Fig. 6

Geometrical relations of leg-grope for the simulation and experiments. Each figure shows the relation in the case of the groping leg a \(L_2\), b \(L_1\), c \(L_3\) and d \(L_4\) on \(O_\mathrm{G}-x_\mathrm{G}y_\mathrm{G}\). For one walking cycle, the robot moves its COG and swings four groping legs \(L_2\), \(L_1\), \(L_3\) and \(L_4\) in sequence by following these geometrical relations. In each graph (a–d), an arrow and a red rectangle represent the moving direction of the robot and the shape of the robot body, respectively. The blue square point is the targeted point of the groping leg, and the other three points (two black circles and black triangle) represent the contact points of the other three legs. The biggest black triangle region represents the supporting leg polygon, except for the groping leg. The green triangle region represents the admissible region of the COG \(\pi _g\), and the green asterisk point represents the targeted position of the COG. The blue triangle region represents the admissible region of the position of the groping leg for the COG \(\pi _{\mathrm{{grp}},g}\), where the float leg is shown by the black triangle point