Nonsmooth Dynamic Modeling of a Humanoid Robot with Parallel Mechanisms.

This paper establishes a nonsmooth dynamic model for a humanoid robot with parallel mechanisms. Firstly, the constraint equations of the parallel mechanism are derived through kinematic analysis. By combining the links involved in closed-loop constraints into aggregate nodes, the topology of the robot can be equivalent to a tree structure. Equivalent physical quantities for the aggregate nodes are defined to unify their treatment with individual nodes during dynamic modeling. Subsequently, the contact and impact dynamics of the robot are modeled using constraint-based methods, with a frictional multiple impacts model employed for impacts. Due to the high degree of freedom of the robot, recursive methods are adopted to calculate the corresponding dynamic matrices. Finally, numerical examples are provided to illustrate the dynamic model of the robot. A comparison with the compliance-based methods of Simscape Multibody demonstrates that our dynamic model can reflect more realistic physical processes, providing a more accurate simulation environment for the motion control of the robot. The simulation of standing balance control is also performed based on our dynamic model.