents the stabilization analysis for a class of nonlinear systems that are represented by a Takagi and Sugeno (TS) discrete fuzzy model (Takagi and Sugeno IEEE Trans. Systems Man Cybern. 15(1)(1985)116). The main result given here concerns their stabilization using new control laws and new nonquadratic Lyapunov functions. New relaxed conditions and linear matrix inequality-based design are proposed that allow outperforming previous results found in the literature. Two examples are also provided to demonstrate the efficiency of the approaches.

An Efficient Lyapunov Function for Discrete T–S Models: Observer Design

This paper deals with the design of a new observer synthesis for discrete Takagi-Sugeno (T-S) fuzzy models. It is well established that quadratic synthesis for discrete T-S models and/or linear parameter-varying systems can be outperformed easily via nonquadratic syntheses. Several Lyapunov functions can be used. Nevertheless, this paper shows that with a “small” change in the initial Lyapunov function, a “better” (in the sense of solutions to the linear matrix inequality constraints problem) Lyapunov function can be reached. This one can introduce very important improvements.

Control laws for Takagi—Sugeno fuzzy models

Abstract This work presents control laws for fuzzy models of Takagi–Sugeno (TS) (Sugeno and Kang, Fuzzy Sets and Systems 28 (1988) 15–33, Takagi and Sugeno, IEEE Trans. Systems Man Cybernet. 15(1) (1985) 116–132). These laws are not directly put in the classical form called PDC for parallel distributed compensation (Wang et al., IEEE Trans. Fuzzy Systems 4(1) (1996) 14–23). On a particular family of TS fuzzy models the approach allows to reduce the conservatism of results found in the literature (Tanaka et al., IEEE Trans. Fuzzy Systems 6(2) (1998) 1–16). This approach utilizes the state-space representation. According to that remark, observers are also considered and a separation principle is also given. Though results are provided mainly for the continuous case, they are also provided for the discrete case. An example in both cases illustrates the results obtained.

Motion control of planar parallel robot using the fuzzy descriptor system approach.

This work presents the control of a two-degree of freedom parallel robot manipulator. A quasi-LPV approach, through the so-called TS fuzzy model and LMI constraints problems is used. Moreover, in this context a way to derive interesting control laws is to keep the descriptor form of the mechanical system. Therefore, new LMI problems have to be defined that helps to reduce the conservatism of the usual results. Some relaxations are also proposed to leave the pure quadratic stability/stabilization framework. A comparison study between the classical control strategies from robotics and the control design using TS fuzzy descriptor models is carried out to show the interest of the proposed approach.

Using the redundant inverse kinematics system for collision avoidance

The present paper relates to the operation of robotic systems to avoid obstacles while positioning end-effectors. A new strategy to on-line collision-avoidance of the redundant robots with obstacles is presented. The strategy allows the use of redundant degrees of freedom such that a manipulator can avoid obstacles while tracking the desired end-effectors trajectory. It is supposed that the obstacles in the workspace of the manipulator are static. The strategy is based on the redundant inverse kinematics and leads to the favorable use of the abilities of redundant robots to avoid the collisions with obstacles. This strategy has the advantage that the configuration of the manipulator can be influenced by further requirements such as joint limits, etc. The effectiveness of the proposed strategy is discussed by theoretical considerations and illustrated by simulation of the motion of the four-joint planar manipulators between symmetric obstacles. It is shown that the proposed collision-free strategy while tracking the end-effector trajectory is efficient and practical.

Compensation and division control law for fuzzy models

Deals with the stability and stabilization of Takagi-Sugeno fuzzy models by the means of a special type of control law, called the compensation and division for fuzzy models. In order to prove the stability results, we use a Lyapunov approach. The whole approach can be put in the form of a list of LMIs that can be conveniently computed. We show that the CDF we get is less conservative than previous control laws.

Design and implementation of a robust fuzzy controller for a rotary inverted pendulum using the Takagi-Sugeno descriptor representation

The rotary inverted pendulum (RIP) is an under-actuated mechanical system. Because of its nonlinear behavior, the RIP is widely used as a benchmark in control theory to illustrate and validate new ideas in nonlinear and linear control. This paper presents a robust Takagi-Sugeno (T-S) fuzzy descriptor approach for designing a stabilizing controller for the RIP with real-time implementation. It is shown in this paper how the modeling of the physical system on descriptor T-S form with a reduced number of rules possible can lead to a simplified controller that is practically implementable. Relaxed linear matrix inequality-based stability conditions for the non quadratic case are given. Experimental results illustrate the effectiveness of the proposed approach.

Optimal motions planning for a GOUGH parallel robot

This article deals with the problem of planning optimal trajectories for a GOUGH parallel robot. The planning process consists of searching for a motion ensuring the accomplishment of the assigned task, minimizing a cost function and satisfying various constraints inherent to the robot kinematics and dynamics. This problem is treated via (i) an adequate parameterization of the operational coordinates of the mobile platform and (ii) the use of the sequential quadratic programming method for solving the resulting nonlinear optimization problem. The proposed approach is applied to tasks involving either point-to-point motions or motions along specified paths.

Real-time control of a force feedback haptic interface via EtherCAT fieldbus

This paper is to present a technological solution for implementing a force feedback haptic interface in the context of virtual reality interaction applications. The real-time haptic algorithms are implemented in TwinCAT runtime environment to control drivers via EtherCAT fieldbus. A 3-dimensional visualization model for the virtual reality interaction is developed through Virtual Reality Toolbox in Matlab/Simulink and interconnected with TwinCAT software through the Automation Device Specification communication protocol. The using of Matlab/Simulink with model-based programming method instead of the C++ programming language allows researchers in haptic domain to focus more on the control engineering issues than programming skills. Some experimental tests and verification of the haptic algorithms with visualization model are presented.

Control of Haptic Systems with Time-Varying Delay: A Novel Approach.

Abstract This paper addresses the stable implementation of high stiffness interactions of objects in the virtual environment. The virtual wall is modeled as a mechanical system including a linear spring characterized by a virtual stiffness and a damper with a virtual damping in parallel. A novel approach for improving the stability of discrete-time haptic systems in the case of time-varying delay is proposed by using an augmented state observer instead of the traditional backward finite differentiator. Based on Lyapunovs stability theory, the delay-dependent asymptotic stability condition expressed in terms of LMI for choosing the virtual-wall parameters is presented. The numerical simulation results in the case of the PHANTOM 1.0 haptic devices are included in order to prove the effectiveness of the proposed method.