Consistent Approximations for the Optimal Control of Constrained Switched Systems

Though switched dynamical systems have shown great utility in modeling a variety of physical phenomena, the construction of an optimal control of such systems has proven difficult since it demands some type of optimal mode scheduling. In this paper, we devise an algorithm for the computation of an optimal control of constrained nonlinear switched dynamical systems. The control parameter for such systems include a continuous-valued input and discrete-valued input, where the latter corresponds to the mode of the switched system that is active at a particular instance in time. Our approach, which we prove converges to local minimizers of the constrained optimal control problem, first relaxes the discrete-valued input, then performs traditional optimal control, and then projects the constructed relaxed discrete-valued input back to a pure discrete-valued input by employing an extension to the classical Chattering Lemma that we prove. We extend this algorithm by formulating a computationally implementable algorithm which works by discretizing the time interval over which the switched dynamical system is defined. Importantly, we prove that this implementable algorithm constructs a sequence of points by recursive application that converge to the local minimizers of the original constrained optimal control problem. Four simulation experiments are included to validate the theoretical developments

Image-guided Control of Flexible Bevel-Tip Needles

Abstract—Physicians perform percutaneous therapies in many diagnostic and therapeutic procedures. Image guidance promises to improve targeting accuracy and broaden the scope of needle interventions. In this paper, we consider the possibility of automating the guidance of a flexible bevel-tip needle as it is inserted into human tissue. We build upon a previously proposed nonholonomic kinematic model to develop a nonlinear observer-based controller. As a first step for control, we show that flexible needles can be automatically controlled to remain within a planar slice of tissue as they are inserted by a physician; our approach keeps the physician in the loop to control insertion speed. In the proposed controller, the distance of the needle tip position from the plane of interest is used as a feedback signal. Numerical simulations demonstrate the stability and robustness of the controller in the face of parametric uncertainty. We also present results from pilot physical experiments with phantom tissue under stereo image guidance. I

Image-Guided Robot-Assisted Needle Intervention Devices and Methods to Improve Targeting Accuracy

This dissertation addresses the development of medical devices, image-guided robots, and their application in needle-based interventions, as well as methods to improve accuracy and safety in clinical procedures. Needle access is an essential component of minimally invasive diagnostic and therapeutic procedures. Image-guiding devices are often required to help physicians handle the needle based on the images. Integrating robotic accuracy and precision with digital medical imaging has the potential to improve the clinical outcomes. The dissertation presents two robotic devices for interventions under Magnetic Resonance Imaging (MRI) respectively Computed Tomography (CT) – Ultrasound(US) cross modality guidance. The MRI robot is a MR Safe Remote Center of Motion (RCM) robot for direct image-guided needle interventions such as brain surgery. The dissertation also presents the integration of the robot with an intraoperative MRI scanner, and preclinical tests for deep brain needle access. The CT-Ultrasound guidance uses a robotic manipulator to handle an US probe within a CT scanner. The dissertation presents methods related to the co-registration of multi-image spaces with an intermediary frame, experiments for needle targeting. The dissertation also presents method on using optical tracking measurements specifically for medical robots. The method was derived to test the robots presented above. With advanced image-guidance, such as the robotic approaches, needle targeting accuracy may still be deteriorated by errors related to needle defections. Methods and associated devices for needle steering on the straight path are presented. These are a robotic approach that uses real-time ultrasound guidance to steer the needle; Modeling and testing of a method to markedly reduce targeting errors with bevel-point needles; Dynamic design, manufacturing, and testing of a novel core biopsy needle with straighter path, power assistance, reduced noise, and safer operation. Overall, the dissertation presents several developments that contribute to the field of medical devices, image-guided robots, and needle interventions. These include robot testing methods that can be used by other researchers, needle steering methods that can be used directly by physicians or for robotic devices, as well as several methods to improve the accuracy in image-guided interventions. Collectively, these contribute to the field and may have a significant clinical impact