# Terrain Irregularity Sensing by Evaluating Feet Coordinate Standard Deviation
## 6 Conclusions, Discussion, and Future Work  
This paper presents a method to evaluate terrain roughness by calculating all the robot's feet \(z\) coordinate standard deviation. This method is inspired by humans' ability to sense their limb position in space without visual feedback. The simulation results show that the feet standard deviation is only affected by local terrain roughness and not by large slopes, proving this method's suitability for terrain roughness evaluation. We also present terrain roughness categorizing based on the robot's size parameter (obstacle clearance). These categories could help select different gaits for different terrains. We present the simulation results that show that the \(SD\) value only depends on terrain roughness and is not influenced by large terrain slopes. The experiments were conducted with real robots to test adaptive locomotion and evaluate terrain standard deviation. The experimental results showed that adaptive robot locomotion needs active foot coordinate corrections. Also, we present experiments with obstacles that provide insights into how the standard deviation changes while the robot is walking on varying terrain using different gaits. Although only a small amount of varied terrain was used, the experiments provided adequate results for method evaluation. The feet \(z\) coordinate standard deviation could be used for terrain roughness estimation as the experimental results showed that the standard deviation changes according to terrain roughness variance, increases when the robot starts to walk on uneven terrain, and decreases when the robot walks on flat terrain. The terrain roughness from robot feet \(z\) coordinates can be estimated by a minimum 60 \(\pm\) 10% accuracy. By calculating the feet \(z\) coordinate standard deviation, the terrain roughness estimation accuracy can be increased by about 25% compared to feet \(z\) coordinate inaccuracies. The accuracy of the terrain roughness evaluation is presumed to be influenced by mechanical robot properties (servomotor reducer freedom, limit switch pretravel, construction elasticity, etc.) and robot foot slippage. The feet placement accuracy was increased using feet \(z\)  
Figure 11: Standard deviation variation during robot locomotion over a rectangular obstacle using different gaits with deviation compensation using robot body inclinations. coordinate error compensation according to the robot's body inclinations measured with an accelerometer. Estimation accuracy may also be distorted by high foot \(z\) coordinate variance. For example, suppose the robot encounters just one very deep (or high) obstacle and puts one foot on it. In that case, the standard deviation may change drastically, giving a wrong roughness evaluation even though the other five feet are on flat terrain. A solution to avoid such instances could be to evaluate roughness after several consequent steps by averaging the standard deviation. But in this case, the terrain roughness evaluation would be lagging. But in the case of just one small obstacle interacting with only one foot for one step, the \(SD\) value change would be visible, although too little to influence the terrain evaluation. Therefore, this method would be more suitable for use in combination with other terrain evaluation systems (visual, LIDAR, SLAM, etc. ), since it does not require high computational power or additional hardware and uses existing information. Also, the experiments showed that different robot gaits perform adequately when estimating terrain roughness. While walking using different gaits, the standard deviation variation remained the same, thus meaning that our method does not depend on walking gait, so it can be used with any walking pattern. In Figure 10, some flanks and overshoots can be noticed that appear due to possible robot feet slippage on the surface, inaccuracies in measuring feet coordinates, etc. We should mention that these inaccuracies are smaller than the overall terrain profile change.