Robust Control of Collaborative Manipulators - Flexible Object System

Abstract

In many manufacturing and automobile industries, flexible components need to be positioned with the help of coordinated operations of manipulators. This paper deals with the robust design of a control system for two planar rigid manipulators moving a flexible object in the prescribed trajectory while suppressing the vibration of the flexible object. Dynamic equations of the flexible object are derived using the Hamiltonian principle, which is expressed as a partial differential equation (PDE) with appropriate boundary conditions. Then, a combined dynamics is formulated by combining the manipulators and object dynamics without any approximation. The resulting dynamics are thus described by the PDEs, having rigid as well as flexible parameters coupled together. This paper attempts to develop a robust control scheme without approximating the PDE in order to avoid measurements of flexible coordinates and their time derivatives. For this purpose, the two subsystems, namely slow and fast subsystems, are identified by using the singular perturbation technique. Specific robust controllers for both the subsystems are developed. In general, usage of the singular perturbation technique necessitates exponential stability of both subsystems, which is evaluated by satisfying Tikhnov's theorem. Hence, the exponential stability analysis is performed for both subsystems. Focusing on two three-link manipulators holding a flexible beam, simulations are performed and simulation results demonstrate the versatility of the proposed robust composite control scheme.

Variable Structure Control for Space Robots Based on Neural Networks

“…Then expression (7) is redesigned as (17) where the 1 τ is the same as the 1 τ of (4). The NN τ is the same as the NN τ of expression (9).…”

“…Intelligent control theory is an advanced stage of control development: a method of human learning and adaptive capacity simulation; a senior information control system, it includes expert systems, fuzzy control and neural network controls [11][12][13][14][15][16][17][18]. Xie Jian [19] proposed a neural network adjustment control strategy for the uncertain space robot, which approximated nonlinear functions and uncertain upper bounds with an RBF neural network.…”

Cooperative control of large flexible space structure by two planar robots

“…Because of its flexibility, elastic vibrations that are continuously distributed in the structure are generated, so the dynamics of the system in which the space robot grasps the flexible structure is constructed by partial differential equation (PDE) and ordinary differential equation (ODE), that is the model is described as a PDE-ODE hybrid infinite-dimensional model. However, the previous studies on transportation of space structure with robots do not consider the flexibility of the structure [9][10][11] or truncate to a finite-dimensional model even if it considered [12][13][14][15]. Finite-dimensional approximated model is derived by neglecting higher order vibration modes.…”