Comparison and Evaluation of Stability-Preserving Model Order Reduction Methods for Rigid Robot Manipulators: A Study on a 4-DOF Robotic Arm

Robust control of robotic systems critically depends on the stability-preserving capabilities of model order reduction (MOR) techniques. However, selecting an optimal MOR method for rigid robot manipulators remains challenging due to trade-offs between model fidelity, stability preservation, and computational efficiency. The research contribution of this study is to systematically compare three MOR methods—Balanced Truncation (BT), Positive-Real Balanced Truncation (PRBT), and Modal Truncation (MT)—applied to a 4-degree-of-freedom (4-DOF) robotic arm modeled as a linear time-invariant (LTI) system. We evaluated the methods based on error metrics, including H-infinity norm differences, and analyzed their time-domain and frequency-domain responses under standard test conditions. Our results demonstrate that BT provides superior reduction quality by maintaining stability and achieving an accurate dynamic response. PRBT, while exhibiting higher error than BT, effectively preserves both stability and passivity, making it advantageous for applications where passivity is essential, such as in mechanical and electrical circuits. In contrast, MT shows significant performance limitations with large errors and inconsistent responses, rendering it unsuitable for precision control applications. In conclusion, this study offers valuable insights into the trade-offs among MOR techniques and highlights practical implications for industrial automation. Future work will focus on expanding the analysis to a broader range of robotic systems and varying operational conditions.