Hexapod model and leg numbering.

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... a hexapod system have legs numbered with integer numbers as shown by Fig. 2. In order to realize locomotion in the desired direction, as shown by the red line of Fig. 2, it is essential to move the legs to maintain the desired locomotion strategy. Let the position of the i-th leg be represented by the vector p i , with i ∈ [1,6]. It is possible to render gait strategies by computing offsets d i that modify the ...

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... a hexapod system have legs numbered with integer numbers as shown by Fig. 2. In order to realize locomotion in the desired direction, as shown by the red line of Fig. 2, it is essential to move the legs to maintain the desired locomotion strategy. Let the position of the i-th leg be represented by the vector p i , with i ∈ [1,6]. It is possible to render gait strategies by computing offsets d i that modify the position of each leg with respect to their initial position p o i , and let the inverse ...

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... m i is the magnitude of the offset of the i-th leg in the plane as a function of the normalized time u ∈ [0, 1), h i is the height offset, and θ is the desired hexapod locomotion orientation in the plane. Fig. 2 shows the direction of the desired locomotion, and considering the orientations of the x-y axis, θ = 0 • in Fig. 2. The value of m i and h i can be computed from the normalized time u, as follows: ...

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... m i is the magnitude of the offset of the i-th leg in the plane as a function of the normalized time u ∈ [0, 1), h i is the height offset, and θ is the desired hexapod locomotion orientation in the plane. Fig. 2 shows the direction of the desired locomotion, and considering the orientations of the x-y axis, θ = 0 • in Fig. 2. The value of m i and h i can be computed from the normalized time u, as follows: ...

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... order to simulate the behavior of a hexapod robot under dynamic considerations, we used the Coppelia Simulation software [19]. Fig. 2 shows the structure of the robot used in our study, for which the hexapod is rotationally symmetric, each of the legs has three degrees of freedom, and the legs are labeled with an index, such as 1, 2, ..., ...

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... we used gradient-free optimization heuristics to study the feasibility of rendering gait recoveries with a low number of fitness function evaluations. For simplicity and without loss of generality, we set the hexapod system to follow according to a desired orientation in the plane as shown by the red line in Fig. 2, that is θ = 0 • . Realizing the locomotion strategies in different orientations is straightforward. Studying the trajectory tracking for non-linear paths is out of the scope of this paper. Also, we let the step amplitude A = 0.11E, and the step height H = 0.02E be fractions of the overall size factor E or the hexapod ...

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... On the other hand, when leg 5 and leg 6 become malfunction, the hexapod tends to move towards the right side in a clock-wise fashion. This phenomenon is due to leg 2/leg 3 (leg 5/leg 6) being located on the left (right) side of the plane that divides the hexapod's x-axis, as shown in Fig. 2; thus, the weight and friction with the floor make the system relatively ...