3D-Simulation of human walking by parameter optimization

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.