Antoine Dequidt

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.

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.

Static output feedback design for a class of constrained Takagi–Sugeno fuzzy systems

Abstract This paper addresses the static output feedback (SOF) control problem of Takagi–Sugeno fuzzy systems subject to both control input and state constraints. A new parameter-dependent sector condition is proposed to deal with the input saturation in SOF control context. Based on a judicious use of Finsler’s lemma in fuzzy Lyapunov control framework, new design conditions guaranteeing the existence of a stabilizing controller are recast as an LMI-based optimization with additional slack variables. These extra variables offer more flexibility to reduce the design conservatism. In particular, the proposed method requires neither special constraints on the state-space system matrices nor linear matrix equalities, which are hard to be satisfied. Several numerical examples are given to demonstrate the interests of the new control method.

Improved LMI Conditions for Local Quadratic Stabilization of Constrained Takagi–Sugeno Fuzzy Systems

This paper is devoted to the control synthesis of constrained Takagi–Sugeno (T–S) fuzzy systems. These systems are subject to multiple constraints, namely actuator saturation, system state constraints, and also

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

{\mathcal {L}}_2

Design of stabilizing controller for uncertain nonlinear systems under input saturation

L2-disturbances. Using descriptor redundancy approach, new design conditions guaranteeing the existence of an input-saturated parallel distributed state feedback compensator are formulated as an LMI optimization problem with extra matrix decision variables. Differently from most of results dealing with the same local control context of constrained T–S systems, a generalized sector condition is used to handle effectively the nonlinearity of the control input. The use of a descriptor redundancy representation in conjunction with a sector condition for actuator saturation allows to reduce significantly the design conservatism while keeping a simple control structure. The effectiveness of the proposed method compared to many recent works is clearly demonstrated by means of numerical examples.