| Current industrial robots are made very heavy to achieve high stiffness which increases the accuracy of their motion. However, this heaviness limits the robot speed and increases the required energy to move the system. The requirement for higher speed and better system performance makes it necessary to consider a new generation of lightweight manipulators as an alternative to today's massive inefficient ones. Lightweight manipulators require less energy to move and they have larger payload abilities and more maneuverability. However, due to the dynamic effects of structural flexibility, their control is much more difficult. Therefore, there is a need to develop accurate dynamic models for design and control of such systems.; There are two types of control problems for such manipulators, namely, trajectory control and time-optimal control (TOC) problems. In the first one, the position of the payload is given versus time while in the second one the path and the joint torque constraints are known. Since feedback control systems are non-collocated and position commands contain high frequency components, they may cause these systems to become unstable. This is why inverse dynamic methods have been recently used by many authors to determine the joint torques such that the end-point of the flexible manipulator follows a given trajectory. Due to the flexibility, a complete model consisting of the kinematic and dynamic equations should be solved simultaneously. But the difficulty is so called non-causality of the inverse dynamics of flexible manipulators. In other words, since the point, for which the prescribed motion is specified, is connected to the application points of control torques by elastic bodies, the joint torques should be applied from negative time to future time in order to control the position of the end-point according to the desired trajectory. The reason for this phenomenon is the fact that elastic waves propagate with finite speeds.; In this dissertation three topics, dynamic modeling, trajectory control, and time-optimal control of multi-link flexible manipulators are studied.; First an efficient finite element/Lagrangian approach is developed for dynamic modeling of planar and spatial manipulators with flexible links and joints. For planar case, the nonlinear and coupled equations of motion of multi-link manipulators are derived using minimum number of coordinates by considering joint or relative coordinates. In the case of spatial manipulators, the equations of motion are obtained using a mixed set of differential equations and algebraic constraints.; Then a technique based on numerical optimization is proposed to solve trajectory control and time optimal control of multi-link flexible manipulators. The proposed technique finds the joint torques required to move the end point from rest to rest along a specified path. The "non-causality" of the inverse dynamics of such systems is taken into account via considering pre-actuation and post-actuation in the solution procedure. The proposed technique is complete and effective and can be used to find joint torques as feedforward controls in order to minimize the work of the feedback controllers. |
