Computational optimal control modeling and smoothing for biomechanical systems

Munzir Said

    Research output: ThesisDoctoral Thesis

    90 Downloads (Pure)


    [Truncated abstract] The study of biomechanical system dynamics consists of research to obtain an accurate model of biomechanical systems and to find appropriate torques or forces that reproduce motions of a biomechanical subject. In the first part of this study, specific computational models are developed to maintain relative angle constraints for 2-dimensional segmented bodies. This is motivated by the fact that there is a possibility of models of segmented bodies, moving under gravitational acceleration and joint torques, for its segments to move past the natural relative angle limits. Three models to maintain angle constraints between segments are proposed and compared. These models are: all-time angle constraints, a restoring torque in the state equations and an exponential penalty model. The models are applied to a 2-D three segment body to test the behaviour of each model when optimizing torques to minimize an objective. The optimization is run to find torques so that the end effector of the body follows the trajectory of a half circle. The result shows the behavior of each model in maintaining the angle constraints. The all-time constraints case exhibits a behaviour of not allowing torques (at a solution) which make segments move past the constraints, while the other two show a flexibility in handling the angle constraints more similar to a real biomechanical system. With three computational methods to represent the angle contraint, a workable set of initial torques for the motion of a segmented body can be obtained without causing integration failure in the ordinary differential equation (ODE) solver and without the need to use the “blind man method” that restarts the optimal control many times. ... With one layer of penalty weight balancing between trajectory compliance penalty and other optimal control objectives (minimizing torque/smoothing torque) already difficult to obtain (as explained by the L-curve phenomena), adding the second layer penalty weight for the closeness of fit for each of the body segments will further complicate the weight balancing and too much trial and error computation may be needed to get a reasonably good set of weighting values. Second order regularization is also added to the optimal control objective and the optimization has managed to obtain smoother torques for all body joints. To make the current approach more competitive with the inverse dynamic, an algorithm to speed up the computation of the optimal control is required as a potential future work.
    Original languageEnglish
    QualificationDoctor of Philosophy
    Publication statusUnpublished - 2007


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