Redundancy Parameterization and Inverse Kinematics of 7-DOF Revolute Manipulators

Основные понятия

Redundancy parameterization is crucial for 7-DOF manipulators, with the SEW angle offering singularity solutions.

Аннотация

The content discusses the importance of redundancy parameterization and inverse kinematics for 7-DOF revolute manipulators. It introduces the concept of the generalized SEW angle to address algorithmic singularities, providing efficient solutions. The conventional SEW angle encounters singularities along a line, while the stereographic SEW angle reduces it to a half-line singularity. Various singularity conditions and their implications are explored, highlighting the necessity of choosing reference vectors carefully to avoid singularities.

Статистика

Seven degree-of-freedom (DOF) robot arms have one redundant DOF.
The stereographic SEW angle encounters a singularity only along a half-line.
Singularity analysis is provided for different redundancy parameterizations.

Цитаты

"A singularity is unavoidable for any redundancy parameterization."
"Algorithmic singularities are the main weakness of parameterizations like the SEW angle."
"Designers must carefully choose the reference direction to avoid singularities."

Ключевые выводы из

Redundancy parameterization and inverse kinematics of 7-DOF revolute manipulators

by Alexander J.... в arxiv.org 03-22-2024

https://arxiv.org/pdf/2307.13122.pdf

Дополнительные вопросы

How can designers mitigate algorithmic singularities in redundancy parameterizations

Designers can mitigate algorithmic singularities in redundancy parameterizations by carefully choosing the reference direction function. By selecting a reference vector that minimizes or avoids collinearity with critical vectors such as the shoulder-wrist line, designers can reduce the likelihood of encountering singularities. Additionally, designers can strategically place the singularity structure out of reach in the robot's workspace to minimize its impact. Another approach is to use alternative parameterization methods that have more favorable singularity structures, such as the stereographic SEW angle introduced in the context.

What impact do algorithmic singularities have on robotic operations

Algorithmic singularities can have a significant impact on robotic operations. These singularities may lead to undesirable behavior near them, including dangerously large joint movements and poor convergence for iterative algorithms. This can result in operational inefficiencies, safety risks, and challenges with achieving precise control over robotic manipulators. Algorithmic singularities also pose issues with numerical precision and may require additional computational resources to address stability problems during robot operation.

How does the choice of reference vectors affect singularity avoidance in robotics

The choice of reference vectors plays a crucial role in singularity avoidance in robotics. When designing redundancy parameterizations for robots, selecting appropriate reference vectors that are orthogonal or non-collinear with critical vectors like joint axes or end effector directions helps prevent algorithmic singularities from occurring. By ensuring that these reference vectors are well-positioned relative to key components of the robot's kinematic chain, designers can create redundancy parameterizations that offer greater manipulability without encountering problematic singularities along specific lines or planes within the workspace.