5. Simulation results

#### 5.1 Control of the robot walking on a planar, stable, and not vibrating surface

First, we considered the robot walking at an oblique direction on a planar, stable, and not vibrating ground (i.e., zGð Þ¼ x, y, t 0, ΔxGðÞ¼ t ΔyGðÞ¼ t ΔzGðÞ¼ t 0, and αGðÞ¼ t βGðÞ¼ t γGðÞ¼ t 0). In the presented simulations, we considered initial, regular, and terminal phases of gait [10]. In turn, we applied non-zero excitations of all six degrees of freedom of the robot's trunk, i.e. ΔxRð Þt 6¼ 0, ΔyRð Þt 6¼ 0, ΔzRð Þt 6¼ 0, αRð Þt 6¼ 0, βRð Þt 6¼ 0, γRð Þt 6¼ 0. Configurations of both the robot's body and all its legs captured in regular time intervals are presented in Figure 3. In the considered case, the robot moves in an oblique direction with respect to the direction determined by the robot's (x'-) axis at the initial time. Changing the position of the whole robot is realized by the appropriate control of individual joints of the robot's legs. In turn, Figure 4 presents fluctuations in displacements and velocities of the robot, both in the forward (x-) and lateral (y-) direction. As can be seen, the presented time histories can be divided into three ranges, which correspond to the initial, regular, and terminal phases of the robot locomotion, respectively. Regardless of the ΔxRð Þt , ΔyRð Þt , ΔzRð Þt , αRð Þt , βRð Þt , γRð Þt controlling all six degrees of freedom of the robot's trunk, both x- and y- components of the robot's speed change linearly. Namely, in the initial phase of the locomotion process, both of these speeds increase linearly from zero to the maximum values. Then, in the rhythmic phase of gait, these speeds are constant over time. In turn, in the terminal phase of the locomotion process, these speeds decrease linearly from maximum values to zero. In the same time, linear deviations, as well as rotations of the robot's body in the global coordinate system, are accurately reflected based on the functions ΔxRð Þt , ΔyRð Þt , ΔzRð Þt , and αRð Þt , βRð Þt , γRð Þt , respectively. These simulations show that the considered robot can be used as a fully controlled walking Stewart platform. As a result, we solved the problem of controlling both the direction of the movement of

On the Controlling of Multi-Legged Walking Robots on Stable and Unstable Ground DOI: http://dx.doi.org/10.5772/intechopen.90208

#### Figure 3.

The chosen configurations of the investigated octopod robot walking on a planar surface, controlled independently by deviations ΔxRð Þt , ΔyRð Þt , ΔzRð Þt and rotations αRð Þt , βRð Þt , γRð Þt of the robot's trunk.

#### Figure 4.

Time histories of the displacements x tð Þ,y tð Þ of the robot's center (a) and velocities vxð Þt , vyð Þt of the robot's center (b) in the forward and lateral directions.

the robot and the control of all six spatial degrees of freedom of the robot's body, namely, independent controlling of three deviations and three rotations along and around three different axes, respectively. As it was mentioned above, these control possibilities can be useful in the natural environment of the robot, where the navigation and obstacle avoidance are especially important.

#### 5.2 Control of the robot standing on not vibrating and unstable ground

In this subsection we considered the problem of control of the robot on not vibrating but unstable ground. Figure 5 presents configurations of the robot standing on unstable ground (i.e., zGð Þ x, y, t 6¼ 0), captured in regular time intervals. To better illustrate the process of controlling individual legs of the robot on unstable

Figure 5. Configurations of the investigated hybrid octopod robot on unstable ground, captured in regular time intervals.

ground, we assumed that ΔxRðÞ¼ t ΔyRðÞ¼ t ΔzRðÞ¼ t 0 and αRðÞ¼ t βRðÞ¼ t γRðÞ¼ t 0. As a result, we can observe the process of stabilizing the linear and angular positions of the robot, when the supporting ground becomes unstable. As we can see, at any time, the robot is supported by all eight legs, through the appropriate changing of the configurations of its all legs, depending on the changes of the ground. It has a positive effect on the robot's stable position. Concluding, it should be emphasized that the presented control algorithm also works for ΔxRð Þt , ΔyRð Þt , ΔzRð Þt 6¼ 0 and αRð Þt , βRð Þt , γRð Þt 6¼ 0. As a result, the considered construction can play a role of a mobile Stewart platform also on unstable ground.
