TIP trajectory tracking of flexible-joint manipulators

In most robot applications, the control of the manipulator’s end-effector along a specified desired trajectory is the main concern. In these applications, the end-effector (tip) of the manipulator is required to follow a given trajectory. Several methods have been so far proposed for the motion control of robot manipulators. However, most of these control methods ignore either joint friction or joint elasticity which can be caused by the transmission systems (e.g. belts and gearboxes). This study aims at development of a comprehensive control strategy for the tip-trajectory tracking of flexible-joint robot manipulators. While the proposed control strategy takes into account the effect of the friction and the elasticity in the joints, it also provides a highly accurate motion for the manipulator’s end-effector. During this study several approaches have been developed, implemented and verified experimentally/numerically for the tip trajectory tracking of robot manipulators. To compensate for the elasticity of the joints two methods have been proposed; they are a composite controller whose design is based on the singular perturbation theory and integral manifold concept, and a swarm controller which is a novel biologically-inspired controller and its concept is inspired by the movement of real biological systems such as flocks of birds and schools of fishes. To compensate for the friction in the joints two new approaches have been also introduced. They are a composite compensation strategy which consists of the non-linear dynamic LuGre model and a Proportional-Derivative (PD) compensator, and a novel friction compensation method whose design is based on the Work-Energy principle. Each of these proposed controllers has some advantages and drawbacks, and hence, depending on the application of the robot manipulator, they can be employed. For instance, the Work-Energy method has a simpler form than the LuGre-PD compensator and can be easily implemented in industrial applications, yet it provides less accuracy in friction compensation. In addition to design and develop new controllers for flexible-joint manipulators, another contribution of this work lays in the experimental verification of the proposed control strategies. For this purpose, experimental setups of a two-rigid-link flexible-joint and a single-rigid-link flexible-joint manipulators have been employed. The proposed controllers have been experimentally tested for different trajectories, velocities and several flexibilities of the joints. This ensures that the controllers are able to perform effectively at different trajectories and speeds. Besides developing control strategies for the flexible-joint manipulators, dynamic modeling and vibration suppression of flexible-link manipulators are other parts of this study. To derive dynamic equations for the flexible-link flexible-joint manipulators, the Lagrange method is used. The simulation results from Lagrange method are then confirmed by the finite element analysis (FEA) for different trajectories. To suppress the vibration of flexible manipulators during the manoeuvre, a collocated sensor-actuator is utilized, and a proportional control method is employed to adjust the voltage applied to the piezoelectric actuator. Based on the controllability of the states and using FEA, the optimum location of the piezoelectric along the manipulator is found. The effect of the controller’s gain and the delay between the input and output of the controller are also analyzed through a stability analysis

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

A steady state tip control strategy for long reach robots

The work presented in this thesis describes the development of a novel strategy for the steady state tip position control of a single link flexible robot arm. Control is based upon a master/slave relationship. Arm trajectory is defined by through 'master' positioning head which moves a laser through a programmed path. Tip position is detected by an optical system which produces an error signal proportional to the displacement of the tip from the demand laser spot position. The error signal and its derivative form inputs to the arm 'slave' controller so enabling direct tip control with simultaneous correction for arm bending. Trajectory definition is not model-based as it is defined optically through movement of the positioning head alone. A critical investigation of vacuum tube and solid state sensing methods is undertaken leading to the development of a photodiode quadrant detector beam tracking system. The effect of varying the incident light parameters on the beam tracker performance are examined from which the optimum illumination characteristics are determined. Operational testing of the system on a dual-axis prototype robot using the purpose-built beam tracker has shown that successful steady state tip control can be achieved through a PD based slave controller. Errors of less than 0.05 mm and settling times of 0.2 s are obtained. These results compare favourably with those for the model-based tip position correction strategies where tracking errors of ± 0.6 mm are recorded

Constrained Optimized Command Shaping for Minimizing Residual Vibration in a Flexible-Joint Robot

Joint flexibility is a natural trait of robotic manipulators, which limits fast point-to-point motion. Remedial measures are often employed to enable these systems to perform their goal in a desired manner. These measures range from either modifying the system dynamics such that the resonance is increasingly damped or by designing cleverly shaped input commands that avoid exciting the resonant modes altogether. In this work, a numerical framework for generating constrained shaped commands for a two-link flexible-joint robot is presented. To optimally select the design parameters for generating shaped commands, the effects of subjecting the optimization to mutually exhaustive constraints of residual vibration performance, speed of motion and size of actuators has been studied. Few important performance metrics to characterize the performance are also introduced and discussed. The framework has been tested for two basis functions, ramped sinusoid and segmented versine, in simulations and experiments and performance is evaluated against one another and an unshaped bang-bang profile. In practice, it has been shown that the constrained numerical approach reduces vibration in the nonlinear robot system in a more effective and efficient manner than the unconstrained closed-form solution

Fuzzy PD control of an optically guided long reach robot

This thesis describes the investigation and development of a fuzzy controller for a manipulator with a single flexible link. The novelty of this research is due to the fact that the controller devised is suitable for flexible link manipulators with a round cross section. Previous research has concentrated on control of flexible slender structures that are relatively easier to model as the vibration effects of torsion can be ignored. Further novelty arises due to the fact that this is the first instance of the application of fuzzy control in the optical Tip Feedback Sensor (TFS) based configuration. A design methodology has been investigated to develop a fuzzy controller suitable for application in a safety critical environment such as the nuclear industry. This methodology provides justification for all the parameters of the fuzzy controller including membership fUllctions, inference and defuzzification techniques and the operators used in the algorithm. Using the novel modified phase plane method investigated in this thesis, it is shown that the derivation of complete, consistent and non-interactive rules can be achieved. This methodology was successfully applied to the derivation of fuzzy rules even when the arm was subjected to different payloads. The design approach, that targeted real-time embedded control applicat.ions from the outset, results in a controller implementation that is suitable for cheaper CPU constrained and memory challenged embedded processors. The controller comprises of a fuzzy supervisor that is used to alter the derivative term of a linear classical Proportional + Derivative (PD) controller. The derivative term is updated in relation to the measured tip error and its derivative obtained through the TFS based configuration. It is shown that by adding 'intelligence' to the control loop in this way, the performance envelope of the classical controller can be enhanced. A 128% increase in payload, 73.5% faster settling time and a reduction of steady state of over 50% is achieved using fuzzy control over its classical counterpart

Robot Manipulators

Robot manipulators are developing more in the direction of industrial robots than of human workers. Recently, the applications of robot manipulators are spreading their focus, for example Da Vinci as a medical robot, ASIMO as a humanoid robot and so on. There are many research topics within the field of robot manipulators, e.g. motion planning, cooperation with a human, and fusion with external sensors like vision, haptic and force, etc. Moreover, these include both technical problems in the industry and theoretical problems in the academic fields. This book is a collection of papers presenting the latest research issues from around the world