An Analysis of the Finite Element Method Applied on Dynamic Motion and Maximum Payload Planning of Flexible Manipulators

This paper is concerned with the dynamic motion analysis and the planning of maximum payload path of flexible manipulators. The finite element method was employed for dynamic modelling of the system and the motion of the model was considered as a combination of the rigid displacement and the elastic deformation of each link. Each manipulator link was treated as a finite number of elements and total displacement was derived by means of the shape functions of flexible elements. The problem of maximum payload trajectory planning was formulated as an optimal control problem. An indirect optimal control solution was employed. This method converts an optimality problem to a two-point boundary value problem. The effect of the number of elements on the dynamic motion, optimal trajectory and maximum allowable dynamic payload of the system was studied. Finally, a number of simulations were performed to verify the applicability and capability of the method for the nonlinear dynamic modelling and the control of flexible manipulators

Dynamic Load Carrying Capacity of Flexible Manipulators Using Finite Element Method and Pontryagin’s Minimum Principle

In this paper, finding Dynamic Load Carrying Capacity (DLCC) of flexible link manipulators in point to-point motion was formulated as an optimal control problem. The finite element method was employed for modelling and deriving the dynamic equations of the system. The study employed indirect solution of optimal control for system motion planning. Due to offline nature of the method, many difficulties such system nonlinearities and all types of constraints can be catered for and implemented easily. The application of Pontryagin’s minimum principle to this problem was resulted in a standard two-point boundary value problem (TPBVP), solved numerically. Then, the formulation was developed to find the maximum payload and corresponding optimal path. The main advantage of the proposed method is that the various optimal trajectories can be obtained with different characteristics and different maximum payloads. Therefore, the designer can select a suitable path among the numerous optimal paths. In order to verify the effectiveness of the method, a simulation study considering a two-link flexible manipulator was presented in details

TRACKING CONTROL OF AN UNDERACTUATED GANTRY CRANE USING AN OPTIMAL FEEDBACK CONTROLLER

Gantry cranes have attracted a great deal of interest in transportation and industrial applications. To increase the effectiveness of gantry cranes, the control of such systems is considered vital. This paper is concerned with tracking the control of an underactuated gantry crane using an optimal feedback controller. The optimal control strategy takes into account a performance index, including integrated time and absolute error criterion. To do this, nonlinear dynamic equations of the system are derived using Lagrange’s Principle. The minimum tracking error of the trolley and the minimum oscillation of the hoisting line are assumed as design parameters, and the best gains of the feedback controller are achieved. Finally, some tracking simulations are performed which demonstrate the capability of the simple proposed method in the optimal tracking control of a gantry crane

Design and analysis of a 2 dimensional micro-gripper by using of rotational displacement of clamped perpendicular micro-beams due to piezoelectric actuation

As regards to daily developments in micro/nano technology and very special intricate missions in micro/nano scale, many researches focused on manipulation and movement in correspond scales. Micro-grippers are end effectors of micro/nano manipulation systems which perform some duties such as holding, picking up, moving and cutting. In this research a micro-gripper has been introduced which consists of two perpendicular Micro-beams. Each Micro-beam has an elastic layer and two piezoelectric layer. One of these piezoelectric layers is used for actuation and another one for sense and feedback control. First static equations of Micro-beam presented. Kinematics of Micro-gripper including direct and inverse kinematics and static displacement has been presented. Eventually Micro-gripper workspace for a Micro-beam’s ultimate displacement has been specified. The results have been verified by FEM software. The difference between the analytical results of displacements in different directions with the corresponding results of finite element software output is about 2 percent. Therefore, the results indicate the accuracy and efficiency of the proposed method and the current research can be a framework and foundation for the analysis of similar systems with more complex geometry

Smooth Jerk-Bounded Optimal Path Planning of Tricycle Wheeled Mobile Manipulators in the Presence of Environmental Obstacles

In this work, a computational algorithm is developed for the smooth-jerk optimal path planning of tricycle wheeled mobile manipulators in an obstructed environment. Due to a centred orientable wheel, the tricycle mobile manipulator exhibits more steerability and manoeuvrability over traditional mobile manipulators, especially in the presence of environmental obstacles. This paper presents a general formulation based on the combination of the potential field method and optimal control theory in order to plan the smooth point-to-point path of the tricycle mobile manipulators. The nonholonomic constraints of the tricycle mobile base are taken into account in the dynamic formulation of the system and then the optimality conditions are derived considering jerk restrictions and obstacle avoidance. Furthermore, by means of the potential field method, a new formulation of a repulsive potential function is proposed for collision avoidance between any obstacle and each part of the mobile manipulator. In addition, to ensure the accurate placement of the end effector on the target point an attractive potential function is applied to the optimal control formulation. Next, a mixed analytical-numerical algorithm is proposed to generate the point-to-point optimal path. Finally, the proposed method is verified by a number of simulations on a two-link tricycle manipulator