Decomposition of a Parallel Cascade Model of Ankle Stiffness Using Subspace Methods

Joint stiffness, defined as the relation between the angular position of a joint and the torque acting about it, can be used to describe the dynamical behavior of the human ankle during posture and movement. Joint stiffness can be separated into intrinsic stiffness and reflex stiffness, which are modeled as a linear system and a Hammerstein system, respectively. A two-pathway parallel cascade model, with the intrinsic stiffness on one pathway and the reflex stiffness on the other, can be used to describe the joint stiffness. In this paper, we present a new method to separate the torque from each pathway from the total torque measurement. A subspace based system identification method is used to estimate the dynamics of each pathway directly from measured data without iteration. Simulation studies demonstrate that the method produces accurate results without the need of iteration