Optimal-Horizon Model-Predictive Control with Differential Dynamic Programming

TL;DR

This paper introduces an optimal-horizon model-predictive control algorithm based on Differential Dynamic Programming that adapts the planning horizon online, demonstrating real-time applicability and improved obstacle avoidance performance.

Contribution

It develops a novel DDP-based algorithm for online horizon determination in MPC, with proven convergence for linear problems and demonstrated effectiveness on nonlinear control tasks.

Findings

Exact one-step convergence for linear quadratic problems

Real-time performance on nonlinear MPC tasks

Improved obstacle avoidance compared to standard MPC

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 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.