  We present an algorithm, based on the Differential Dynamic Programming
framework, to handle trajectory optimization problems in which the horizon is
determined online rather than fixed a priori. This algorithm exhibits exact
one-step convergence for linear, quadratic, time-invariant problems and is fast
enough for real-time nonlinear model-predictive control. We show derivations
for the nonlinear algorithm in the discrete-time case, and apply this algorithm
to a variety of nonlinear problems. Finally, we show the efficacy of the
optimal-horizon model-predictive control scheme compared to a standard MPC
controller, on an obstacle-avoidance problem with planar robots.
