机器人避障问题

摘要：本文要解决机器人避障行走的最短路径和最短时问问题．主要研究了在一个区域中有12个不同形状的小区域是机器人不能与之发生碰撞的障碍物，机器人从区域中的0点出发避开各种障碍物到达最终目标点的最短路径和最短时问数学模型．我们对问题1采用初等数学中的解析几何和三角函数知识，建立基本线圆结构求路径的数学模型，分内公切线、外公切线和经过定点的动圆三种情形讨论，对动圆我们采用将圆形障碍物的半径增加r，或把切线转角用由定圆心到定点连线的夹角近似代替，都分解为基本线圆结构数学模型来求解，用穷举法结合matlab编程算出可能的走法的总路径的最小值．对问题2我们采用建立时间与行走转弯半径的数学模型，用搜索法结合matlab编程，求出最短时间．结果是：㈣的最短路径为471．0372．D→B的最短路径为858．6000．O→C的最短路径为1093．7000．O→A→B→C→O的最短路径为2783．7000O→A．的最短时间为94．5649．

Onthe Problems of Robots Avoiding Obstacle

This paperwants to solve the problems of the shortest path and time for robots avoid- ingobstacle. Thereare 12 s=alldifferent shapes in aregion that arobot cannot occurcollisionwith them, it mainly researches the shortest path and the shortest time=athematical model for the robot. For question 1, we use analytic geometrY and trigonometric knowledge of elementarymathematics, set up a line and round structure mathematical model, we discuss it from three cases the internal common tangent, external common tangent, and the circle. For the circle, we will increase the radius of the circuiarobstacler, orsubstitutethe tangent angleby centeringangle, break it down intobasic line and round structure to solve a=athematicalmodel, using exhaustivemethod combinedwithMATLABpro- gr~ingtocalculate theminimumvalueofthetotal pathofpossiblemoves. Forquestion2, we set upa timeandwalkingradius=athematicalmodel, usingthe searchmethod combinedwithMATLABprogramming tocalculatethe shortest time. Theresults： the shortest pathofO→A is471. 0372, O→B is858. 60000, O→C is1093.70000, O→A→B→C→O is2783.70000, the shortest timeofO→A is94.5649.