## 2 Methods and Materials
### CoT Optimization Using Red Fox Optimization (RFO) Algorithm
To evaluate the efficiency of our hexapod robot, we compared its CoT with different walking robots and micro-robots (Table 1): medium-sized high mobility hexapod robot RHex, Gregor I six-legged robot, a resilient high-speed hexapod robot DASH, tiny quadruped robot MEDIC (Millirobot Enabled Diagnostic of Integrated Circuits), micro hexapod robot HAMR2 from Harvard University, and larger hexapod robot AMOS (Advanced Mobility Sensor Driven-Walking Device). Low CoT value for the HexaV4 robot was obtained due to the good trade-off between the robot's mass, current consumption, and movement speed. In our case, the servos' current was minimal during all experiments (each servo can consume up to ~0.9 A, but the total current consumption of the robot did not exceed 3.5 A). ### Maintaining Minimum Energy Consumption

The algorithm shown in Figure 2 was implemented and tested with the hexapod robot several times with and without an additional delay time between speed changes. The speed was increased by the algorithm and the current was measured throughout the tests. The example of the results of the algorithm test is shown in Figure 6. We also varied the delay time to obtain better intervals for calculating the average current. No additional load was used during the experiments. The current time diagram of the full program run without the delay is shown in Figure 7. Due to a large amount of noise, a filter was applied. We used smooth signal processing and the percentile filter method (50%) with 3 points of the window. By calculating the average current for each interval, we managed to obtain power consumption dependence on the speed of a full program run with a gait switching algorithm. We can see from Figure 7 that power consumption changes from ~12 W to ~24 W. The same results and curve form can be seen in Figure 3, where each result was obtained by a separate experiment. This demonstrates that our proposed method leads to power consumption minimization. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Name** & **Rhex** & **Gregor I** & **DASH** & **MEDIC** & **HAMR2** & **AMOS** & **HexaV4** & **Big Dog** \\ \hline Mass (kg) & 7 & 1 & 0.0062 & 0.0055 & 0.002 & 5.4 & 1.5 & 110 \\ COT & 3.7–14 & 70 & 14.7 & \textgreater{}12,000 & 128 & 3.4–11.7 & 5.75 & 15 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Cost of transport of different walking robots: RHex hexapod robot [56]; Gregor I hexapod [57]; DASH hexapod [58]; MEDIC quadruped robot [59]; HAMR2 hexapod microrobot [42]; AMOS hexapod robot [50]; HexaV4 hexapod robot; Big Dog robot [60]. Figure 6: Current-time diagram, achieved by varying robot speed and gaits. Black curve—filtered experimental data; red line—exponential approximation. ### Maintaining Minimum Cost of Transport Using Red Fox Optimisation

The algorithm shown in Algorithm 1 was implemented and tested with the hexapod robot several times to calculate the average CoT value. No additional load was used during the experiments. The variable search space and corresponding CoT values are shown in Figure 8. The application of the RFO algorithm allows finding an optimal combination of gait step length and gait resolution for minimal CoT. In our experiment, the optimal solution found corresponds to the step length of 100 mm, resolution of 12 mm, and wave gait type. ## 4 Discussion and Conclusions

The problem of high energy consumption has always limited the wide-spread use of multi-legged walking robots. The benefits to be achieved by rising task time without upgrading the power supply unit mean that optimization of energy efficiency is an area of significant importance. In this paper, we analyzed and proposed a method for optimizing the hexapod robot's energy consumption. We performed experiments with different gaits and speeds with no

Figure 8: Comparison of Cost of Transport upon gait type, gait step length, and resolution. Figure 7: Influence of gait switching on energy consumption. Speed for switching from wave gait to tripod gait is equal to 0.046 m/s. load, 1.16 kg, and 2.9 kg loads.