The kinematic structure of a manipulator with hyper degrees of freedom is discussed from a theoretical viewpoint. Conditions for the kinematic structure are derived from a geometrically natural requirement that its direct kinematics tends to Frenet-Serret formula as its number of degrees of freedom increases. It is shown that the manipulator has to have two-degree-of-freedom joints, each of which consists of a twist and a one-directional bend.

In this paper, we give a definition of a shape correspondence between a manipulator with hyper degrees of freedom and a spatial curve. The shape correspondence is defined by using the solution of a nonlinear optimization problem, termed the shape inverse problem. We also provide results on the existence and a well-posed region of the solution.

In this paper, a shape tracking control problem for a hyper degrees of freedom manipulator is discussed. The objective of shape tracking is to control its shape, which is characterized by all the joints and the tip positions, to follow a given time-varying curve. Crucial key to solve this problem is to introduce a 2nd-order estimator that infers the curve parameters corresponding to the target positions of the joints and the tip on the curve. The coupled dynamics of the manipulator and this estimator has the same properties as the manipulator dynamics which is useful for control design purposes. Therefore, familiar design methods for manipulator trading can be utilized to solve the shape tracking problem. Examples are shown to illustrate how to find shape tracking laws by two famous methods, that is, the ID (inverse dynamics)-based and Lyapunov-based method.

In this paper, a new shape control law is proposed to bring a serial rigid link manipulator with hyper degrees of freedom into a specified shape. Shape control is one of the most characteristic controls for a hyper degrees of freedom manipulator. This control law is derived by the Lyapunov design method. A homogeneously decentralized control scheme is also proposed for practical application of the control law to a hyper degrees of freedom manipulator, and it is shown that the derived control law can be realized in a homogeneously decentralized control scheme. The effectiveness of this control law is verified by a hardware model experiment.

This paper proposes a con- trol law for a hyper redundant manipulator which has huge number of links. and moves in 3-dimensional gravity free space. Each controller can independently determine the way how to move each link. The necessary information for the controller is only on the target position, the po- sition of the end-effector and the position of the link. Each controller has the same control law and requires common information on the target position and the end-effector position. Thus we can call it distributed autonomous. The proposed control architecture has two other advantages: robustness and obstacle avoid- ance. The robustness means a property that: even if several number of links are out of order, the total sy5 tern still works normally. And the obstacle avoidance is a property: if the obstacle satisfles some conditions, the robotic manipulator avoids it automatically with- out adding any supplemental control.

Describes a distributed autonomous control for an ultra-multi plane manipulator. Each controller independently determines the way how to move each link. The necessary information for the controller is the target position, the position of the end-effector and the position of the link. Each controller has the same control law and common information on the target position and the end-effector position. Thus, the authors call it 'distributed autonomous'. The proposed control architecture has two main advantages: (1) robustness, even if several number of links are out of order, the total system will still work normally; and (2) obstacle avoidance, if the obstacle satisfies some conditions, the robotic manipulator will avoid it automatically.>