Study of redundant kinematics for industrial manipulators: case study of the 7 axes robot

A robot a robot is kinematical redundant for the task if N > R where:
• N are the degrees of freedom of the structure (usually the number of the joints).
• M are the number of variables needed to describe the operational space.
• R are the number of variables of the operational space needed to describe a task.

In other words we can say that a robot is redundant when it has more degrees of freedom than strictly needed for describing and executing the task. By the way the redundancy is a relative concept, a robot could be redundant for a task but not for another one.

In terms of operational space and joints space, a manipulator is intrinsically redundant when the dimension of the operational space is smaller than the dimension of the joints space: M < N.
A generic task can be represented in the space with 6 variables (3 positional and 3 orientational values). For this reason a robot that has more than 6 degrees of freedom is intrinsically redundant.

As said before a generic anthropomorphic industrial robot has 6 degrees of freedom, than it is not intrinsically redundant. All the consideration in this thesis refers to industrial robots that have more than 6 DOF, usually 7.
Redundant robots don’t add additional complexity to the resolution of the direct kinematics. It is different for the inverse kinematics, where increasing the degrees of freedom the solutions in terms of joints that realize a certain position of the end effector in the space become potentially infinite. For this reason it is necessary to add additional complexity to kinematic inversion, in order to solve the problem, selecting a solution according to a certain methodology.

It is possible to take advantage to this adding some interesting control task like:
• stay within the feasible joint ranges
• avoid kinematic singularities (in joint space)
• avoid collision with obstacles (in Cartesian workspace) …
• uniformly distribute/limit joint velocities and/or accelerations
• increase manipulability in specified directions
• optimize execution time
• minimize energy consumption or needed motion torques
• increase dependability with respect to faults

Unfortunately take under control other parameters it is not easy, but we will talk in detail about this later.