In this paper, aiming at the planar motion characteristics of wheeled robots, the Red Green Blue Depth Camera (RGBD camera) was used as an image acquisition device to reduce the motion of wheeled robots to two-dimensional plane processing, which simplified the calculation method of visual mileage of planar wheeled robots. In addition, according to the two-dimensional motion characteristics of the robot camera, the contour constraint condition of feature point matching between frames was proposed, and the linear constraint condition was proposed by linearizing the motion equation of the camera between frames. The research showed that the contour constraint condition and linear constraint condition could be used to screen the mismatched feature points, this condition could not only screen the mismatched point pairs of color images, but also screen the matching point pairs with correct color image matching but large depth error, which provided high quality matching point pairs for inter-frame motion estimation of visual odometer. Finally, the filtered matching point pairs were reduced in dimension and combined with the two-dimensional Iterative Closest Point (ICP) algorithm to estimate the trajectory of the robot camera. The experimentation results showed that compared with the original three-dimensional ICP algorithm, the combination of contour constraint condition, linear constraint condition and two-dimensional ICP algorithm could significantly improve the computational speed of visual odometry.