9.15. Redundancy in Manipulators

A manipulator is redundant if it has more DOF than required for a task. E.g., a 7-DOF robot arm in a 6-DOF task is redundant.

In robotics, redundancy refers to the situation where a robot manipulator has more degrees of freedom (DOF) than what is necessary to perform a given task. For instance, if a task only requires six degrees of freedom to achieve a certain position and orientation in space, a robot that has seven degrees of freedom is considered redundant. This additional freedom allows the robot greater flexibility and options in how it accomplishes the task without changing the end-effector's position.

Imagine a professional basketball player who can shoot, pass, dribble, and perform various plays. While they only need to be in a certain position to shoot the basketball, having additional skills (like fancy dribbling or passing abilities) makes them more versatile and effective in different game situations, much like how a redundant robot can choose from multiple configurations to achieve a task.

Avoids joint limits and singularities. Optimizes secondary goals:

• Minimizing energy
• Avoiding obstacles
• Balancing payload

Redundancy in manipulators comes with several advantages, primarily because it provides flexibility and robustness in robot operations. Firstly, having more DOF allows robots to avoid joint limits and singularities, which are problematic positions where the robot’s motion is restricted or becomes unstable. Secondly, redundancy enables the optimization of secondary goals. For instance, a robot can minimize energy consumption, navigate around obstacles, or adjust its configuration for better load distribution, enhancing its operational efficiency.

Consider a delivery service vehicle equipped with multiple route options. If one route is blocked due to construction (an obstacle), the vehicle can choose another path that might use less fuel (minimizing energy) or avoid heavy traffic (balancing load). Similarly, a robot with redundant configurations can choose the best way to complete its task while avoiding potential pitfalls in its environment.

Optimization-based methods Null-space projection Common in mobile manipulators used in bridge inspection or high-rise maintenance.

When working with redundant manipulators, it is essential to resolve how to properly utilize the extra degrees of freedom. Various techniques are employed to do so, such as optimization-based methods, which aim to choose the best configuration for the robot based on given criteria, and null-space projection, which focuses on movements that do not affect the end-effector's position. These methodologies are especially useful in applications like mobile manipulators for bridge inspections or high-rise maintenance, where the ability to alternate configurations can be critically beneficial.

Think of a photographer taking pictures of a busy street. They can choose how to adjust their camera angle, height, or position to get the best shot without moving into traffic (that’s the null-space projection). If they decide to shift to a less crowded position while still capturing the same scene, they are employing an optimization technique. Just like the photographer selects the optimal shot while avoiding hurdles, redundant manipulators can adapt their movements for the best operational outcomes.

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