Dynamics and control of flexible manipulators

Flexible link manipulators (FLM) are well-known for their light mass and small energy consumption compared to rigid link manipulators (RLM). These advantages of FLM are even of greater importance in applications where energy efficiency is crucial, such as in space applications. However, RLM are still preferred over FLM for industrial applications. This is due to the fact that the reliability and predictability of the performance of FLM are not yet as good as those of RLM. The major cause for these drawbacks is link flexibility, which not only makes the dynamic modeling of FLM very challenging, but also turns its end-effector trajectory tracking (EETT) into a complicated control problem. The major objectives of the research undertaken in this project were to develop a dynamic model for a FLM and model-based controllers for the EETT. Therefore, the dynamic model of FLM was first derived. This dynamic model was then used to develop the EETT controllers. A dynamic model of a FLM was derived by means of a novel method using the dynamic model of a single flexible link manipulator on a moving base (SFLMB). The computational efficiency of this method is among its novelties. To obtain the dynamic model, the Lagrange method was adopted. Derivation of the kinetic energy and the calculation of the corresponding derivatives, which are required in the Lagrange method, are complex for the FLM. The new method introduced in this thesis alleviated these complexities by calculating the kinetic energy and the required derivatives only for a SFLMB, which were much simpler than those of the FLM. To verify the derived dynamic model the simulation results for a two-link manipulator, with both links being flexible, were compared with those of full nonlinear finite element analysis. These comparisons showed sound agreement. A new controller for EETT of FLM, which used the singularly perturbed form of the dynamic model and the integral manifold concept, was developed. By using the integral manifold concept the links’ lateral deflections were approximately represented in terms of the rotations of the links and input torques. Therefore the end-effector displacement, which was composed of the rotations of the links and links’ lateral deflections, was expressed in terms of the rotations of the links and input torques. The input torques were then selected to reduce the EETT error. The originalities of this controller, which was based on the singularly perturbed form of the dynamic model of FLM, are: (1) it is easy and computationally efficient to implement, and (2) it does not require the time derivative of links’ lateral deflections, which are impractical to measure. The ease and computational efficiency of the new controller were due to the use of the several properties of the dynamic model of the FLM. This controller was first employed for the EETT of a single flexible link manipulator (SFLM) with a linear model. The novel controller was then extended for the EETT of a class of flexible link manipulators, which were composed of a chain of rigid links with only a flexible end-link (CRFE). Finally it was used for the EETT of a FLM with all links being flexible. The simulation results showed the effectiveness of the new controller. These simulations were conducted on a SFLM, a CRFE (with the first link being rigid and second link being flexible) and finally a two-link manipulator, with both links being flexible. Moreover, the feasibility of the new controller proposed in this thesis was verified by experimental studies carried out using the equipment available in the newly established Robotic Laboratory at the University of Saskatchewan. The experimental verifications were performed on a SFLM and a two-link manipulator, with first link being rigid and second link being flexible.Another new controller was also introduced in this thesis for the EETT of single flexible link manipulators with the linear dynamic model. This controller combined the feedforward torque, which was required to move the end-effector along the desired path, with a feedback controller. The novelty of this EETT controller was in developing a new method for the derivation of the feedforward torque. The feedforward torque was obtained by redefining the desired end-effector trajectory. For the end-effector trajectory redefinition, the summation of the stable exponential functions was used. Simulation studies showed the effectiveness of this new controller. Its feasibility was also proven by experimental verification carried out in the Robotic Laboratory at the University of Saskatchewan