ARTICLE IN PRESSThe goal of the present work was assess the feasibility of using a pseudo-inverse and null-space optimization approach in the modeling of the shoulder biomechanics. The method was applied to a simplified musculoskeletal shoulder model. The mechanical system consisted in the arm, and the external forces were the arm weight, 6 scapulo-humeral muscles and the reaction at the glenohumeral joint, which was considered as a spherical joint. The muscle wrapping was considered around the humeral head assumed spherical. The dynamical equations were solved in a Lagrangian approach. The mathematical redundancy of the mechanical system was solved in two steps: a pseudo-inverse optimization to minimize the square of the muscle stress and a null-space optimization to restrict the muscle force to physiological limits. Several movements were simulated. The mathematical and numerical aspects of the constrained redundancy problem were efficiently solved by the proposed method. The prediction of muscle moment arms was consistent with cadaveric measurements and the joint reaction force was consistent with in vivo measurements.This preliminary work demonstrated that the developed algorithm has a great potential for more complex musculoskeletal modeling of the shoulder joint. In particular it could be further applied to a non-spherical joint model, allowing for the natural translation of the humeral head in the glenoid fossa.

Abstract-A double-stage feedback control structure for a double-stage mechanical system, with a single optical metrology is developed to reach nanometer accuracy at high bandwidth over large displacements. A piezoelectric stack actuator is used for fine positioning, while a permanent magnet (PM) stepper motor handles the coarse positioning.Two different control approaches are compared for driving the PM stepper motor, while a classical PID controller is designed to drive the piezoelectric actuator. Since only a single measurement device is used, the references for both control loops (fine and coarse) must be appropriately obtained. An adequate control structure including a partial observer is designed so as to take into account the influence of the fine actuator on the position estimation of the coarse actuator. The complete control mechanism and strategy ensure the tracking of the real reference with sufficient accuracy and bandwidth.

A new dynamical model of the shoulder has been developed. It consisted of eleven muscles. The glenohumeral joint is modeled as a spherical joint, allowing for three rotations. Muscle wrapping around a spherical humeral head is calculated analytically. The problem of indeterminated muscle forces is solved in two steps. First, an intermediate solution is calculated using the pseudo-inverse of the moment arms matrix providing the mapping between the muscle forces (actuators) and the generalized forces (system). In a second step the intermediate solution is modified using the column vectors of the moment arms matrix's null space in order to verify the constraints on the muscle forces. This approach of modifying the muscle forces assures that the predicted movement is followed precisely. The joint reaction force calculated by the model for abduction is comparable to results found in the litterature.

Context. The ESPRI project relies on the astrometric capabilities offered by the PRIMA facility of the Very Large Telescope Interferometer for discovering and studying planetary systems. Our survey consists of obtaining high-precision astrometry for a large sample of stars over several years to detect their barycentric motions due to orbiting planets. We present the operation's principle, the instrument's implementation, and the results of a first series of test observations. Aims. We give a comprehensive overview of the instrument infrastructure and present the observation strategy for dual-field relative astrometry in the infrared K-band. We describe the differential delay lines, a key component of the PRIMA facility that was delivered by the ESPRI consortium, and discuss their performance within the facility. This paper serves as reference for future ESPRI publications and for the users of the PRIMA facility. Methods. Observations of bright visual binaries were used to test the observation procedures and to establish the instrument's astrometric precision and accuracy. The data reduction strategy for the astrometry and the necessary corrections to the raw data are presented. Adaptive optics observations with NACO were used as an independent verification of PRIMA astrometric observations. Results. The PRIMA facility was used to carry out tests of astrometric observations. The astrometric performance in terms of precision is limited by the atmospheric turbulence at a level close to the theoretical expectations and a precision of 30 µas was achieved. In contrast, the astrometric accuracy is insufficient for the goals of the ESPRI project and is currently limited by systematic errors that originate in the part of the interferometer beamtrain that is not monitored by the internal metrology system. Conclusions. Our observations led to defining corrective actions required to make the facility ready for carrying out the ESPRI search for extrasolar planets.