acados#
Fast and embedded solvers for nonlinear optimal control.
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, the Systems Control and Optimization Laboratory, 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 to implement 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 is demonstrated in theleap-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 to utilize linear dependencies within dynamical system models.modularity:
acados
offers an extremely flexible problem formulation, allowing to not only formulate problems which 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 to conveniently specify commonly used problem formulations via theAcadosOcp
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 to increase 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 24, 2025