An Approach to Formulate the Hessian Matrix for Dynamic Control of Parallel Robots

The Hessian matrix, one of the most pivotal parts in a robotic system's acceleration model, is a prerequisite for dynamic modeling and control of parallel robots. Aimed at providing a straightforward and effective way for modeling, design, and control of parallel robots, a new approach to formulate the Hessian matrix using the finite and instantaneous screw theory is presented in this paper. The new approach is generalizable in that it can be used to formulate the Hessian matrix of any parallel robot in a simple and concise manner. It also provides a theoretical foundation for the dynamic control of industrial robotic systems with parallel structures. The new approach is verified through comparison with the traditional exponential matrix method. The Exechon parallel robot and a hybrid serial-parallel robot are used as examples to further detail the procedures of this approach. The acceleration model formulated in this paper is closely related with the topological and parametric models, resulting in a unified mathematical framework for modeling and control of parallel robots.