Delay time compensation based on coefficient of restitution for collision hybrid motion simulator

A hybrid motion simulator embeds a hardware experiment in a numerical simulation loop. However, it is often subjected to the inherent problem of an energy increase in the collision of two pieces of hardware in a loop because of the delay time. This paper proposes a delay time compensation method based on contact dynamics model for a collision hybrid motion simulator under delay time and establishes a compensation method for coupled translational and rotational motion. The model developed in this paper describes linear uniform motion of a floating object during the period of the delay time until the force and torque are observed and non-linear motion according to environmental stiffness after the initial delay time period in contact. By using the above model, compensation parameters are designed based on desired coefficient of restitution with iterative calculation. The proposed method achieves accurate delay time compensation and simultaneously realizes a variable desired coefficient of restitution over a wide range of frequencies. Furthermore, the compensation method for multi-dimensional motion is established under the assumption that the friction effect is very small. The efficiency of the proposed method is verified through collision experiments for the coupled motion in two dimensions. Graphical Abstract