Dynamic analysis of a two-link flexible manipulator subject to different sets of conditions

A three stage development procedure for formulating expert knowledge based fuzzy logic controllers is presented in this work; its practical applications are demonstrated via active vibration control and position regulation experiments of a very flexible link manipulator Experimental results are presented and conclusion drawn

Fuzzy logic control of flexible link manipulators-controller design and experimental demonstrations

A cubic-splines trajectory planning of a constrained rigid-flexible manipulator to minimize the contact force is considered. Based on the general dynamic model of the chain of flexible links, equations of motion for the manipulator are derived using the extended Hamilton’s principle. An analytical solution for the inverse dynamics problem using the assumed modes method is presented to compute the required joint torques for the tip mass to move along the constrained surface. Cubic-splines interpolation has been adjusted for the joint motion profiles to make sure that the end-effector will follow the prescribed trajectory without degradation. The knot points of the trajectories have been chosen on the constrained surface to achieve minimum contact force as possible.

Cubic-Spline Trajectory Planning of a Constrained Flexible Manipulator

Many of today’s flexible robots are required to perform tasks that can be considered as constrained motions. A robot is considered to be in constrained maneuvering when its end-effector contacts and/or interacts with the environment as the robot moves. These applications include grinding, deburring, cutting, polishing, and the list continues. For the last two decades many researchers have investigated the constrained motion problem through different techniques such as hybrid position/force control (Raibert, M. & Craig, J., 1981 and Shutter et al., 1996), force control (Su, et al., 1990) , nonlinear modified CorlessLeitman controller (Hu, F. & Ulsoy, G., 1994), two-time scale force position control (Rocco, P. & Book, W., 1996), multi-variable controller (Shi, et al., 1990), parallel force and position control (Siciliano & Villani, L.,2000) , and multi-time-scale fuzzy logic controller (Lin, J., 2003). Luca et al. (Luca, D. & Giovanni, G., 2001) introduced rest-to-rest motion of a twolink robot with a flexible forearm. The basic idea is to design a set of two outputs with respect to which the system has no zero dynamics. Ata and Habib have investigated the open loop performance of a constrained flexible manipulator in contact with a rotary surface (Ata, A. & Habib, J., 2004) and arbitrary shaped fixed surfaces (Ata, A. & Habib, J., 2004). The effect of the contact force on the required joint torques has been simulated for different contact surfaces. Despite the voluminous research done, the study of dynamics and control of the constrained motion of the flexible manipulators remains open for further investigations. The present study aims at investigating the dynamic performance of a constrained rigid/flexible manipulator. The Cartesian path of the end-effector is to be converted into joint trajectories at intermediate points (knots). The trajectory segments between knots are then interpolated by cubic-splines to ensure the smoothness of the trajectory for each joint. To avoid separation between the end-effector and the constraint surface and to minimize the contact surface as well, these knots are chosen at the contact surface itself. Simulation results have been carried out for three contact surfaces.

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Trajectory Planning of a Constrained Flexible Manipulator

The present work investigates the dynamic analysis of a single link flexible manipulator with a tip mass using Tangential Coordinate System (TCS) and the Virtual Link Coordinate System (VLCS). The equations of motion are derived using the extended Hamilton's Principle. A third order polynomial trajectory is designed in the joint space. Numerical analysis is carried out for both types of coordinate systems and the total deflection is compared for both types of the coordinate.

Kinematic analysis of a single link flexible manipulator

The main objective of this work is to study the performance of a flexible single hub-arm system. The equations of motion are derived using the extended Hamilton principle. The Liapunov functional is used as a condition for the stability analysis. The Liapunov functional is considered as the sum of the internal energy of the flexible beam. The required drive torque was obtained directly through the solution of the inverse dynamic problem. Although the flexible link is nonminimum phase in nature, the use of Liapunov and the PD controller guarantee the causality for the stable case. The effects of tip mass as well as its inertia in the case of stable and asymptotic stable systems were investigated to ensure the validity of this procedure.

Causal inverse dynamics of a flexible hub-arm system through Liapunov's second method

The main objective of this work is to study the control performance of a flexible single hub-arm system. The equations of motion were derived using the extended Hamilton principle. Liapunov function is used as a condition for the stability analysis. The Liapunov functional is considered as the sum of the internal energy of the flexible beam. A Gaussian velocity profile was assumed and the required drive torque was obtained directly through the solution of the inverse dynamic problem. Causality was assured through Liapunov second method. The effect of tip mass as well as its inertia in the case of stable and asymptotic stable systems were investigated. The solution was also obtained for the cases of Fixed-Free and Fixed-Mass with Inertia; to ensure the validity of this method in the time domain.

Inverse dynamics of a flexible hub-arm system through liapunov second method

There are some important parameters that must be taken into consideration in the design process of the actuator for a flexible single link robot. Among these important factors are the hub inertia and the proper tip mass (including the payload) for optimum performance of the flexible arm system. The main objective of the paper is to study the effect of the actuator inertia as well as the tip mass in the flexible hub torque through the solution of the inverse dynamics problem. For comparison, two reference trajectories; Gaussian velocity, and a polynomial profile are applied. The equations of motion are derived with the help of the extended Hamilton principle using the virtual link coordinate system and the pinned-pinned boundary conditions.

Salwa M. Elkhoga

Papers

Causal inverse dynamics of a flexible hub-arm system through Liapunov's second method

Inverse dynamics of a flexible hub-arm system through liapunov second method

Effects of tip mass and actuator inertia on the behavior of a flexible arm robot