Optimal trajectory control for a two‐link rigid‐flexible manipulator with ODE‐PDE model

Abstract

Summary In this paper, the optimal trajectory control problem for a two‐link rigid‐flexible manipulator is considered. Since the two‐link rigid‐flexible system is a distributed system, an ordinary differential equation and partial differential equation (ODE‐PDE) dynamic model of the manipulator is established by Hamilton's principle. Based on the ODE‐PDE model, an optimal trajectory controller is proposed in this paper, which includes 2 stages. In the first stage, the optimal trajectory is created by using the differential evolution algorithm. Energy consumption and deflection of the flexible link are chosen as performance indexes. Cubic spline interpolation is applied to obtain the continuous trajectory. In the second stage, the aim is to regulate 2 joints to follow the optimal trajectory and simultaneously suppress vibration of the flexible link. To achieve it, boundary control laws are designed and the stability analysis is given. In simulations, the effectiveness of the optimal controller is verified by MATLAB.

Concurrent Design of a 2 Dof Five-Bar Parallel Robot a Hybrid Design of Rigid and Flexible Links

“…Currently, there is no known method to ensure global optimum for nonlinear problems, thus meta-heuristics have been used to solve these problems, [38]. Some of the advantages of evolutionary algorithms are that they do not require prior knowledge about the problem to be solved, they operate on a population which prevents the search from being optimally local, [39], they can be combined with other search techniques, etc. Differential Evolution [40] (DE/rand/1/bin) 2 was developed by Rainer Storn and Kenneth V. Price as an evolutionary algorithm for global optimization whose pseudocode is shown in Algorithm 1, where g represents the current generation, N P individuals or solution vectors are created randomly at first if nothing is known previously of the problem.…”

Review on Modeling and Control of Flexible Link Manipulators

“…Zhang and Liu (2012c) proposed the optimal trajectory boundary control of the two-link flexible manipulator based on the PDE model. Cao and Liu (2018b) studied the optimal trajectory control problem for the trajectory tracking and vibration suppression of a two-link rigid-flexible manipulator based on the ODE-PDE model of the system.…”

Vibration control for a flexible single‐link manipulator and its application

“…An active vibration control is presented to guarantee the vibration reduction, and achieve the exponential stability for a flexible moving beam with a translating tension in [27]. Boundary vibration control is proposed to reduce the oscillation of the beam structure and to ensure the flexible manipulator tracking the desired trajectory for a rigid-flexible manipulator in [28]. Besides, some advanced boundary control strategies are developed to address the oscillation reduction for the flexible beam-like structures, such as sliding-mode control [29], fuzzy logic control [30,31], robust control [32], resonant control [33], force control [34], iterative learning control [35], and so on.…”

“…It has been commonly accepted that control design for the flexible system is not a trivial task, especially when it involves coupling problems. In previous works [9,28,34,36], the authors focus on the oscillation reduction of the beam-like structures, and propose effective control laws to reduce the deflection of beams. However, these designed controllers are designed at the free end of beam, whose implementation is anti-collocated with common actuators.…”