A Geometrical Approach to Compute Upper Limb Joint Stiffness

Exoskeletons are designed to control the forces exerted during the physical coupling between the human and the machine. Since the human is an active system, the control of an exoskeleton requires coordinated action between the machine and the load so to obtain a reciprocal adaptation. Humans in the control loop can be modeled as active mechanical loads whose stiffness is continuously changing. The direct measurement of human stiffness is difficult to obtain in real-time, thus posing a significant limitation to the design of wearable robotics controllers. Electromyographic (EMG) recordings can provide an indirect estimation of human muscle force and stiffness, but current methods for the acquisition of the signals limit their use and efficiency. This work proposes a hybrid method for the estimation of upper limb joint stiffness during reaching movements that combines EMG-driven muscle models and constrained optimization. Using these two stages process, we estimated an optimal joints' stiffness bounded in a physiologically sound variability range. This information is crucial when designing exoskeletons user interfaces in which the limb stiffness is an integral part of the control loop. Point-to-point human reaching movements were analyzed to reconstruct the joint stiffness of the upper limb. An accurate 3D model of the arm, encompassing all bones from the hand to the scapula and the majority of the upper limb muscles, was developed to represent the sliding center of rotation of the joints. A well-posed parallel mechanism between the skeleton and the configuration of the tracking markers was implemented. Thus, the muscles' force and joint stiffness were calculated using a generalized pseudo-inversion of the Jacobian transformation between the muscles and Cartesian Space. The maximal and minimal forces exertable by the muscles were set as the boundary condition for the generalized pseudo-inverse by means of a state-of-the-art muscle model.