$\pi$MPC: A Parallel-in-horizon and Construction-free NMPC Solver

TL;DR

The paper introduces $ ext{ extpi}$MPC, a novel parallel-in-horizon nonlinear MPC solver that operates directly on system matrices, enabling efficient horizon-wise parallelization without explicit QP construction.

Contribution

It presents a new variable-splitting scheme and velocity-based system representation within ADMM, allowing horizon-wise parallel execution in nonlinear MPC without QP formulation.

Findings

Enables horizon-wise parallelization of nonlinear MPC.

Operates directly on system matrices, avoiding explicit QP construction.

Validated through numerical experiments and provided code.

Abstract

The alternating direction method of multipliers (ADMM) has gained increasing popularity in embedded model predictive control (MPC) due to its code simplicity and pain-free parameter selection. However, existing ADMM solvers either target general quadratic programming (QP) problems or exploit sparse MPC formulations via Riccati recursions, which are inherently sequential and therefore difficult to parallelize for long prediction horizons. This technical note proposes a novel \textit{parallel-in-horizon} and \textit{construction-free} nonlinear MPC algorithm, termed $\pi$MPC, which combines a new variable-splitting scheme with a velocity-based system representation in the ADMM framework, enabling horizon-wise parallel execution while operating directly on system matrices without explicit MPC-to-QP construction. Numerical experiments and accompanying code are provided to validate the effectiveness of the proposed method.