Abstract
The kinematic and dynamic models of robots with complex mechanisms such as the closed-chain mechanism and the branch mechanism are often very complex and difficult to be calculated. Aiming at this issue, in this paper, the pose of the component in robots is represented by the Euclidean group and its subgroups with the proposed method. The component’s velocity is derived using the relationship between the Lie group and Lie algebra, and the acceleration and Jacobian matrix are then derived on this basis. The Lagrange equation is expressed by the obtained kinematic parameter expressions. Establishing the model with this method can obtain clear physical meaning and make the expressions uniform and easy to program, which is convenient for computer-aided calculation and parameterization. Calculating by the properties of the Lie group can reduce the calculation and model complexity, especially for calculating the velocity and acceleration, which reduces the calculation error and eases the calculation. Therefore, the proposed modeling and calculation method of kinematics and dynamics of robots is especially suitable for robots with complex mechanisms. As an example, the kinematic and dynamic model of the manipulator developed in our laboratory is established and a working process of it is numerically calculated. Then, the results of the numerical calculation are compared with the results of virtual prototype simulation in ADAMS to verify the correctness.
Highlights
Industrial robots are usually composed of the base, the endeffector, and several links connected by joints
Robot dynamic model establishes the mapping relation between driving forces needed on joints and the angles or displacements of joints. e establishment of robot kinematic and dynamic models is the basis of robot kinematic analysis, path planning, dynamic analysis, motion control, and so on [1]
The theory of the Lie group is connected with the motion of the rigid body and the description formulas of rigid body motion under the framework of the Lie group are derived. en, we propose a kinematic modeling method to describe the pose of rigid bodies in the multi rigid body system with the Lie group. e pose of the component in the robot mechanism is expressed by the Euclidean group and the displacement subgroup. e component’s body velocity Lie algebra and the velocities in the body fixed system derived from it are adopted to express the Lagrange equation in the framework of the Lie group
Summary
Industrial robots are usually composed of the base, the endeffector, and several links connected by joints. Using the relationship between Lie groups and Lie algebra will avoid a large number of derivations of trigonometric functions and greatly simplify the solution of the component’s velocity and the solutions of the acceleration and the Lagrange equation are simplified. Establishing the model in the form of Lie group and Lie algebra can obtain clear physical meaning and make the expressions uniform and easy to program, which is convenient for computer-aided calculation and parameterization. Calculating in the form of the Lie group and Lie algebra and by their properties can avoid a large number of trigonometric functions in the middle calculation process, which reduce the calculation and model complexity, especially for calculating the velocity and acceleration.
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