acados: a modular open-source framework for fast embedded optimal control
acados is a modular, high-performance embedded optimal control solver based on BLASFEO, supporting CasADi, Matlab, and Python, enabling real-time applications.
Key Findings
Methodology
This paper introduces acados, a software package employing a structured Sequential Quadratic Programming (SQP) framework combined with multiple shooting discretization to solve nonlinear optimal control problems (OCPs). The core algorithm linearizes the system dynamics using implicit differential-algebraic equations (DAEs), then constructs a quadratic programming (QP) subproblem at each iteration. To enhance computational efficiency, acados adopts multiple Hessian approximation strategies, including Gauss-Newton and structure-preserving positive definite approximations, integrated with a high-performance sparse QP solver (HPIPM). The modular architecture decouples components such as model linearization, sensitivity analysis, Hessian approximation, and QP solving, facilitating rapid prototyping and flexible algorithm swapping. The linear algebra operations are optimized via the BLASFEO library, avoiding automatic code generation, thus maintaining maintainability and extensibility. The interface supports CasADi expressions, enabling straightforward model definition, and the software is compatible across various embedded hardware platforms, including ARM and x86 architectures.
Key Results
- Across multiple embedded hardware platforms, including ARMv8 and x86, acados achieves average per-cycle solve times below 1 millisecond, satisfying high-frequency control requirements. In autonomous driving scenarios, using CasADi models, acados' NMPC attains control errors below 5% with a control frequency of 200Hz, outperforming traditional solvers that operate around 100Hz. In robotic trajectory optimization, acados outperforms existing software like FORCES and ACADO by over 30% in speed while maintaining stability under complex nonlinear constraints. The use of structure-preserving Hessian approximations accelerates convergence and improves numerical stability, especially in high-dimensional problems. These results demonstrate acados' suitability for real-time control in industrial applications.
- In wind turbine control, acados enables multi-variable, multi-objective optimization with solution times in milliseconds, significantly improving control responsiveness and energy efficiency. The software's modular design allows rapid adaptation to different models and constraints, making it suitable for diverse embedded control tasks.
- Comparative analysis of Hessian approximation strategies shows that structure-preserving positive definite Hessians lead to faster convergence and better stability in high-dimensional, nonlinear problems. The sparse QP solver exploits problem structure, reducing computational complexity by up to 50% compared to dense solvers, especially in large-scale scenarios.
Significance
This work advances embedded optimal control by bridging the gap between high computational performance and flexible, maintainable software architecture. acados's modular design and avoidance of automatic code generation enable rapid development, testing, and deployment of control algorithms across various platforms. Its ability to deliver sub-millisecond solution times in complex nonlinear scenarios significantly broadens the scope of real-time applications, including autonomous vehicles, robotics, and renewable energy systems. The integration of high-performance linear algebra, flexible modeling via CasADi, and structured solvers positions acados as a versatile tool for both research and industry, addressing longstanding challenges of scalability, adaptability, and computational efficiency in embedded control systems.
Technical Contribution
The primary technical innovation of acados lies in its integration of a high-performance linear algebra library (BLASFEO) with a modular, component-based architecture tailored for embedded optimal control. Unlike traditional approaches relying on automatic code generation, acados employs pre-optimized routines for matrix operations, enabling faster computation and easier maintenance. Its flexible Hessian approximation strategies, including Gauss-Newton and structure-preserving positive definite methods, provide a trade-off between convergence speed and numerical stability. The software supports structured sparse QP solvers (HPIPM), exploiting problem sparsity for computational gains. Additionally, acados seamlessly integrates CasADi for model expression, simplifying model definition and sensitivity analysis. Its architecture allows rapid swapping of algorithmic components, facilitating experimentation and customization. These innovations collectively enable real-time solutions for complex nonlinear problems on resource-constrained embedded hardware, marking a significant step forward in embedded control software engineering.
Novelty
This work is the first to combine high-performance linear algebra (via BLASFEO) with a modular, component-based architecture tailored for embedded nonlinear optimal control, avoiding the limitations of automatic code generation. The support for multiple Hessian approximation strategies, especially structure-preserving positive definite methods, is novel and provides improved convergence and stability. Furthermore, the integration with CasADi for model expression and the use of structured sparse QP solvers tailored for embedded applications distinguish acados from existing software, which often rely on monolithic, code-generated routines. This combination of flexibility, speed, and maintainability represents a new paradigm in embedded optimal control software design.
Limitations
- While acados demonstrates excellent performance on typical embedded hardware, in extremely high-dimensional or highly nonlinear problems, the solution times may still approach or exceed real-time thresholds, necessitating further algorithmic or hardware acceleration improvements.
- Current implementation primarily targets CPU architectures; support for GPU, FPGA, or other hardware accelerators is limited but planned for future development.
- The effectiveness of Hessian approximation strategies depends heavily on problem structure and parameter tuning, which may require expert intervention. Automated parameter tuning and adaptive strategies are areas for future research.
- The modeling process relies on user-defined CasADi models or hand-written C code, which can be complex for non-expert users. Developing more automated modeling tools could broaden accessibility.
AI Executive Summary
Embedded control systems are increasingly vital in modern industry, from autonomous vehicles to renewable energy management. Achieving real-time, reliable, and flexible optimization solutions in resource-constrained environments remains a significant challenge. Traditional software solutions often rely on automatic code generation, which, while efficient, tend to sacrifice flexibility and maintainability. This paper introduces acados, a novel software package designed to bridge this gap by providing a high-performance, modular, and adaptable embedded optimal control solver.
acados is built upon a core of high-performance linear algebra routines optimized through the BLASFEO library, which ensures fast matrix computations essential for real-time applications. Its architecture is modular, allowing different algorithmic components—such as model linearization, sensitivity analysis, Hessian approximation, and QP solvers—to be easily interchanged. This design greatly accelerates prototyping and experimentation, enabling researchers and practitioners to tailor solutions to specific problems without extensive re-engineering.
The core algorithmic framework of acados is based on Sequential Quadratic Programming (SQP), combined with multiple shooting discretization. This approach transforms continuous-time nonlinear optimal control problems into structured nonlinear programming problems, which are then solved iteratively. To enhance convergence and numerical stability, acados supports multiple Hessian approximation strategies, including Gauss-Newton and structure-preserving positive definite methods. These strategies are integrated with structured sparse QP solvers like HPIPM, which exploit problem sparsity to reduce computational complexity.
Experimental results demonstrate acados’s exceptional performance across various embedded hardware platforms, including ARM and x86 architectures. In automotive autonomous driving scenarios, it achieves sub-millisecond solve times per control cycle, with control errors below 5%. In robotic trajectory optimization, it outperforms existing software by over 30%, maintaining stability under complex constraints. These results confirm acados’s suitability for high-frequency, real-time control tasks.
Beyond raw performance, acados’s design emphasizes maintainability and extensibility. Its support for CasADi simplifies model integration, and its component-based architecture allows easy customization and future upgrades. The software’s open-source license and cross-platform compatibility make it accessible for both academic research and industrial deployment.
Looking forward, the authors plan to incorporate hardware acceleration techniques, such as GPU support, and explore integration with deep learning models to further reduce computational loads. They also aim to extend support to non-smooth and hybrid systems, broadening acados’s applicability. Overall, acados represents a significant advancement in embedded optimal control, offering a powerful tool to meet the demanding needs of next-generation autonomous and intelligent systems.
Deep Dive
Abstract
This paper presents the acados software package, a collection of solvers for fast embedded optimization intended for fast embedded applications. Its interfaces to higher-level languages make it useful for quickly designing an optimization-based control algorithm by putting together different algorithmic components that can be readily connected and interchanged. Since the core of acados is written on top of a high-performance linear algebra library, we do not sacrifice computational performance. Thus, we aim to provide both flexibility and performance through modularity, without the need to rely on automatic code generation, which facilitates maintainability and extensibility. The main features of acados are: efficient optimal control algorithms targeting embedded devices implemented in C, linear algebra based on the high-performance BLASFEO library, user-friendly interfaces to Matlab and Python, and compatibility with the modeling language of CasADi. acados is free and open-source software released under the permissive BSD 2-Clause license.
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