Computationally Efficient Inverse Dynamics of a Class of Six-DOF Parallel Robots: Dual Quaternion Approach

Computationally efficient inverse dynamics is crucial to the real-time application of parallel robots. This paper provides a computationally more efficient solution to the inverse dynamics of a class of six-DOF parallel robots based on the dual quaternion approach under the principle of virtual power. A unit dual quaternion is selected as the generalized coordinates of the system. The equations of motion are then constructed by the principle of virtual power. The dual quaternion constraints are eliminated by the null space formulation to obtain the inverse dynamic solution. It is revealed that in the new solution, the Jacobian matrices and the orthogonal complement matrix are all linear with respect to the generalized coordinates. Additionally, the positions, velocities and accelerations of all bodies are quadratic with respect to the generalized coordinates, velocities and accelerations. Such succinct expressions render the new solution computationally more efficient. The execution time of the dual quaternion approach and the traditional one are compared under the same condition by two different six-DOF parallel robots: 6-UPS and 6-PUS. The results show that the new solution can save the computational cost by 43.45% and 38.45% respectively for the two robots, illustrating the effectiveness of the proposed approach.