The Application Of Differential Evolutionary Algorithms In Trajectory Planning Of Industrial Robot

Robot's trajectory planning is belonged to the bottom planning of robot design, which is based on the kinematics of robot's hand, discussing the trajectory and its generation during robot's motion. Trajectory is referred to the displacement, velocity and acceleration of the robot during its movement. The trajectory planning is to calculate the anticipative motion trajectory according to a certain task. And the time-optimal trajectory planning optimize the joint trajectory of a robot by minimizing the traveling time so that the traveling time of a robot's hand between two points or along a specified path would be the minimum solution.As a newly developed evolutionary algorithm, Differential Evolution (DE) is simple to understand and to implement, has only a few control variables and adapts a random, parallel, global searching method which makes DE more efficient, parallel and robust. DE has proven to be promising candidate for the optimization problem. So far, DE has been widely applied in many areas such as constraint optimal problems, Neural Networks optimal problems, the optimal design of fuzzy controller, filter design and so on.Due to its greedy search strategy, DE could get a faster convergence rate. But on the other hand, the faster convergence rate also leads to a higher probability of falling in a local optimum, because of the reduction of diversity of the population in the mean time. To overcome this shortcoming, a modified DE (MDE) is developed in this paper, which introduces two new operations, acceleration operation and migration operation, and also including an adaptive crossover operation. The MDE is trying to maintain the diversity of the population as well as the rate of convergence.On summarizing the relative research results of time-optimal trajectory planning problem of robot, this paper adopts a spline function of a quadratic polynomial plus a cosine function as the joint trajectory, and applies the MDE to solve the optimum time interval sequence of the robot motion. Under the non-linear kinematical constraints, the planned joint trajectories are continuous not only in the displacements, the velocities, or the accelerations of the joints but also in the jerk (the rate of change of the acceleration). In addition, the traveling time a robot spends between two points or along a specified path is the minimum one. On comparing the optimization result by the method of MDE with the method of GA and traditional DE, it proves that the MDE is feasible and efficient.This paper is organized as follows:1. A modified Differential Evolutionary (MDE) algorithm is presented in this paper. The MDE is based on the traditional DE which adopts an adapted crossover operator DE and introduces two new operators, acceleration operator and regeneration operator. An adapted crossover operator can maintain the population diversity during the initial phase of optimization, and have a good ability of local search during the late phase; when the mutation and crossover operations can not make further improvement on the best fitness at the present population, the acceleration operator will be applied to push the best individual towards obtaining a better one; the regeneration operator is used to regenerate the current population when the population diversity is too small to guarantee the global search ability of MDE.2. The kinematics model of KUKA KR210-2 type industrial robot is established using D-H method, and the equations of forward and inverse kinematics of the robot are also derived in this paper. Then a simulation model in computer is established to do the further research on the trajectory planning.3. This paper adopts a new kind of spline function which consists of a quadratic polynomial and a cosine function, ? , to construct the joint trajectory of the robot. The derivation of the spline function is presented and also its constraint equation so that the optimal function for the time-optimal trajectory planning problem of the robot can be confirmed. 4. This paper applies Genetic Algorithms, traditional Differential Evolutionary Algorithms and modified Differential Evolutionary Algorithms in the time-optimal trajectory planning problem, which takes KUKA KR210-2 type industry robot as example. On comparing the results of the optimization, the MDE proves to be a efficient optimization method, better than the GA and traditional DE.