Unified Framework of Gradient Computation for Hybrid-Link System and Its Dynamical Simulation by Implicit Method

Flexible tools such as golf clubs and sports prostheses used for exercise are generally constructed from materials that are both strong and lightweight enough to withstand the weight and speed of human movement. The authors have previously proposed a hybrid-link system that integrates a rigid-link system with a flexible structure, achieving forward dynamics simulations of the hybrid-link system with floating base-link, such as a human and a humanoid. However, numerical simulations of models with stiff and light flexible structures diverge and are difficult to realize. Using implicit integration as a forward dynamics calculation method is expected to improve the stability of the calculation. However, it requires information on the gradient of the equations of motion. Therefore, this study extends the comprehensive dynamic gradient calculation method proposed for rigid-link systems to hybrid-link systems with floating base-link; moreover, a forward dynamics simulation with contact force calculation is realized using implicit integration in a simple pendulum model, a robot arm and a humanoid with flexible structures.