The 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.

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.

The consequence of the loss of involutivity of a specific set of vector fields on the periodicity of the joint motion is examined for redundant robots. An output task, defined as a one dimensional periodic closed curve embedded in a two dimensional working surface, is realized through the computation of joint velocities in the configuration space. Depending on the manner in which the joint velocity is computed from the end-effector velocity, the resulting joint motion can become unpredictable and of a chaotical nature, even though the end-effector movement is periodic and predictable. The paper proposes an improvement over classical pseudo-inverse computation of the joint motion by suitably selecting two involutive vector fields. This then leads to a constructive sufficient condition for the periodicity of the joints based on the usage of both the 1-form defining the output manifold and complementary integrable 1-forms. The results are illustrated on a five-link rotary redundant robot (5R robot).

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

Introducing automatic control has always been challenging. As a technology, control is generally hidden by the enclosing application. As a methodology, control is often seen as a theoretical subject. Therefore, to grasp the interest of both practitioners enrolled in continuing education programs and students enrolled in introductory control courses, novel applications should be exploited. This paper presents an approach to demonstrate basic control concepts using a nanopositioning experiment. It also shows that the importance of real-time interaction and teleoperation features in today control solutions can be implicitly underlined by providing a remote access to the experiment.