Hyper-Redundant Manipulators

The word “redundant” is used in the context of robotic manipulators to indicate that the number of actuated degrees of freedom exceeds the minimum number required to perform a particular task. For instance, a manipulator required to position and orient an object in space needs six actuated degrees of freedom, and so a manipulator with seven or more is redundant with respect to this task. “Hyper-redundant” manipulators are redundant manipulators with a very large degree of redundancy. These manipulators can be analogous in morphology and operation to “snakes,” “elephant trunks,” or “tentacles.” Because of their highly articulated structures, these robots are well suited for operation in highly constrained environments, and can be designed to have greater robustness with respect to mechanical failure than manipulators with a low degree of redundancy

Suppose a manipulator is required to position an object in space at a specified point and with a specified orientation. If the point is in the manipulator's workspace, there is at least a set of joint posture positions that configure the manipulator such that it can position and orient the object as required. Finding the set of joint postures is known as inverse kinematics problem. Solving the inverse kinematics problem for non-redundant manipulators is straight forward, because the number of unknowns (joint posture positions) is equal to the number of task space constraints. But for redundant manipulators this is not the case, and the problem is complicated.

The inverse kinematics problem for redundant manipulators is usually solved using the Jacobian pseudo-inverse. However, this technique is not suited for hyper-redundant manipulators, due to computational burden. For solving the inverse kinematics problem for hyper-redundant manipulators, a method is used called “the modal approach.”

The modal approach is very efficient and is suited for real-time applications. It is useful for implementing different locomotion, and motion planning. But the workspace if a robot kinematically controlled by this method, highly depends on the mode shape functions defined to solve their inverse kinematics problem. Furthermore, the method solves the problem in joint position level and velocity analysis was not introduced to complete the manipulator kinematic analysis.

We improved this method by defining generalized modal shape functions that incorporate the orientation of the end-effector. The generalized modal functions make the robot able to reach a larger workspace. We also introduced a velocity solution procedure to complete the inverse kinematics analysis.

A spatial hyper-redundant manipulator reaching a point in space with different orientations

Hyper-redundant manipulators have highly articulated structures. These robots are well suited for operation in highly constrained environments with many obstacles. Therefore, obstacle avoidance schemes are also needed to control these manipulators such that they reach their goal position and avoid obstacle

Using the flexibility and power of the potential approach based on harmonic potential fields we developed an obstacle avoidance theory for planar hyper-redundant manipulators. A planar hyper-redundant robot has a large number of links, which always lie in the same plane. The theory enables the end-effector of the planar manipulator to reach any specified point behind some predefined two-dimensional obstacles while the arm itself avoids the obstacles.

A planar hyper-redundant manipulator reaching inside a tunnel

We extended the mentioned theory to spatial hyper-redundant manipulators working in three-dimensional environments containing three-dimensional obstacles. The theory controls the spatial manipulator such that its end-effector reaches a specified point in space, while the links avoid colliding the obstacles.

A spatial hyper-redundant manipulator avoiding obstacles

The research described here was carried out in collaboration with Dr. Farbod Fahimi and Dr. Hashem Ashrafiuon. Also, a former graduate student, Farshid Asl.