# Terrain Irregularity Sensing by Evaluating Feet Coordinate Standard Deviation
### Terrain Feature Identification Methods  
The most universal solution to evaluate terrain is analyses of three-dimensional images obtained using two cameras or a combination of other visual sensor combinations [8]. Such a system can extract information about surroundings or terrain using proper methods. The most significant disadvantage of visual systems is the complex algorithms and techniques needed for information extraction and the lack of such efficient methods. Furthermore, image processing is very computation-heavy, usually requiring a separate controller. These disadvantages are the main reason that vision system employment in mobile robots is limited [9; 10; 11]. However, the considerable viability of such systems has generated significant interest in improving and developing such systems. Video cameras have several advantages over other sensor systems: higher resolution, lower sensitivity to obstacle form, reflections, etc. [12]. Robots often use two video cameras as visual systems [7; 9; 12]. To obtain the depth or distance to objects, it is necessary to have two slightly offset images of the same view. Insect research led to the development of a method that allows for analyzing images using the optical flow principle [13; 14; 15]. Ref. [14] presents the optical flow method for walking robots. This method allows for noticing speed variations in two directions, Equations (1) and (2):  
\[\frac{dx}{dt}\propto\int\frac{E_{t}\Big{(}\
abla E\cdot\left[1\;0\right]^{T} \Big{)}}{\left\|\
abla E\right\|^{2}}, \tag{1}\]  
\[\frac{dy}{dt}\propto\int\frac{E_{t}\Big{(}\
abla E\cdot\left[0\;1\right]^{T} \Big{)}}{\left\|\
abla E\right\|^{2}}, \tag{2}\]  
where Equation (1) is the lateral speed, and Equation (2) is the longitudinal speed. By calculating the vertical and horizontal image point coordinate changes, it is possible to identify terrain features or irregularities. The main problem with the optical flow is the up and down flow deviations while the robot moves, even on flat terrain. Predicting and eliminating this problem is possible because these motions are periodic. Although the optical flow method allows for the detection and evaluation of obstacles and their parameters [12; 14], the received signal is very noisy, and it still struggles to detect minimal terrain features. This method is best suited for wheeled robots moving on flat roads because the received image is very stable. The most crucial task in determining terrain roughness, obstacle density, and parameters is to assess the camera image depth. Laser distance sensors for environment recognition could quickly solve this problem. Laser sensors represent the environment image as a matrix of distances to the nearest obstacles. The need to determine the distance to the nearest objects in the image is eliminated with laser distance scanners. Laser sensor measurement inaccuracies mainly depend on physical light properties, like light dispersion, reflection, absorption, etc. This method was used on a six-legged walking robot to calculate foot placement positions [16]. Finally, laser vision was even used on wheeled cars and robots to calculate speed to avoid obstacles [17; 18]. A fairly common method of surface recognition, especially in multi-legged robots, is the interaction of the robot with the surface. This method is based on changes in various robot parameters as the robot interacts with the surface. One of the most popular methods is detecting changes in the torque or current of a robot's actuators as the robot pushes against the surface, either reading data directly from the actuators themselves or from additionally installed sensors [19]. Other methods use sensors to directly detect the robot's interaction with the surface, e.g., force sensors on the robot's feet [20; 21; 22]. A recent and the most popular approach to terrain identification is machine learning. As can be seen from [23; 24; 25], there has been a significant amount of research conducted using various neural network architectures.