Publication

Squash-box feasibility driven differential dynamic programming

Conference Article

Conference

IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

Edition

2020

File

Download the digital copy of the doc pdf document

Abstract

Recently, Differential Dynamic Programming (DDP) and other similar algorithms have become the solvers of choice when performing non-linear Model Predictive Control (nMPC) with modern robotic devices. The reason is that they have a lower computational cost per iteration when compared with off-the-shelf Non-Linear Programming (NLP) solvers, which enables its online operation. However, they cannot handle constraints, and are known to have poor convergence capabilities. In this paper, we propose a method to solve the optimal control problem with control bounds through a squashing function (i.e. a sigmoid, which is bounded by construction). It has been shown that a naive use of squashing functions damage the convergence rate. To tackle this, we first propose to add a quadratic barrier that avoids the difficulty of the plateau produced by the sigmoid. Second, we add an outer loop that adapts both the sigmoid and the barrier; it makes the optimal control problem with the squashing function converge to the original control-bounded problem. To validate our method, we present simulation results for different types of platforms including a multi-rotor, a biped, a quadruped and a humanoid robot.

Categories

dynamic programming, nonlinear programming, predictive control, robot dynamics.

Author keywords

Differential Dynamic Programming, Trajectory Generation, nMPC

Scientific reference

J. Martí, J. Solà, C. Mastalli and A. Santamaria-Navarro. Squash-box feasibility driven differential dynamic programming, 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems, 2020, Las Vegas, NV, USA, to appear.