Geometric Algebra-based Method for Inverse Dynamic Modeling of Parallel Robots

doi:10.3901/JME.2022.07.001

Abstract

Abstract: Inverse dynamic modeling is the basis of dynamic performance evaluation and actual control of parallel robots. Using geometric algebra as a mathematical tool, a general method for the analytical inverse dynamic modeling of parallel robots is proposed. Based on the property of outer product, the intensities of velocities and accelerations of joints in the limbs can be directly determined, and then the mapping relationship between the actuated and passive velocities of robots is developed, followed by the derivation of velocities and accelerations of centers of mass of links. Combined with the principle of virtual work, the inverse dynamic modeling of parallel robots can be established, and then analytical expressions of actuated forces/torques can be obtained. No judgment of geometric relations, and no derivations or partial derivations are involved in the calculation of joint velocities and accelerations. In addition, only the addition and multiplication are involved in the whole calculation process, and there is no need to solve the symbolic linear equations, which significantly improves the calculation efficiency. Taken two parallel robots, 6-UPS with six degrees of freedom (DOFs) and 2PUR-PRU with three DOFs (where U denotes a universal joint, P denotes a prismatic joint, S denotes a spherical joint, and R denotes a revolute joint), as examples, the actuated forces of two parallel robots in the given trajectories can be obtained, and the correctness of the proposed theoretical method is verified by the simulations of ADAMS software. Meantime, by comparing the calculation efficiency with the natural orthogonal complement method based on the Newton-Euler equation, it is proved that the proposed method has the advantage of high efficiency, and can be chosen as an alternative to ADAMS simulation and original theoretical methods for the inverse dynamic modeling and analysis of parallel robots.

Key words: dynamic modeling, parallel robot, geometric algebra, principle of virtual work

CLC Number:

TG156

XU Lingmin, YE Wei, LI Qinchuan. Geometric Algebra-based Method for Inverse Dynamic Modeling of Parallel Robots[J]. Journal of Mechanical Engineering, 2022, 58(7): 1-11.

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