Ball and plate system,BPVS-JLU Ⅱ,researched and developed independently byControl Theory and Intelligent System Laboratory of Jilin University, is the secondgeneration of ball and plate system which is a kind of typical multivariable nonlineardynamic systems.Its structure is complex,there are certain uncertainty and the characteristicsof a typical nonlinear system, which can inspect all kinds of control algorithm and trajectoryplanning algorithm.There is high research value in the system.For the ball and plate system,a multi-objective path planning algorithm is presented inthis paper,the main contents are as follows:(1) The multi-objective particle swarm optimization algorithm,is selected as multi-objective path planning algorithm of ball and plate system. During the initialization of thealgorithm, shouldn’t like ordinary multi-objective optimization algorithm,evaluatedrandomly particle’s position.In other words, the starting position and target of particlesposition are known beforehand,but the paths of particles from the starting position to thetarget position are unknown. In order to make the path diversity in the process of operation,this paper adopts the method of the random initial velocity of particles.(2) Selection of fitness function is more important, this step provides the interface ofoptimization algorithm and practical problems. Choose a function which can moreaccurately use the size of the function value to reflect the merits of the solution.There arethree optimization goals in the ball and plate system: the length of the path, the risk of thepath,the time of the path. Three optimization goals are different, in this paper, according tothe characteristics of the three goals, mathematical models are established respectively.(3) In the ball and plate system with obstacles and traps, the position of the obstaclesand traps is random,for different environment, we need to consider three targets, andaccording to the characteristics of the environment to select weights properly. The threetarget weights should be adjusted according to the environment. On the basis of determiningplanning path, in order to obtain a better path we can get more detailed regulation on thebasis of the original weight.(4) Establish a multi-objective path planning scoring system. For the multi-objective path planning algorithm, in order to meet the requirements of different production andliving,the different optimization indexex are proposed. On this basis of the above, accordingto multi-objective optimization problems, we set up a ball and plate score standard tocompare various multi-objective path planning algorithm.It has been the difficulty ofmulti-objective optimization study to evaluate the optimization of pareto solution set,it isdifficult to find a suitable and effective quantitative evaluation criterion.Some veryprofessional formulae are proposed by researchers,some even from the perspective ofmathematics, to evaluate the stand or fall of algorithm. In this paper, from the perspective ofscoring criteria, we give a multi-objective path planning scoring rules for the ball and platesystem.In conclusion,the main research goal of the paper is a multi-objective path planningproblem of the ball and plate system. Based on grid map, we use the multi-objective particleswarm optimization algorithm to plan the path for unconstrained object in complexenvironment. For the three objective functions,this paper gives the mathematical expressionof minimizing the objective function, the selection of the dynamic weighting is relativelyflexible, rather than average distribution value. We establish grading rules system,mark themulti-objective path planning algorithm used in the ball and plate system. By scoring,wecan come to the conclusion that, for the multi-objective path planning problem of the balland plate system,using multi-objective particle swarm optimization algorithm can playcomparatively well path planning. |