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Published in:
2006 | OriginalPaper | Chapter
Rivalling Optimal Control in Robot-Assisted Surgery
Authors : G.F. Schanzer, R. Callies
Published in: Progress in Industrial Mathematics at ECMI 2004
Publisher: Springer Berlin Heidelberg
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Miniaturized robotic manipulators are a key element in future highprecision minimally invasive surgery and telesurgery. This development is supported by the rapidly decreasing size of robotic sensors and actuators. Severe limitations are currently induced by the drives of the micro-joints.
The present paper deals with the optimal control of an advanced six-sectional branched manipulator. Joints are driven by weak, but fast, and strong, but slow, actuators acting in parallel. This results in the new and challenging problem of constrained optimal control of multibody systems subject to rivalling controls. For efficient treatment the differential equations of the state and adjoint variables are recursively defined. Geometric constraints lead to state constraints of second order. The complete problem of optimal control is transferred into a piecewise defined, highly nonlinear multi-point boundary value problem. The numerical solution of the boundary value problem is by the advanced multiple shooting method
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