Analysis of inverse kinematic solution for 6R robot based on screw theory and Sylvester resultant

作者：Li, Shengqian; Xie, Xiaopeng^*

来源：Transactions of the Chinese Society of Agricultural Engineering, 2015, 31(20): 48-54.

DOI：10.11975/j.issn.1002-6819.2015.20.007

• Algorithm efficiency
• Geometric relationships
• Inverse kinematic models
• Inverse kinematic solutions
• Multi degree-of-freedom
• Screw theory
• Six-degree-freedom
• Sylvester resultant

The traditional denalit-hartenber (D-H) method is very popular to set up kinematic model for robot, but this method has lots of disadvantages, which include complexity, singularity and difficulties in inverse kinematic model solving. therefore the kinematic model of six degree freedom robot using traditional denalit-hartenber (D-H) method, can not get the high precision for inverse solution, and make the robot instantaneity for working. This article applied a product-of-exponential (POE) kinematic model based on screw theory for multi-degree of freedom series robots. Firstly, we used the screw theory to set up model for every joint of robot;then put matrix of every joint model multiply, which could get the POE of kinematic model for multi degree of freedom series robot. As we known from the above, the screw theory method was not limited by the form of joint, and could set up the kinematic model of robot very conveniently. This method was applicable to all types of multi degree of freedom series robot with versatility. Then the sylvester resultant method was used to solve these equations. The sylvester resultant method could solve high-dimensional nonlinear equations in advantage, and get the result of the nonlinear equations fast. The process of solving was used Maple software to calculate, due to the Maple software can use the symbol instead of the number to algorithm. Finally, in order to prove this method was correct and useful, we got special data, which was put into the forward kinematics formula to calculate the terminal attitude of robot, then we put this result of terminal attitude into the inverse kinematics formula, and got turning angle of each joint for the 6R robot, which was correct in the result from the calculation. In order to prove this method is correct further, we calculated from the perspective of geometry, which was through the geometric relationship of the robot to calculate each joint turning angle, and this result was as the same. At last, this inverse kinematic model and solving method was proved as an efficient and accurate method by calculating an example. In general, this method has efficient, accurate, reliable, and clear significance at physical and mathematician, also can apply to other robots with differences in configuration in kinematic modeling and inverse kinematic solution, providing a reference to quickly solution in inverse kinematic of robots. Meanwhile, this method can improve the algorithm efficiency 30% more than the general method of elimination.

• 出版日期2015-10-15
• 单位华南理工大学