The effects of constraint curvature on projective and set stabilization controllers

Virtual holonomic output constraints define a set in the output space of a robot to which the end-effector should be confined. We propose the use of set stabilization for implementing virtual constraints, conducting analyses and experimental comparisons between existing control schemes and a set stabilization controller to justify our choice. The existing methods combine geometric projections and PD control, which ignores the higher-order properties of the constraint like curvature. The set stabilization method inherently incorporates constraint curvature information, allowing it to decouple the dynamics towards and along the set. It is shown that the two methods are equivalent on a line constraint, but that only the set stabilization method simultaneously guarantees asymptotic stability on a circle.