The proposed control method uses an adaptive feedforward-based controller to
establish a passive input-output mapping for the CDPR that is used alongside a
linear time-invariant strictly positive real feedback controller to guarantee
robust closed-loop input-output stability and asymptotic pose trajectory
tracking via the passivity theorem. A novelty of the proposed controller is its
formulation for use with a range of payload attitude parameterizations,
including any unconstrained attitude parameterization, the quaternion, or the
direction cosine matrix (DCM). The performance and robustness of the proposed
controller is demonstrated through numerical simulations of a CDPR with rigid
and flexible cables. The results demonstrate the importance of carefully
defining the CDPR's pose error, which is performed in multiplicative fashion
when using the quaternion and DCM, and in a specific additive fashion when
using unconstrained attitude parameters (e.g., an Euler-angle sequence)