Simulating human movements using optimal control

This paper presents an optimization based technique for solving optimal control problems. Unlike the spacetime constraint approach which discretizes both the state and control variables, our method transforms the optimal control problem into an optimization task that depends only upon the control variables. Using a spline to represent the control trajectory, we derive an efficient, analytic technique for computing the gradient of the objective function in terms of the spline control points. Our approach has the advantage of reducing the number of unknowns and ensuring consistency between the state and control variables. We demonstrate the viability of our algorithm by using it to simulate a human figure performing a high jump.