Otman El Baji, Nabil Ben Said Amrani, Driss Sarsri
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引用次数: 0
Abstract
In this paper, an explicit dynamic model for the 6-DOF Stewart platform parallel manipulator is established using a new formulation. The main principle of this formulation is to provide the final form of dynamic models based on a direct and systematic procedure; in more detail, the analytical expression of each term due to the dynamic effects, that is, the system inertia tensor, centrifugal/Coriolis tensor and the environment forces are developed according to only the physical parameters of the system (i.e., mass, inertia tensor, position of the center of mass and geometrical parameters) and generalized coordinates without the need for any complicated intermediate calculations such as the potential, kinetic and acceleration energy development. In this approach, the parallel manipulator is first opened into six serial legs and a free platform. Next, the dynamic models of each sub-structure can be easily obtained based on the new formulation in their own local space. The Jacobian and Hessian matrices of the constraint equations, resulting from the closed-loop chains, are then used to combine the substructure dynamics. Finally, a detailed dynamics model of the entire robot with respect to the workspace or the actuation space is developed. After that, a simulation of the suggested methodology is investigated and analyzed in comparison to the more established dynamic modeling techniques provided in the literature; the efficiency and correctness of our approach are then verified. It is shown that our method requires a lower computational cost and even competes with the implicit form of dynamic models. Finally, a trajectory-tracking problem using model-based control is presented. It is shown that our approach can be totally and efficiently computed online without the need for symbolic form of equations of motion, which is highly challenging for parallel manipulators.
本文采用一种新公式建立了 6-DOF Stewart 平台并联机械手的显式动态模型。更详细地说,只需根据系统的物理参数(即质量、惯性张量、质心位置和几何参数)和广义坐标,就能建立动态效应引起的各项,即系统惯性张量、离心力/科里奥利力张量和环境力的分析表达式,而无需进行任何复杂的中间计算,如势能、动能和加速度能的建立。在这种方法中,首先将并联机械手分成六个串联支腿和一个自由平台。然后,根据新的计算公式,在各自的局部空间内轻松获得每个子结构的动态模型。然后,利用闭环链产生的约束方程的雅各布矩阵和赫塞斯矩阵来组合子结构动力学。最后,针对工作空间或执行空间建立整个机器人的详细动力学模型。之后,对所建议的方法进行了仿真研究和分析,并与文献中提供的更成熟的动态建模技术进行了比较;然后验证了我们方法的效率和正确性。结果表明,我们的方法所需的计算成本更低,甚至可以与隐式动态模型相媲美。最后,介绍了一个使用基于模型控制的轨迹跟踪问题。结果表明,我们的方法可以完全高效地在线计算,而无需符号形式的运动方程,这对并行机械手来说极具挑战性。
期刊介绍:
The Journal of Mechanical Engineering Science advances the understanding of both the fundamentals of engineering science and its application to the solution of challenges and problems in engineering.