Dynamic Analysis Base on Lie Algebra of a 2-DOF Spatial Mechanism for a Bio-Inspired Manta Ray Robot

In the field of underwater robotics, the development of efficient and precise locomotion systems is crucial for enhancing the operational capabilities of robots in complex aquatic environments. This work presents the dynamic analysis of a spatial mechanism with two degrees of freedom (2 DOF) implemented in the locomotion system of a bio-inspired underwater robot. The dynamic analysis is conducted using Lie algebra and the results obtained are subsequently compared with those provided by the commercial software <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{o}\mathbf{r} ^{\mathbf{T}\mathbf{M}}$</tex>. Then, by applying Lie algebra methodology a robust framework for modeling and understanding the complex dynamics of the system, enabling an accurate representation of its behavior is reported. The comparative analysis with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{I}\mathbf{n}\mathbf{v}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{o}\mathbf{r} ^{\mathbf{T}\mathbf{M}}$</tex> simulations validates the theoretical results, offering a comprehensive evaluation of the mechanism's performance. This study contributes to the development of more efficient and versatile underwater robots, with potential applications in marine exploration, rescue operations, and underwater maintenance tasks.