Leg-like motion with an under-actuated two DOF linkage using differential flatness

Biped walking is an application where following a predefined trajectory is entirely not critical as long as the trajectory allows the foot to clear the ground. Since a biped need not follow a trajectory exactly, instead of using a fully actuated leg an underactuated leg might also serve the purpose. The ability of a particular underactuated system to generate leglike motion is investigated in this paper. The system studied is a two DOF gravity balanced linkage. Each of the two joints has a torque spring attached to it. The spring at the knee joint ensures controllability of the system and the equilibrium position of the hip spring is taken as the input. The energy consumption of this underactuated system is compared with the energy consumption in a fully actuated case. Planning is done using the differential flatness property of the system with numerical optimization as a tool to generate flat output trajectories