Understanding Robot Degrees of Freedom (DOF)

The degree of freedom (DOF) of a robot refers to the number of independent parameters that define its configuration in space. For a typical robot arm designed to position and orient an object in 3D space, 6 degrees of freedom are usually sufficient (3 for position and 3 for orientation). A 7-degree-of-freedom (7-DOF) robot, therefore, has one extra degree of freedom compared to what is strictly necessary for basic manipulation tasks in free space.

Why 7-DOF Robots Present Challenges

When a robot has more degrees of freedom than required for a specific task, it is called a redundant robot. A 7-DOF robot is redundant for tasks that can be accomplished by a 6-DOF robot.

The main challenge with redundant robots, like a 7-DOF robot, lies in solving the inverse kinematics problem. Inverse kinematics is the process of calculating the required joint angles of the robot to achieve a desired position and orientation of the end-effector.

The Issue of Non-Unique Solutions

• For a non-redundant robot (like a 6-DOF robot for a 6-DOF task), the inverse kinematics problem typically yields a unique solution or a finite, small number of possible solutions for the joint angles.
• For a redundant robot (like a 7-DOF robot for a 6-DOF task), there are infinitely many combinations of joint angles that can result in the same end-effector position and orientation. This means the inverse kinematics solution is not unique.

Consider a 7-DOF arm reaching for an object. It can reach the same point with its end-effector while bending its elbow joint in different ways. This extra flexibility is the source of redundancy and the non-unique solution problem.

Computational Implications

Because there are infinitely many possible joint configurations for a given end-effector pose, the robot's control system must decide which one to choose. This decision process involves selecting a preferred solution based on various criteria, such as:

• Avoiding obstacles
• Staying away from joint limits
• Minimizing energy consumption
• Maintaining a comfortable configuration for future movements

Choosing the optimal or most suitable solution from an infinite set requires significant computational effort. The control algorithm needs to consider multiple factors and perform complex calculations in real-time.

Conclusion: Why Not Widely Used in Industry

The need to constantly solve a non-unique inverse kinematics problem and select an optimal solution introduces significant computational complexity. This requires high computing power and takes more time compared to controlling a non-redundant robot.

While 7-DOF robots offer advantages in terms of dexterity and ability to maneuver in cluttered environments, the increased complexity and computational cost make them less practical and more expensive for standard industrial tasks where 6-DOF robots suffice. Therefore, they are not as widely used in typical industrial automation settings.

Option 1 accurately describes this primary reason: it requires high computing power and time because there is no unique solution for a 7-DOF robot doing a standard task.