3D-Simulation of human walking by parameter optimization

Abstract

The simulation of human gait is a complex dynamical problem that requires accounting for energy consumption as well as dealing with a redundantly actuated multibody system. If muscle forces and generalized coordinates are parameterized, optimization techniques allow the simulation of the muscle forces and of the walking motion. An optimization framework is presented for non-symmetrical gait cycles found in the presence of one-sided gait disorders. The motion of each leg is independently parameterized for a whole walking cycle. The non-linear constraints used to fulfill the equations of motion and the kinematical constraints of the different walking phases are implemented in an efficient way. Fifth-order splines are used for the parameterization to reduce the oscillatory behavior coming from non-periodicity conditions. To achieve the computational performance required for three-dimensional simulations, the spline interpolation problem has been split in two parts, one is performed in a preprocessing stage and the other during the optimization. Numerical differentiation via finite differences is avoided by implementing analytical derivatives of the splines functions and of the contractile element force law. The results show good numerical performance, and the computational efficiency for 3D-simulations with one-sided gait disorders is highlighted.

Human walking dynamics: modeling, identification and control

“…The optimization problem described in Chapter 4 has been solved by Sequential Quadratic Programming (SQP) from MATLAB Optimization Toolbox for planar models [7] and spatial models [8].…”

“…10. Ground reaction forces of both feet during spatial motion: measured (solid thin line), simulated (solid thick line) and simulated with gait disorder (dahed thick line) [8] …”

“…The kinematic tree in Fig. 2 is described by the following vector of 16 generalized coordinates (1) as shown in [8] where the subscript I refers to the inertial frame, subscript 1 refers to body HAT, which is in composed of the pelvis and the trunk, subscripts 3 and 6 refer to right and left thighs, respectively, subscripts 4 and 7 refer to right and left shanks, respectively, and subscripts 5 and 8 refer to right and left feet, respectively. When a subscript is written as i j, it means a relative motion of body j with respect to body i .…”

Dynamical analysis and design of active orthoses for spinal cord injured subjects by aesthetic and energetic optimization

“…Among other approaches, parameter optimization techniques have been frequently used for motion synthesis of biped robots [5]. These optimization techniques have been proven to be also a powerful tool in human walking dynamics research [6,7]. In these works, muscle forces and generalized coordinates are described in terms of a certain set of parameters, whose optimal values are found by minimizing cost functions that include an energy expenditure estimation and a measure of deviation from normal gait patterns.…”

“…As an example, Ackermann [6] used a two-dimensional (2D) model to analyze the walking motion of humans with bilateral disorders, which are in fact less common than unilateral disorders. Based on this approach, García-Vallejo and Schiehlen [7] developed a three-dimensional (3D) model to simulate unilateral disorders. Most of these models are composed of seven bodies (2 feet, 2 shanks, 2 thighs and a pelvis-trunk body) or eight bodies (2 feet, 2 shanks, 2 thighs, pelvis and separate trunk), where the arms and head are lumped into the trunk body by adding its mechanical properties to this body and ignoring their own dynamics.…”