Optimization-based motion prediction of mechanical systems: sensitivity analysis

Optimization-based prediction of asymmetric human gait

“…In addition, analytical gradient expressions are provided for the kinematics and dynamics variables for use in the optimization process. Detailed formulas to calculate the recursive kinematics, dynamics, and their sensitivities are provided by Xiang et al (2009a).…”

“…In contrast, inverse dynamicsbased optimization formulation treats motion as solution variables, and the joint forces are computed from EOM that avoids their numerical integration (Bessonnet et al, 2010;Channon et al, 1992;Chevallereau and Aoustin, 2001;Ren et al, 2007). Besides these two methods, the predictive dynamics approach has been recently used to simulate human motions Chung et al, 2007;Kim et al, 2005Kim et al, , 2008Kim et al, , 2009Wang et al, 2005Wang et al, , 2007Xiang, 2008;Xiang et al, 2007Xiang et al, , 2009aXiang et al, , 2009bXiang et al, , 2010aXiang et al, , 2010bXiang et al, , 2010c. Similar efforts on alternative formulations for dynamic human motion prediction were also made in the literature, such as direct collocation method (Ackermann and van den Bogert, 2010) and temporal finite element method (Eriksson, 2008;Kaphle and Eriksson, 2008;Eriksson and Nordmark, 2010).…”

Predictive simulation of human walking transitions using an optimization formulation

“…Recursive formulation is used to calculate the kinematics and dynamics of the skeletal model because of its computational efficiency (Hollerbach 1980;Fu et al 1987;Toogood 1989;Xiang et al 2009a). The forward kinematics transfers the motion from the origin towards the end-effector along the branch.…”

“…The joint torques are computed using the recursive Lagrangian formulation. In addition, the closed-form analytical gradients are provided for the kinematics and dynamics variables for use in the optimization process (Xiang et al 2009a).…”

Motion Planning of Uncertain Ordinary Differential Equation Systems

“…al. [2][3][4][21][22][23][24][25] where analytic derivatives for the optimization cost of general open, branched, and closed looped systems, described by recursive Lagrangian Dynamics, is presented. Formulations are based on the Denavit-Hartenberg kinematic methods, cubic B-Splines, and SQP-based solvers.…”