The Research On Optimal Planning Of Industrial Trajectories

The optimal trajectory planing is one of the problem of the optimal control.Infact,planning is a technology to solve a problem, That is starting at the initial,with aseries of operators,get the target status,can solve the problem.Among these strategies on trajectory planning for industrial robots,With relationto the working efficiency,time-optimal trajectory planning of robot,is raised first.Itsaim is minium the motion time.Planning of robot trajectory using energetic criteriaprovides several advantages.On the one hand,it yields smooth trajectories easy totrack and reduce the stresses to the actuator and to the manipulator structure.Moreover,saving energy may be very important in several applications,such as thosewith a limited capacity of the energy source.Without the two criteria,there are jointjerk and joint accelerations and the manipulability measure.But none of literaturesconsidered all the criteria.In this paper,we consider all the objective fuctions in acombined manner to get all the benefits.This paper is organized as follow:(1)With the research on Multi-objective Optimization Problem,using two EAAlgorithms-NSGA-ⅡAlgorithms，DE Algorithms to solve the problem.(2)With the research on the kinematics and dynamics of robot,formulate the robotmodel.At last taking STANDFORD robot as example,structure its model.(3)The cost function is a weighted balance of transfer time,mean average ofactuators power,joint jerks and joint accelerations,singularity.(4) In this paper we use a clamped cubic spline curves to construct the jointtrajectory of the robot.The derivation of the spline function is presented and also itsconstraint equation.(5) This paper applies NSGA-ⅡAlgorithms，DE Algorithms in the minimum costtrajectory planning problem,which takes STANDFORD robot as example. Comparingthe results of the two optimizations.