Tracking and controlling the shape of continuum dexterous manipulators (CDM) in constraint environments is a challenging task. The imposed constraints and interaction with unknown obstacles may conform the CDM's shape and therefore demands for shape sensing methods which do not rely on direct line of sight. To address these issues, we integrate a novel Fiber Bragg Grating (FBG) shape sensing unit into a CDM, reconstruct the shape in real-time, and develop an optimization-based control algorithm using FBG tip position feedback. The CDM is designed for less-invasive treatment of osteolysis (bone degradation). To evaluate the performance of the feedback control algorithm when the CDM interacts with obstacles, we perform a set of experiments similar to the real scenario of the CDM interaction with soft and hard lesions during the treatment of osteolysis. In addition, we propose methods for identification of the CDM collisions with soft or hard obstacles using the jacobian information. Results demonstrate successful control of the CDM tip based on the FBG feedback and indicate repeatability and robustness of the proposed method when interacting with unknown obstacles.
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