A Systematic Approach for Generating Efficient Inverse Dynamics of Moving Parallel Platforms: The Redundantly Actuated SO(3) Case

This work describes a case study for a very fast approach for inverse dynamics of parallel platforms with moving base. The case study regards a roller coaster system in which a parallel platform with spherical motion actuated by four legs is mounted along a 3D track. The inverse dynamics of the system is derived based on Euler equations decomposed in the most efficient reference frame. Special attention is given to: (1) inertia tensors featuring special properties such as symmetry or negligible moments of inertia along one axis, and (2) terms not contributing to precision substantially as their respective mass effects are negligible compared to other leading terms. This paper derives for the first time minimal FLOPS (floating points operations) expression for such cases. A comparison is made with a full model in ADAMS. The paper shows three levels of simplification, with the simplest rendering a force precision of 0.54% at a performance factor of 625 over ADAMS, and the most complete at 0.0007% precision and performance factor of 482. This shows that sufficiently accurate models can be implemented in high-speed applications if proper detailed geometric properties are considered.