Complex Exponential Transformation In The Industrial Robot Trajectory Planning

Aimed at the situation lack of efficient analysis tool in the study of the industrial robots' executor motion, a new method, the complex index form of the 3 dimensional vectors, is put forward. The way of coordinate transformation and the derivative are also explored while expressing vectors by using this method.when it being used in several examples, the motion analysis of the industrial robots' executor can be simplified. Numerical solution can also be got with computer. Consequently, trajectory planning for the industrial robots'executor can simply be implemented in this way.Firstly, this paper introduces industrial robots, their development, their engineering application, their category and their composing in broad outline. Secondly, the basic concept of the complex index form of the 3 dimensional vectors and the way of coordinate transformation, the complex index form transformation, are discussed. In order to simplify the further analysis, the derivative of this form is also put forward. Thirdly, the coordinate matrix transformation that is popularly used and the complex index form transformation are applied to the living examples of industrial robots respectively with the proper referent and motive coordinate systems. While two solutions being contrasted, it is shown that the complex index form transformation presented by the paper is an intuition!stic and convenient tool to analyze the industrial robots' executor motion. Finally, for the definite mechanism and indefinite size of industrial robots'executor as well as the size^optimization goal, the mathematic model is set up to optimize the executor'size with using complex optimization method. Next, for the optimized executor, the desired trajectory and planning goal, the kinematics model and proper referent and motive coordinates systems are set up. By making use of the result of the previous motion analysis, genetic algorithm is applied to the trajectory planning of executor. Next, the practical trajectory is simulated with the optimized parameters. Then the simulated result is also evaluated with the planning goal. The practical mechanism design and motion control of industrial robots can be carried out according to the optimized parameters.