In this paper, stable hopping of a one-legged, articulated robot with a flat foot is investigated. The robot has a special feature that before taking off, it goes through an underactuated phase in which the foot rotates about the unactuated toe on the ground. By having the underactuated phase, the robot can perform stable human-like hops with longer hopping distances. To devise a systematic trajectory design methodology for the robot, its dynamics including the ground-foot impact and the hopping constraints are carefully studied. An optimization procedure is then proposed to plan the feasible actuated trajectories which not only meet specific performance requirements but also attain certain optimality with respect to actuation energy. The hopping strategy and the optimal trajectories are verified by simulations and hardware implementation. Experiments indicate that the robot not only can stably perform hops with different hopping distances on the level ground but also can successfully hop up/down staircases.

In this paper, a semi-active biped which combines the merits of both powered and passive bipeds is proposed. The semi-activeness of the biped is due to the fact that, during most of a walking cycle, only half of the joints are actuated, and the other half remain unactuated, but have passive joint springs to induce their motions. To devise a systematic design methodology for the biped, its dynamics as well as the walking constraints are carefully studied. Furthermore, an optimization procedure is proposed to compute the optimal trajectories for the actuated joints and spring constants which can lead to minimum energy consumption. The feasibility of the proposed biped is verified by hardware implementation. Experiments indicate that the semi-active biped consumes 80% less the electrical power of the powered biped that performs the same gait and is more energy-efficient than several state-of-the-art bipeds.