The paper is aimed at generating optimal swing motions during the single-support phase of sagittal gait. Unlike the previous Part 1 which deals with passive motions, all joints of the biped are assumed to be active in the present Part 2. The final conditions specify an impactless heel-touch in order to avoid a destabilizing effect on the biped motion. As the biped is essentially submitted to gravity forces, the motion is generated by minimizing the joint actuating torques. Feasible motions are defined by state inequality constraints limiting joint motions, and defining foot clearance and obstacle avoidance during the swing. The optimization problem is dealt with using Pontryagin's Maximum Principle. A final two-point boundary value problem is solved by implementing a shooting method. The approach presented is illustrated by various numerical simulations applying to a seven-body planar biped which has four or five active joints during the swing phase.

It has been shown that compass-like bipeds can walk passively by gravity-induced motion. Similarly, it has been stated that the unipodal phase of human gait may be regarded as a passive motion. This paper is aimed at determining precisely to what extent the swing phase of human-like walking can be considered as a non-actuated motion. More specifically, a method is developed that makes it possible to adjust initial conditions, step length and walk speed, as well as mass and inertia distribution of a bipedal robot, in order to generate a passive swing motion. The approach is demonstrated by using a 7-link planar biped. Numerical simulations show that purely passive unipodal transferring cannot be fully satisfactory. This approach is further considered in Part 2 of the paper which consists in computing optimal actuating joint torques to create perfectly feasible motions.