基于线性规划下的机器人最优避障路径模型

Optimal Obstacle Avoidance Path Model for Robots Based on Linear Programming

近年来随着科技的快速发展,机器人技术被广泛地应用于家庭服务、工业指导、军事作业等多个领域。本文运用栅格建模以及线性规划模型,建立了机器人从区域中一点到达另一点的避障最短路径和最短时间路径的数学模型。其中最短路径模型给出了机器人行走的原则,为机器人可能路径的选择提供了依据,同时讨论了行走路径中机器人直线段长度和弧线段长度的计算方法,以及直线与圆弧切点坐标的计算方法,为后续问题的解决提供了很好的工具;最短时间模型以行走时间最短为目标,找出了最合适的转弯圆心和半径,然后通过建立线性规划模型求得了最优解。

With the rapid development of technology in recent years, robotics is widely used in many fields such as home services, industrial guidance, and military operations. This paper uses raster modeling and linear programming model to establish the mathematical models of the shortest path and the shortest time path for the robot to avoid obstacles from one point in the region to another point—the shortest path model gives the principles of robot walking and provides the basis for the selection of possible paths for the robot;it also discusses the calculation methods of the lengths of the straight-line and arc segments of the robot in the walking path, as well as the coordinates of the tangent points of the straight line and the arc, which provides a good tool for solving follow-up problems;the shortest time model takes the shortest walking time as the goal, finds out the most suitable turning circle center and radius, and then finds the optimal solution by establishing a linear programming model.