acados#
Fast and embedded solvers for real-world applications of nonlinear optimal control.
Important links#
🎦 Get inspired by real-world applications using acados 🚀
⭐ The acados
source code is hosted on Github.
Contributions via pull requests are welcome!
🤝 acados
has a discourse-based forum.
🏘️ acados
is mainly developed by the syscop group around Prof. Moritz Diehl, at the University of Freiburg.
About acados
#
acados
is a modular and efficient software package for solving nonlinear programs (NLP) with an optimal control problem (OCP) structure.
Such problems have to be solved repeatedly in model predictive control (MPC) and moving horizon estimation (MHE).
The computational efficiency and modularity make acados
an ideal choice for real-time applications.
It is designed for high-performance applications, embedded computations, and has been successfully used in a wide range of applications.
acados
is written in C
, but control problems can be conveniently formulated using the CasADi symbolic framework via the high-level acados
interfaces to the programming languages Python
, MATLAB
, and Octave
.
Some key features of acados
are summarized in the following.
The software design allows implementing many algorithms beyond this list:
Nonlinear and economic model predictive control (NMPC): Solve challenging control problems with nonlinear dynamics and cost functions.
Moving horizon estimation (MHE): Estimate states and parameters of dynamic systems in real-time.
Support for differential algebraic equations (DAE): Efficiently handle systems with algebraic constraints.
Multiple shooting method: Leverage the multiple shooting approach for time discretization, enabling fast and robust solutions.
Efficient integration methods: Include advanced integrators for solving ODEs and DAEs, with support for first- and second-order sensitivities.
Real-time performance: Optimized for high-frequency control loops, enabling reliable solutions for time-critical applications.
High-performance solvers: Implement fast SQP-type solvers tailored for optimal control problems.
Modular design: Easily extend and combine components for simulation, estimation, and control to fit diverse applications.
Solution sensitivity computation and combination with reinforcement learning (RL): The combination of MPC and RL is a hot research topic in control. Many learning algorithms can profit from the availability of solution sensitivities or, in particular, policy gradients.
acados
offers the possibility to embed an NLP solver as a differentiable layer in an ML architecture, as demonstrated in the leap-c project.
The back-end of acados
uses the high-performance linear algebra package BLASFEO, in order to boost computational efficiency for small to medium-scale matrices typical of embedded optimization applications.
MATLAB
, Octave
, and Python
interfaces can be used to conveniently describe optimal control problems and generate self-contained C code that can be readily deployed on embedded platforms.
Design paradigms#
The main design paradigms of acados
are:
Efficiency: Realized by rigorously exploiting the OCP structure via tailored quadratic programming (QP) solvers, such as
HPIPM
, and (partial) condensing methods to transform QPs, enabling their efficient treatment. Moreover, the common structure of slack variables, which, for example, occur when formulating soft constraints, can be exploited. Additionally, a structure-exploiting Runge-Kutta method is implemented, allowing the utilization of linear dependencies within dynamical system models.Modularity:
acados
offers an extremely flexible problem formulation, allowing not only the formulation of problems that occur in MPC and MHE. More precisely, all problem functions and dimensions can vary between all stages. Such problems are often called multi-stage or multi-phase problems. Different NLP solvers, QP solvers, integration methods, regularization methods, and globalization methods can be combined freely. Moreover, cost and constraint functions can be declared by explicitly providing general convex-over-nonlinear structures, which can be exploited in the solvers.Usability: The interfaces to Python, MATLAB, Simulink, and Octave allow users to conveniently specify their problem in different domains and to specify their nonlinear expressions via the popular CasADi symbolic software framework. The interfaces allow users to conveniently specify commonly used problem formulations via the
AcadosOcp
class and additionally expose the full flexibility of the internalacados
problem formulation, via multi-phase formulations andAcadosMultiphaseOcp
.
Fields of applications#
A non-exhaustive list of projects featuring acados
is available here.
Contributions to this list are very welcome and allow increasing the visibility of your work among other acados
users.
Robotics: Real-time NMPC for quadrotors, legged locomotion, and agile robotic platforms.
Autonomous Vehicles: Used in projects like openpilot in driving assistance systems.
Energy Systems: Optimization-based control for microgrids and wind turbines.
Biomechanics: Optimal control in biomechanics through libraries like bioptim.
Aerospace: Applications in trajectory optimization and control for drones and morphing-wing aircraft.
Documentation page overview#
Documentation latest build: Apr 25, 2025
User Guide