Joint-Angle Invariance of Jacobian-Based Performance Indices for Serial Robotic Manipulators

TL;DR

The paper identifies conditions under which key performance metrics derived from the Jacobian matrix remain unchanged with respect to the first and last joint angles in serial manipulators. This invariance enables a reduction in the dimensionality of the configuration space, streamlining performance evaluation. The approach is validated in workspace mapping and task planning, showing significant computational savings.

Why It Matters

Reducing computational complexity in performance analysis allows for faster design and optimization of robotic systems, especially in real-time or resource-constrained environments. This enables more efficient workspace exploration and task planning without sacrificing accuracy.

Key Findings

• Certain Jacobian-based performance indices are invariant to variations in the first and last joint angles under specific kinematic configurations.
• This invariance permits a reduction in the effective dimensionality of the configuration space used for performance evaluation.
• The method improves efficiency in constructing workspace performance maps and optimizing task layouts, with minimal impact on solution quality.