Kinematically optimal hyper-redundant manipulator configurations

Hyper-redundant robots have a very large or infinite degree of kinematic redundancy. The authors develop methods for determining the optimal configurations which satisfy task constraints while minimizing a weighted measure of mechanism bending and extension. These methods are based on a continuous backbone curve which captures the robot´s essential macroscopic geometric features. The calculus of variations is used to develop differential equations whose solution is the optimal backbone curve shape. The optimal distribution of frames along the backbone curve is also considered