Optimal-Horizon Model-Predictive Control with Differential Dynamic Programming

Abstract

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 onestep 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.

Parameterized Differential Dynamic Programming

“…For a single mode, this objective is an approximation to a free-horizon optimal control problem, where the terminal time of the trajectory parameterizes the dynamics and can be optimized using PDDP. Similar parameterizations have been discussed in previous works such as [20,26].…”