This document discusses redundancy in robotics. It defines a kinematically redundant robot as having more degrees of freedom than needed to place an end effector in a desired location. For example, a robot with more than six degrees of freedom can be redundant for tasks in three-dimensional space which only require six degrees. Redundancy allows for multiple feasible inverse kinematics solutions and can be used to achieve additional objectives like avoiding obstacles or singularities. However, redundant robots are also more complex, expensive, and difficult to control.

1. REDUNDACY IN ROBOTICS
GUIDED BY:
Dr. H.J.NAGARSETH
Prof. ANIL MAHTO
PREPARED BY:
MIHIR PATEL
P18CC002
SARDAR VALLABHBHAI PATEL NATIONAL INSTITUTE OF TECHNOLOGY

2. WHAT IS REDUNDACY ?
• A kinematically redundant robot manipulator is a manipulator that has
more degrees of freedom than necessary to place the end effector at a
desired location.
• For example, if we want to place the end effector in a three
dimensional-space, we need six degrees of freedom: three for
translation and three for orientation.
• Thus, a robot manipulator with more than six degrees of freedom is
kinematically redundant in the three-dimensional space.

3. • When dealing with redundant manipulators, as the robot has more
degrees of freedom than necessary to perform a certain task, the
remaining degrees of freedom give a set of feasible solutions of the
inverse kinematics. Among these solutions, it is recommended to
choose the one satisfying a certain criterion
• “redundancy” of a robot is thus a relative concept, i.e., it holds with
respect to a given task.

4. Some tasks and their dimensions
• A planar robot with N=3 joints is redundant for the task of positioning
its E-E in the plane (M=2), but NOT for the task of positioning AND
orienting the E-E in the plane (M=3).
TASKS [ For the end-effector(E-E)] DIMENSION(M)
 Position in the plane 2
 Position in 3D space 3
 Orientation in the plane 1
 Pointing in 3D space 2
 Position and orientation in 3D space 6

5. INVERSE KINEMATICS
• By analysing a bit the geometry of the robot,
• x = l1cos(θ1) + l2cos(θ1+θ2) + l3cos(θ1+θ2+θ3)
y = l1sin(θ1) + l2sin(θ1+θ2) + l3sin(θ1+θ2+ θ3)
ø = θ1 + θ2 + θ3
• In fact, we can compute point P as P = (x − l3cos(ø), y − l3sin(ø)) and so
we have
• Px = l1cos(θ1) + l2cos(θ1+θ2)
Py = l1sin(θ1) + l2sin(θ1+θ2)

6. Graphical solution of
inverse kinematics

7. Typical cases of redundant robots
• 6R robot mounted on a linear track/rail
(For positioning and orienting its end-effector in 3D space)
• 6-dof robot used for arc welding tasks
(Task does not prescribe the final roll angle of the welding gun)
• Manipulator on a mobile base
• Team of cooperating manipulators (or mobile robots)
• Humanoid robots ...
• “kinematic” redundancy is not the only type…
1.Redundancy of components (actuators, sensors)
2.Redundancy in the control/supervision architecture

8. Uses of robot redundancy
• Avoid collision with obstacles (in Cartesian space) …
• … or kinematic singularities (in joint space)
• Stay within the admissible joint ranges
• Increase manipulability in specified directions
• Uniformly distribute/limit joint velocities and/or accelerations
• Minimize energy consumption or needed motion torques
• Optimize execution time
• Increase dependability with respect to faults
All objectives should be
Quantitatively “measurable”

9. Disadvantages of redundancy
• Potential benefits should be traded off against
• A greater structural complexity of construction
• Mechanical (more links, transmissions, ...)
• More actuators, sensors, ...
• Costs
• More complicated algorithms for inverse kinematics and motion
control

10. References
• Smooth Inverse Kinematics Algorithms for Serial Redundant Robots by Adri`a
Colom´
• Robots with kinematic redundancy by Prof. Alessandro De Luca
• Analysis and Control of Robot Manipulators with Kinematic Redundancy by
Pyung H. Chang(MIT Artificial Intelligence Laboratory)
• Inverse Kinematics Solution for Redundant Robot Manipulator using Combination
of GA and NN by Hind Z. Khaleel (Department of Control and Systems
Engineering/ University of Technology/ Baghdad/ Iraq)