Dynamic modelling and control of a flexible manipulator.

This thesis presents investigations into dynamic modelling and control of a flexible manipulator system. The work on dynamic modelling involves finite element and symbolic manipulation techniques. The control strategies investigated include feedforward control using command shaping techniques and combined feedforward and feedback control schemes. A constrained planar single-link flexible manipulator is used as test and verification platform throughout this work. Dynamic model of a single-link flexible manipulator incorporating structural damping, hub inertia and payload is developed using the finite element method. Experiments are performed on a laboratory-scale single-link flexible manipulator with and without payload for verification of the developed dynamic model. Simulated and experimental system responses to a single-switch bang-bang torque input are presented in the time and frequency domains. Resonance frequencies of the system for the first three modes are identified. The performance and accuracy of the simulation algorithm are studied in comparison to the experimental results in both domains. The effects of damping and payload on the dynamic behaviour of the manipulator are addressed. Moreover, the impact of using higher number of elements is studied. The application of a symbolic manipulation approach for modelling and performance analysis of a flexible manipulator system is investigated. System transfer function can be retained in symbolic form using this approach and good approximation of the system transfer function can be obtained. Relationships between system characteristics and parameters such as payload and hub inertia are accordingly explored. Simulation and experimental exercises are presented to demonstrate the effectiveness of the symbolic approach in modelling and simulation of the flexible manipulator system. Simulation and experimental investigations into the development of feedforward control strategies based on command shaping techniques for vibration control of flexible manipulators are presented. The command shaping techniques using input shaping, low-pass and band-stop filters are considered. The command shaping techniques are designed based on the parameters of the system obtained using the unshaped bang-bang torque input. ii Abstract Performances of the techniques are evaluated in terms of level of vibration reduction, time response specifications, robustness to error in natural frequencies and processing times. The effect of using higher number of impulses and filter orders on the system performance is also investigated. Moreover, the effectiveness of the command shaping techniques in reducing vibrations due to inclusion of payload into the system is examined. A comparative assessment of the performance of the command shaping techniques in vibration reduction of the system is presented. The development of hybrid control schemes for input tracking and vibration suppression of flexible manipulators is presented. The hybrid control schemes based on collocated feedback controllers for rigid body motion control with non-collocated PID control and feedforward control for vibration suppression of the system are examined. The non-collocated PID control is designed utilising the end-point deflection (elastic deformation) feedback whereas feedforward control is designed using the input shaping technique. The developed hybrid schemes are tested within the simulation environment of the flexible manipulator with and without payload. The performances of the control schemes are evaluated in terms of input tracking capability and vibration suppression of the flexible manipulator. Initially, a collocated PD utilising the hub-angle and hub-velocity feedback signals is used as a feedback controller. Subsequently, to achieve uniform performance in the presence of a payload, a collocated adaptive control is designed based on pole-assignment self-tuning control scheme. Lastly, a comparative assessment of the performance of the hybrid control schemes is presented

Learning Reach-to-Grasp Motions From Human Demonstrations

Reaching over to grasp an item is arguably the most commonly used motor skill by humans. Even under sudden perturbations, humans seem to react rapidly and adapt their motion to guarantee success. Despite the apparent ease and frequency with which we use this ability, a complete understanding of the underlying mechanisms cannot be claimed. It is partly due to such incomplete knowledge that adaptive robot motion for reaching and grasping under perturbations is not perfectly achieved. In this thesis, we take the discriminative approach for modelling trajectories of reach-to-grasp motion from expert demonstrations. Throughout this thesis, we will employ time-independent (autonomous) flow based representations to learn reactive motion controllers which can then be ported onto robots. This thesis is divided into three main parts. The first part is dedicated to biologically inspired modelling of reach-to-grasp motions with respect to the hand-arm coupling. We build upon previous work in motion modelling using autonomous dynamical systems (DS) and present a coupled dynamical system (CDS) model of these two subsystems. The coupled model ensures satisfaction of the constraints between the hand and the arm subsystems which are critical to the success of a reach-to-grasp task. Moreover, it reduces the complexity of the overall motion planning problem as compared to considering a combined problem for the hand and the arm motion. In the second part we extend the CDS approach to incorporate multiple grasping points. Such a model is beneficial due to the fact that many daily life objects afford multiple grasping locations on their surface. We combine a DS based approach with energy-function learning to learn a multiple attractor dynamical system where the attractors are mapped to the desired grasping points. We present the Augmented-SVM (ASVM) model that combines the classical SVM formulation with gradient constraints arising from the energy function to learn the desired dynamical function for motion generation. In the last part of this thesis, we address the problem of inverse-kinematics and obstacle avoidance by combining our flow-based motion generator with global configuration-space planners. We claim that the two techniques complement each other. On one hand, the fast reactive nature of our flow based motion generator can used to guide the search of a randomly exploring random tree (RRT) based global planner. On the other hand, global planners can efficiently handle arbitrary obstacles and avoid local minima present in the dynamical function learned from demonstrations. We show that combining the information from demonstrations with global planning in the form of a energy-map considerably decreases the computational complexity of state-of-the-art sampling based planners. We believe that this thesis has the following contributions to Robotics and Machine Learning. First, we have developed algorithms for fast and adaptive motion generation for reach-grasp motions. Second, we formulated an extension to the classical SVM formulation that takes into account the gradient information from data. We showed that instead of being limited as a classifier or a regressor, the SVM framework can be used as a more general function approximation technique. Lastly, we have combined our local methods with global approaches for planning to achieve arbitrary obstacle avoidance and considerable reduction in the computation complexity of the global planners