Closed-form and generalized inverse kinematics solutions for the analysis of human motion

Inverse Kinematics (IK) calculates internal joint angles for a kinematic chain given constraints on the end-effector [1]. This study evaluates the advantages and limitations of algebraic, geometric, and iterative IK solutions reported in the literature. This analysis is used to develop a solution for animating arbitrary articulated structures such as robots and humans. For iterative solutions, various minimization and root finding algorithms described in the literature are compared through the analysis of experimental results. The minimization algorithm of Broyden, Fletcher, Goldfarb, and Shanno (BFGS) [2] is shown to converge quickly using a small number of objective function evaluations, making it the best method for solving IK systems of those considered in this study. This observation has led to a generalized IK solution for actuators with N Degrees of Freedom, extending the work of Goldenberg and Lawrence [3], Goldenberg et al. [4], and Sasaki [5] by considering additional minimization and root-finding algorithms. It is indicated that the new generalized IK solution will enhance the visual analysis of human joint range and ergonometric studies, provide the foundation for new interactive tools to teach functional anatomy, and enhance virtual environments which require realistic interactive human animation.