On the computation of optimal high-dives

In this paper we describe a technique to generate realistic human movement, specifically platform dives, by solving an optimal control problem requiring little a priori information. Solving the optimal control problem reliably requires computing exact analytic gradients of the objective function, which is made possible by a hybrid recursive algorithm that calculates the dynamics of the system. This algorithm is formulated with Lie algebra techniques and matrix exponentials, resulting in equations that are easily differentiable. This quality is essential when solving ill-conditioned systems such as the diver. Also, the importance of initial conditions in light of the constant angular momentum constraint is discussed