The robot obstacle avoidance problem diagram 1 in question D is an 800×800 plane scene diagram. There is a robot at the origin o (0,0), which can only move in the plane scene. There are 12 areas with different shapes in the picture, which are obstacles that robots cannot collide with. The mathematical description of the obstacle is as follows: the name of the numbered obstacle, the description of the lower left vertex coordinates, the side length of 1 square (300,400), the center coordinates of 2002 (550,450), the base length of a parallelogram with a radius of 703 (360,240) and 65430. Top left vertex coordinate (400,330) 4 triangle (280, 100) top vertex coordinate (345,210) and bottom right vertex coordinate (4 10, 100)5 square (80,600. The lower right vertex coordinate (235,300) 7 rectangle (0,470) is 220, the width 608 parallelogram (150,600) is 90, and the upper left vertex coordinate (180,680) 9 rectangle (370,680) is 60. 600) side length 130 1 1 square (640,520) side length 80 12 rectangle (500, 140) length 300, width 60 in figure/kloc-0. It is stipulated that the walking path of the robot consists of a straight line segment and an arc, in which the arc is the turning path of the robot. Robots can't turn on a broken line. A turning path consists of an arc tangent to a straight path or two or more tangent arc paths, but the radius of each arc is at least 10 units. In order not to collide with obstacles, it is required that the shortest distance between the robot walking line and obstacles is 10 units, otherwise collision will occur, and if collision occurs, the robot cannot complete walking. The maximum speed of a robot walking in a straight line is one unit/second. When the robot turns, the maximum turning speed is, where is the turning radius. If this speed is exceeded, the robot will roll over and cannot walk. Please establish the mathematical model of the shortest path and the shortest time path for the robot to reach another point from one point in the area. For the four points o (0,0), a (300,300), b (1 00,700) and c (700,640) in the scene diagram, the concrete calculation is as follows: (1) The robot starts from o (0,0). Note: It is necessary to give the coordinates of the starting point and ending point of each straight line segment or arc in the path, the coordinates of the center of the arc, and the total distance and time for the robot to walk. Figure 1 800×800 plane scene map