Analysis and Control of a Variable-Curvature Continuum Manipulator for the Treatment of Osteolysis
Murphy, Ryan Joseph
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Continuum manipulators have become prevalent in many minimally invasive surgeries; typically, these surgeries involve only soft tissues. The exponential growth of this field has resulted in a variety of manipulator designs and associated models to understand and control the manipulators. Many of the existing models rely on constant-curvature (or piecewise-constant) assumptions that are borne out in manipulators under study. However, such constant-curvature assumptions fail to accurately describe a single-body manipulator specifically designed for orthopaedic surgery. This planar, underactuated manipulator exhibits variable curvature bending and complex responses to environmental constraints. This work investigates the utility of such a manipulator for the treatment of osteolysis (bone degradation) occurring behind a total hip replacement by examining the workspace, inverse kinematics, and control. Defining the manipulator workspace using convolution on group elements shows the manipulator is capable of achieving over 95% coverage in an osteolytic lesion, compared to the nominal 50% reported by clinicians. Several inverse kinematic models are presented, including (a) constrained energy minimization using tip position (or position and orientation) feedback and (b) interpolation among discrete shape-sensing elements simulated along the manipulator length. These approaches are examined with and without external loads applied to the manipulator; the position and orientation constrained function offers the best results, but all achieve sub-millimeter accuracy on average. The research concludes with the design and implementation of an efficient, model-less controller using feedback from curvature sensors; the controller reliably predicts control inputs. While the motivating manipulator bends in a single plane, these methods may be extended to consider variable curvature manipulators capable of three-dimensional bending.