Virtual constraints for the underactuated walking design: Comparison of two approaches

The virtual constraints method is used here to design and control the walking-like trajectory of the 4-link having 4 degrees of freedom: stance angle, 2 knees angles and 1 hip angle and 3 actuators only as the stance leg angle is not actuated. Two different approaches are compared. First, the well-known approach consists in setting virtual constraints as the dependencies of knees and hip angles on the stance leg angle. Therefore there are 3 virtual constraints enforced by all 3 available inputs and reducing thereby overall 4 degrees of freedom to a single degree of freedom unactuated system. Selecting suitable constraints functions, various walking-like trajectories can be designed. Secondly, this three constraints approach is compared with the alternative one developed very recently. Here, only two constraints are imposed being dependencies of knees angles on the hip angle thereby reducing the 4-link to 2 degrees of freedom system with a single actuator at the hip angle. Such a system may be naturally called as the generalized Acrobot. Comparison of both approaches is performed by numerical simulation using 4-link mathematical model of real laboratory equipement. In the future, the most suitable method would be selected for the real implementation, in particular, based on the current comparative study.