This paper addresses the challenge of teleoperating continuum instruments for minimally invasive surgery (MIS). We develop and adopt a novel task-priority-based kinematic formulation to quantitatively investigate teleoperation commands for continuum instruments under remote center of motion (RCM) constraints. Using redundancy resolution methods, we investigate the kinematic performance during teleoperation, comparing linear and angular commands within a task-priority scheme. For experimental validation, an instrument module (IM) was designed and integrated with a 7-DoF manipulator.Assessments, simulations, and experimental validations demonstrated the effectiveness of the proposed framework. The experiments involved several tasks: trajectory tracking of the IM tip along multiple paths with varying priorities for linear and angular teleoperation commands, pushing a ball along predefined paths on a silicon board, following a pattern on a pegboard, and guiding the continuum tip through rings on a ring board using a standard surgical kit.
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