Equilibrium point trajectory for goal-directed fast movements using a novel second-order mass-spring-damping model

The second-order mass-spring-damping (KBI) model has traditionally been used to represent the dynamic properties of the musculoskeletal system. However, it has been proposed this model does not adequately represent all the properties within this system, which is at least third-order. In this paper, we propose a viewpoint the dynamics of passive movement and active movement can be represented by two separate second-order KBI models. To explore this idea, we use the original KBI model (named P-KBI model in this paper) set forth by Gomi and colleagues to fit the dynamic responses of small perturbations (passive movements), and introduce a novel KBI model (A-KBI model) to reconstruct equilibrium point (EP) trajectories from actual movement trajectories (active movements). These models are subsequently implemented to simulate single-joint and double-joint fast movement. The results show “simple” EP trajectories obtained from a second-order mass-spring-damping model (A-KBI) are feasible for fast goal-directed single-joint movement as well as double-joint movement, with “simple” EP trajectories varying as a function of the accuracy requirements.