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Variational techniques are used to develop a theory for the time evolution of a thin strand of viscous fluid suspended from two points. The shape of the strand is approximated to be a parabola and energy conservation is used to derive a differential equation modeling the change in height over time. Data is collected with a high resolution camera and a strobe light to obtain the position and shape of the strand over multiple intervals of time. Three very different and unexpected types of behaviors are observed depending on the initial thickness and shape of the filament. The approximation fits well with one type of behavior but variations in the thickness of the strand, and consequently in the center of mass, need to be factored in to predict the others.

published_or_final_version / Mechanical Engineering / Doctoral / Doctor of Philosophy

The deformation control problem arises in applications where a mechanical system needs to actively modify the shape of a soft object. This problem is needed in surgical robotics to automate delicate procedures with soft tissues, e.g. suturing and needle insertion, in food industry to automate the shaping of food materials such as dough, or in textile industry to automate the folding and positioning of extensible fabrics, to name a few cases. However, despite the recent progress in physically interactive and soft robotics, the active deformation of compliant objects remains an open research problem with many economically important applications. One of the main issues that complicates the implementation of these types of tasks is the difficulty to identify the deformation properties of soft materials. / The aim of this thesis is to provide model-free solutions to this challenging control design problem. For that, new adaptive methods to servo-control unknown elastic deformations are presented. First, this thesis proposes a kinematic controller that estimates the deformation Jacobian matrix in real-time, hence, avoids the identification of the object’s deformation model. This method computes the unknown matrix based on measurements of the deformation flow and the velocity input to the manipulator; the matrix is then used to map the deformation control action into end-effector velocities. Next, this thesis presents a conceptually different adaptive control approach that does not require to numerically estimate the deformation Jacobian matrix or to numerically compute the optical flow. However, to compute the velocity control input, offline testing deformations must be performed. In this method, the deformation control action is mapped to end-effector velocities by an adaptively varying transposed matrix, thus no matrix inversion is required. / This thesis also tackles the simultaneous vision-based control of multiple elastic deformations. This method incorporates the attitude of a fully-constrained gripper and the measurements from multiple vision sensors into the Jacobian estimation algorithm; by doing this, the number of controllable deformation degrees-of-freedom is increased. Additionally, this thesis addresses the vision-based deformation problem but with torque-controlled manipulators. The presented adaptive method exploits the passivity properties of the system and computes the controller with the online estimated Jacobian matrix. Finally, this thesis formulates the deformation control problem but in terms of force sensory feedback, in other words, the control objective is the regulation of the applied force onto the elastic object; the presented energy shaping controller preserves in closed-loop the Hamiltonian structure of the dynamical system. / The originality of this work lies in the uncalibrated nature of the control methods, i.e. none of the proposed controllers require the identification of the object’s deformation/stiffness model and the camera’s parameters. This uncalibrated feature allows to control on-the-fly elastic deformations of unknown compliant objects. It must be remarked that for each of the control methods, its stability is analysed with Lyapunov theory, and its performance is experimentally verified with robot manipulators. / Navarro Alarcon, David. / Thesis (Ph.D.) Chinese University of Hong Kong, 2014. / Includes bibliographical references (leaves 123-132).