Fig. 4

Process to determine the region where the groping leg can be set. This figure shows the process in the case (\(h_\mathrm{{ref}}^i = h_\mathrm{{ref}}^j = h_\mathrm{{ref}}^k = h_\mathrm{{ref}}^\mathrm{{grp}} = 1/2\)) on \(O_\mathrm{G}-x_\mathrm{G}y_\mathrm{G}\) plane. In figure a, when three legs (position \(\varvec{p}_{i,j,k}\)) are on the ground, the admissible region of COG can be calculated as in the gray triangle, where each top point of the gray triangle is the middle point of the side of \(\triangle {\varvec{p}_i \varvec{p}_j \varvec{p}_k}\). Then, in figure b, the admissible region of the groping leg for fixed COG (position \(\varvec{p}_g\)) and a particular float leg (\(L_k\)) can be calculated as in the dark gray triangle, where the dark gray triangle and \(\triangle {\varvec{p}_i \varvec{p}_j \varvec{p}_g}\) are congruent. In figure c, the admissible region of the groping leg for all admissible COG positions (grey triangle in figure a for a particular float leg (\(L_k\)) can be calculated as in the gray trapezoid. Finally, in figure d, by repeating the same procedure for the other float legs (\(L_{i,j}\)), the admissible region of groping leg can be calculated as in the gray triangle