The Parallelization of Riccati Recursion

TL;DR

This paper introduces a parallelized Riccati recursion method for solving large-scale discrete-time LQR problems efficiently, enabling faster computation while retaining feedback control policies, crucial for robotic trajectory optimization.

Contribution

We develop a novel parallelization approach for Riccati recursion that accelerates LQR problem solving without losing the feedback control policy output.

Findings

Our method outperforms existing parallel solutions in speed.

It maintains the quality of feedback control policies.

Empirical results show significant speedup on complex robotic problems.

Abstract

A method is presented for parallelizing the computation of solutions to discrete-time, linear-quadratic, finite-horizon optimal control problems, which we will refer to as LQR problems. This class of problem arises frequently in robotic trajectory optimization. For very complicated robots, the size of these resulting problems can be large enough that computing the solution is prohibitively slow when using a single processor. Fortunately, approaches to solving these type of problems based on numerical solutions to the KKT conditions of optimality offer a parallel solution method and can leverage multiple processors to compute solutions faster. However, these methods do not produce the useful feedback control policies that are generated as a by-product of the dynamic-programming solution method known as Riccati recursion. In this paper we derive a method which is able to parallelize the computation of Riccati recursion, allowing for super-fast solutions to the LQR problem while still generating feedback control policies. We demonstrate empirically that our method is faster than existing parallel methods.