Motion planning for active cannulas

An active cannula is a medical device composed of thin, pre-curved, telescoping tubes that may enable many new surgical procedures. Planning optimal motions for these devices is challenging due to their kinematics, which involve both beam mechanics and space curves. In this paper, we propose an optimization-based motion planning algorithm that computes actions to guide the device to a target point while avoiding obstacles in the environment. The planner uses a simplified active cannula kinematic model that neglects beam mechanics, and focuses on planning for the (piecewise circular) space curves. The method is intended for use in image-guided procedures where the target and obstacles can be segmented from pre-procedure images. Given the target location, the start position and orientation, and a geometric representation of obstacles, the algorithm computes the insertion length and orientation angle for each tube of the active cannula such that the device follows a collision-free path to the target. We formulate the planning problem as a constrained nonlinear optimization problem and use a penalty method to convert this formulation into a sequence of more easily solvable unconstrained optimization problems. Simulations demonstrate optimal paths for a 3-tube active cannula with spherical obstacles. The algorithm typically computes plans in less than 1 minute on a standard PC.