Motion planning in underactuated systems with impulsive phenomenon via dynamic shaping of virtual holonomic constraints

Rhythmic motions are traditionally achieved by developing predetermined paths for the states of the space system to follow. Since these paths are obtained offline, the dynamic behavior fails to adapt to changes in environmental conditions or user command desires. The solution we propose is a new strategy called dynamic shaping, in which the paths are formed online to allow the system to create an orbit with the characteristics we need. Hereupon, this paper focuses on applying this strategy to Dynamics with One Degree of Under-actuation and Impulsive Phenomenon (DSODUIP) to adapt the characteristics of outcomes to be in line with the demands.

This research was conducted by leveraging the advantages of virtual holonomic constraints (VHCs) to establish these paths. Therefore, a novel two-level hierarchical control method is designed considering a stability criterion to avoid divergence. At the Low-Level, the controllers stabilize the output of system to follow the VHCs on the system. At the High-Level, the VHCs are modified to shape an orbit with our desired characteristic in the motion. As an illustrative example, the algorithm is implemented to adjust the average angular velocity of a devil stick and the hip velocity of a Three-Link biped robot. Their results vividly demonstrate smooth adjustments and efficient performance in achieving our desired outcomes.