A case study of flexible object manipulation
International Journal of Robotics Research
Lagrangian Aspects of the Kirchhoff Elastic Rod
SIAM Review
Robot Motion Planning
A Mathematical Introduction to Robotic Manipulation
A Mathematical Introduction to Robotic Manipulation
Collision detection for deforming necklaces
Computational Geometry: Theory and Applications - Special issue on the 18th annual symposium on computational geometrySoCG2002
Knotting/Unknotting Manipulation of Deformable Linear Objects
International Journal of Robotics Research
Planning Algorithms
ACM SIGGRAPH 2008 papers
Maxwell strata in the Euler elastic problem
Journal of Dynamical and Control Systems
International Journal of Robotics Research
Conjugate Points in the Euler Elastic Problem
Journal of Dynamical and Control Systems
Surgical retraction of non-uniform deformable layers of tissue: 2D robot grasping and path planning
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
Extracting Object Contours with the Sweep of a Robotic Whisker Using Torque Information
International Journal of Robotics Research
Equilibrium Conformations of Concentric-tube Continuum Robots
International Journal of Robotics Research
Design and Kinematic Modeling of Constant Curvature Continuum Robots: A Review
International Journal of Robotics Research
IEEE Transactions on Robotics
Representation for knot-tying tasks
IEEE Transactions on Robotics
Mobile manipulation of flexible objects under deformation constraints
IEEE Transactions on Robotics
Path planning for deformable linear objects
IEEE Transactions on Robotics
Three-dimensional contact imaging with an actuated whisker
IEEE Transactions on Robotics
Manipulation Planning for Deformable Linear Objects
IEEE Transactions on Robotics
Mechanics Modeling of Tendon-Driven Continuum Manipulators
IEEE Transactions on Robotics
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Consider a thin, flexible wire of fixed length that is held at each end by a robotic gripper. Any curve traced by this wire when in static equilibrium is a local solution to a geometric optimal control problem, with boundary conditions that vary with the position and orientation of each gripper. We prove that the set of all local solutions to this problem over all possible boundary conditions is a smooth manifold of finite dimension that can be parameterized by a single chart. We show that this chart makes it easy to implement a sampling-based algorithm for quasi-static manipulation planning. We characterize the performance of such an algorithm with experiments in simulation.