Learning Mixed-Integer Convex Optimization Strategies for Robot Planning and Control

TL;DR

This paper introduces CoCo, a framework that combines offline learned strategies with online convex optimization to solve mixed-integer convex problems in robotics rapidly, enabling real-time control with near-optimal solutions.

Contribution

The paper presents a novel approach that encodes combinatorial solutions into strategies and uses machine learning to predict these strategies, significantly speeding up MICP solutions in robotic applications.

Findings

Achieves 10 to 100 times faster solutions than state-of-the-art solvers.

Provides control solutions with performance close to global optima.

Demonstrates effectiveness on diverse robotic systems.

Abstract

Mixed-integer convex programming (MICP) has seen significant algorithmic and hardware improvements with several orders of magnitude solve time speedups compared to 25 years ago. Despite these advances, MICP has been rarely applied to real-world robotic control because the solution times are still too slow for online applications. In this work, we present the CoCo (Combinatorial Offline, Convex Online) framework to solve MICPs arising in robotics at very high speed. CoCo encodes the combinatorial part of the optimal solution into a strategy. Using data collected from offline problem solutions, we train a multiclass classifier to predict the optimal strategy given problem-specific parameters such as states or obstacles. Compared to previous approaches, we use task-specific strategies and prune redundant ones to significantly reduce the number of classes the predictor has to select from, thereby greatly improving scalability. Given the predicted strategy, the control task becomes a small convex optimization problem that we can solve in milliseconds. Numerical experiments on a cart-pole system with walls, a free-flying space robot, and task-oriented grasps show that our method provides not only 1 to 2 orders of magnitude speedups compared to state-of-the-art solvers but also performance close to the globally optimal MICP solution.