Robotic control of deformable continua and objects therein
This dissertation describes design, modeling, planning and control of robot-assisted manipulation tasks dealing with deformable objects, which have many important applications in surgery, food handling, automobile manufacturing, aerospace, leather, and packaging. Most of the tasks involving the handling of deformable objects are done by skillful human operators. However, robot-assisted manipulation of deformable objects is a difficult and challenging task primarily due to the low stiffness of the deformable object. Therefore, this dissertation investigates three robotic manipulation tasks dealing with deformable objects, which have many practical applications: (i) autonomous shape control of a deformable object by multiple manipulators, (ii) robot-assisted internal target point manipulation of a deformable object, and (iii) robot-assisted flexible bevel-tip needle insertion into a deformable tissue/organ. Shape control of a deformable object by a robotic system is challenging problem because of the difficulty of imposing shape change by a finite number actuation points to an infinite dimensional object. In this dissertation, a new approach to shape changing task of deformable objects by a system of manipulators is presented. An integrated dynamic equation of motion for a system of multiple manipulators handling a deformable object is developed. We model the deformable object using mass-spring-damper system. The initial and the final shapes of the deformable object are specified by curves that represent the boundary of the object. We discuss two different approaches to find the contact locations on the desired shapes of the object given the initial contact locations to perform the task. First, we design an optimization-based planner that minimizes an energy-like criterion to determine the locations of the contact points on the desired curve representing the final shape of the object. Second, a shape correspondence between the initial contact points of the multiple manipulators on a deformable object and a two dimensional curve that represents the final desired shape is determined. A shape Jacobian that contains the local shape information of the desired shape of the object is formulated and is introduced into the control law. We develop a shape estimator with second-order dynamics that is used to estimate the curve parameters corresponding to the end-effectors position in each time-step as the initial object is deformed to its desired final shape. The motion of each manipulator is controlled independently without any communication between them. Finally we design a robust controller for a shape changing task that can work in the presence of modeling uncertainty. The simulation results demonstrate the efficacy of the proposed method. Manipulative operation of internal target points of a deformable object by a robotic system is another challenging problem because of the difficulty of imposing the motion of the internal target points by a finite number actuation points located at the boundary of the deformable object. In this work, an optimal contact formulation and a control action are presented in which a deformable object is externally manipulated with three robotic fingers such that an internal target point is positioned to a desired location. We formulate an optimization technique that minimizes the total force applied to the object to determine the location of actuation points to effect the desired motion of the target. A physics-based deformable object model using mass-spring-damper system is considered in this work. We develop a proportional-integral controller to control the motion of the robotic fingers. We also develop a passivity-based control approach by designing a passivity-observer to monitor the net energy flow during the interaction between the robotic fingers and the deformable object, and a passivity-controller that will dissipate the required energy by supplying necessary damping force to ensure stability of the whole system. The simulation results demonstrate the efficacy of the proposed method. Manipulation of a surgical needle inside deformable human tissue is similarly challenging. In many cases, needles are used to access designated targets inside a deformable tissue/organ to remove a cancerous cell or to inject drug at the target location. Needle can also be used for biopsy, prostate brachytherapy, neurosurgery, and thermal ablation. In this dissertation, we develop a robot-assisted needle insertion system to access targets inside the deformable tissue/organ for various medical interventions. We design a closed loop feedback controller for a flexible bevel-tip needle to position its tip to the desired target using a robotic device. The needle trajectory is described using a non-holonomic model. We derive the control law based on input-output feedback linearization technique. A continuous-discrete extended Kalman filter is presented to estimate the states of the system from noisy measurements. A robust controller is also derived, which compensates for modeling uncertainty. The performance of the proposed controller is verified with extensive simulations. Finally we verify the controller with experiments in an artificial tissue phantom and in bovine liver.