HPIPM: a high-performance quadratic programming framework for model predictive control
HPIPM offers a high-performance quadratic programming framework, significantly improving speed and robustness for model predictive control.
Key Findings
Methodology
HPIPM employs a modular design supporting three QP types (dense, OCP, tree-structured) and multiple IPM variants. Core algorithms optimize the KKT system solving by exploiting matrix structure, integrated with BLASFEO for high-efficiency linear algebra. It incorporates (partial) condensing techniques to transform multi-stage OCP problems into dense QPs, enabling faster solutions. Multiple IPM variants balance speed and robustness, with memory management optimized for embedded systems. Extensive numerical validation demonstrates superior speed and reliability over existing solvers.
Key Results
- In mass-spring system benchmarks, HPIPM's speed mode outperformed HPMPC by 10-15%, especially on longer horizons. On the Maros-Mészáros convex QP set, HPIPM in speed mode solved about 50% of problems faster than qpOASES, with the robust mode solving nearly all successfully. Riccati recursion-based linear system solutions enabled handling large-scale, multi-stage, and tree-structured problems efficiently, supporting real-time applications.
- The solver's modularity and structure-aware algorithms allowed for flexible problem formulations, including multi-stage and scenario-based OCPs, with computational complexity scaling linearly with horizon length and tree size. Experimental results confirmed the framework's ability to solve complex control problems with high speed and stability.
- Parameter tuning (regularization, step size, condensing) further optimized performance, demonstrating HPIPM's adaptability across diverse control scenarios, from robotics to automotive applications.
Significance
This work addresses the critical bottleneck in MPC—fast and reliable QP solving—by delivering a highly optimized, open-source framework. HPIPM's architecture enables deployment in embedded systems, facilitating real-time control in autonomous vehicles, robotics, and industrial automation. Its ability to handle large-scale, complex problems with high efficiency paves the way for broader industrial adoption of advanced predictive control strategies, fostering smarter, more responsive automation solutions.
Technical Contribution
HPIPM introduces structure-exploiting KKT system solvers combined with BLASFEO's optimized matrix routines, supporting multiple IPM variants. Its modular design allows seamless extension to new QP types and problem formulations. The integration of (partial) condensing techniques and Riccati recursion-based linear system solutions significantly reduces computational complexity, enabling real-time performance for large-scale problems. The framework's flexible parameterization and memory management further enhance its practical utility.
Novelty
This is the first high-performance, modular QP solver supporting multiple problem structures (dense, OCP, tree) with adaptable speed-robustness trade-offs. Its innovative use of structure-aware KKT solving, combined with BLASFEO's optimized routines, sets it apart from traditional solvers like qpOASES or OSQP, especially in large, complex control scenarios. The framework's flexibility and efficiency represent a significant leap forward in embedded predictive control.
Limitations
- Currently optimized for linear-quadratic problems; extension to nonlinear or non-convex problems remains future work. Handling extremely high-dimensional problems still poses computational challenges, especially in memory usage.
- Robustness may degrade under highly ill-conditioned or unstable system dynamics, requiring further algorithmic enhancements. Parameter tuning can be complex and problem-dependent.
- While highly efficient, the framework's performance depends on problem structure; unstructured sparse problems are not directly supported, limiting some applications.
Future Work
Future developments include extending HPIPM to nonlinear and non-convex problems, integrating sparse matrix techniques, and adaptive condensing strategies. Enhancing automatic parameter tuning and robustness under extreme conditions are also planned. Additionally, deeper integration with machine learning-based predictive models could further expand its industrial impact, enabling smarter, more autonomous control systems.
AI Executive Summary
Model predictive control (MPC) has become a cornerstone in modern automation, offering optimal decision-making over predictive horizons. However, its widespread industrial adoption is hindered by the computational burden of solving large-scale quadratic programs (QPs) in real time. Traditional solvers often struggle with the speed and robustness required for embedded applications, especially as problem complexity grows.
Addressing this challenge, Frison and Diehl introduce HPIPM, a high-performance, open-source framework tailored for quadratic programming in MPC. The framework's core strength lies in its modular architecture supporting three QP types—dense, optimal control problems (OCP), and tree-structured problems—and multiple interior point method (IPM) variants. By leveraging structure-aware algorithms, particularly optimized Riccati recursion and structure-exploiting KKT solvers, HPIPM dramatically reduces computational complexity. Its integration with BLASFEO enables high-efficiency matrix operations, critical for embedded real-time applications.
Extensive numerical experiments validate HPIPM's capabilities. In benchmark tests involving mass-spring systems, the speed mode outperformed HPMPC by 10-15%, while on the Maros-Mészáros convex QP set, it solved about half the problems faster than qpOASES, with near-perfect success in robustness mode. The solver's ability to handle multi-stage and tree-structured problems efficiently demonstrates its scalability and practicality for industrial control systems. Its flexible parameterization allows balancing speed and robustness, making it adaptable to diverse application needs.
The significance of HPIPM extends beyond mere speed. Its open-source, modular design facilitates integration into existing control frameworks, fostering innovation in autonomous vehicles, robotics, and process automation. By enabling real-time, reliable MPC solutions at scale, HPIPM paves the way for smarter, more responsive automation technologies. Future work aims to extend its capabilities to nonlinear and sparse problems, further broadening its industrial relevance and impact.
Deep Dive
Abstract
This paper introduces HPIPM, a high-performance framework for quadratic programming (QP), designed to provide building blocks to efficiently and reliably solve model predictive control problems. HPIPM currently supports three QP types, and provides interior point method (IPM) solvers as well (partial) condensing routines. In particular, the IPM for optimal control QPs is intended to supersede the HPMPC solver, and it largely improves robustness while keeping the focus on speed. Numerical experiments show that HPIPM reliably solves challenging QPs, and that it outperforms other state-of-the-art solvers in speed.