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.

Analysis of exclusively-kinetic two-link underactuated mechanical systems is undertaken in this paper. It is first shown that such systems are not full-state feedback linearizable around any equilibirium point. Also, the equilibrium points for which the system is small-time locally controllable (STLC) is at most a one dimensional submanifold. A concept less restrictive than STLC, termed the small-time local output controllability (STLOC) is introduced, the satisfaction of which guarantees that a chosen configuration output can be controlled at its desired value. It is shown that the class of systems considered are STLOC, if the inertial coupling between the input and output is non-zero. Also, in such a case, the system is nonminimum phase (NMP). An example section illustrates all results presented.

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Abstract:A simple output feedback PD controller is proposed that stabilizes a nonlinear crane. Global asymptotic stability is achieved at any equilibrium point specified by the controller. The control scheme relies solely on the winches position and velocity and hence no cable angle measurement, or no direct measurement of the load position, is needed. The controller can be extended to many different kinds of existing cranes.

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The synthesis of shoulder kinematics, either for simulation in a model or imitation in a robot, is a challenging task because of the contact between shoulder blade and ribcage. As the shoulder moves, the shoulder blade glides over the ribcage. In kinematic models used to predict musculoskeletal kinetics, the contact is included using equality constraints, creating interdependencies between the kinematic coordinates. Such interdependencies make motion planning complex. Robotic mechanisms often imitate the shoulder's end-effector kinematics but not the gliding shoulder blade architecture It is only recently that a gliding shoulder blade architecture has been mechanically achieved. The goal of this paper is to propose a novel kinematic parallel model of the shoulder that includes the contact without using constraints. Mechanically, the gliding architecture is replaced with a parallel architecture. A shoulder model with constraints is used to build the parallel model. It is shown that replacing the contact constraints with kinematically equivalent kinematic chains, leads to a 2-3 parallel platform model of the shoulder. The scaffold model and parallel model parameterisations of the shoulder's kinematics are analysed in terms of the forward kinematic map. The coordinate spaces of the kinematic maps are analysed, resulting in three minimal parameterisations. Each minimal parameterisation uses a set of coordinates equal to the number of degrees of freedom. The minimal coordinates are independent and considerably simplify motion planning.

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