Stability Analysis of Underconstrained Cable-Driven Parallel Robots

Marco Carricato; Jean-Pierre Merlet

doi:10.1109/tro.2012.2217795

An approach on stability analysis of cable-driven parallel robots considering cable mass

AIP Advances ◽

10.1063/5.0047101 ◽

2021 ◽

Vol 11 (5) ◽

pp. 055014

Author(s):

Huiling Wei ◽

Yuanying Qiu ◽

Lufeng Luo ◽

Qinghua Lu

Keyword(s):

Stability Analysis ◽

Parallel Robots

Download Full-text

A stable proportional–proportional integral tracking controller with self-organizing fuzzy-tuned gains for parallel robots

International Journal of Advanced Robotic Systems ◽

10.1177/1729881418819956 ◽

2019 ◽

Vol 16 (1) ◽

pp. 172988141881995

Author(s):

Francisco G Salas ◽

Jorge Orrante-Sakanassi ◽

Raymundo Juarez-del-Toro ◽

Ricardo P Parada

Keyword(s):

Stability Analysis ◽

Performance Index ◽

Closed Loop ◽

Tracking Error ◽

Parallel Robots ◽

Control Loop ◽

Closed Loop System ◽

Proportional Integral ◽

The Stability ◽

Self Organizing

Parallel robots are nowadays used in many high-precision tasks. The dynamics of parallel robots is naturally more complex than the dynamics of serial robots, due to their kinematic structure composed by closed chains. In addition, their current high-precision applications demand the innovation of more effective and robust motion controllers. This has motivated researchers to propose novel and more robust controllers that can perform the motion control tasks of these manipulators. In this article, a two-loop proportional–proportional integral controller for trajectory tracking control of parallel robots is proposed. In the proposed scheme, the gains of the proportional integral control loop are constant, while the gains of the proportional control loop are online tuned by a novel self-organizing fuzzy algorithm. This algorithm generates a performance index of the overall controller based on the past and the current tracking error. Such a performance index is then used to modify some parameters of fuzzy membership functions, which are part of a fuzzy inference engine. This fuzzy engine receives, in turn, the tracking error as input and produces an increment (positive or negative) to the current gain. The stability analysis of the closed-loop system of the proposed controller applied to the model of a parallel manipulator is carried on, which results in the uniform ultimate boundedness of the solutions of the closed-loop system. Moreover, the stability analysis developed for proportional–proportional integral variable gains schemes is valid not only when using a self-organizing fuzzy algorithm for gain-tuning but also with other gain-tuning algorithms, only providing that the produced gains meet the criterion for boundedness of the solutions. Furthermore, the superior performance of the proposed controller is validated by numerical simulations of its application to the model of a planar three-degree-of-freedom parallel robot. The results of numerical simulations of a proportional integral derivative controller and a fuzzy-tuned proportional derivative controller applied to the model of the robot are also obtained for comparison purposes.

Download Full-text

Robust Visual PID Control of Planar Parallel Robots Under Constant Disturbances

Volume 4A: Dynamics, Vibration and Control ◽

10.1115/imece2013-63329 ◽

2013 ◽

Cited By ~ 1

Author(s):

Miguel A. Trujano ◽

Ruben Garrido

Keyword(s):

Stability Analysis ◽

Pid Control ◽

Visual Servoing ◽

Parallel Robot ◽

Parallel Robots ◽

End Effector ◽

Pid Algorithm ◽

Control Scheme ◽

The Stability ◽

Invariance Theorem

This work presents an image-based visual servoing scheme applied to planar parallel robots. A PID algorithm regulates the robot end-effector position, and rejects constant disturbances perturbing the active robot joints. Instead using the La Salle invariance theorem, the stability analysis provided here relies on a strict Lyapunov function. Experiments on a redundant planar parallel robot validate the proposed control scheme.

Download Full-text