Mathematical Modeling and Rolling Motion Generation of Planar Seven-link Robot That Forms Passive Closed and Active Open Chains

This paper investigates the mathematical modeling and basic motion properties of planar seven-link robots that forms passive closed and active open chains. The passive closed model is formed by connecting seven rigid frames via seven viscoelastic joints, and the active open model is formed by connecting them via actuated joints. The former is a convex heptagonal model and can exhibit passive-dynamic rolling on a gentle downhill, whereas the latter virtually forms a forward-leaning octagonal shape by controlling the six relative joint angles. In the first half of this paper, we describe the model assumptions and develop the mathematical equations of motion and collision of the passive closed model, and numerically analyze the motion characteristics by changing the slope angle while checking the conditions necessary for stable motion generation. In the second half, we outline the active open model, develop the PD control system, and numerically analyze the motion characteristics by changing the target angle parameter that controls the degree of forward lean of the virtual octagon.