acados · sandmaennchen · Apr 24, 2025 · Apr 23, 2025 · Apr 23, 2025 · Apr 24, 2025
diff --git a/README.md b/README.md
@@ -6,14 +6,28 @@
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 <!-- [![codecov](https://codecov.io/gh/acados/acados/branch/master/graph/badge.svg)](https://codecov.io/gh/acados/acados) -->
 
-`acados` provides fast and embedded solvers for nonlinear optimal control.
+`acados` provides fast and embedded solvers for nonlinear optimal control, specifically designed for real-time applications and embedded systems.
 It is written in `C` and offers interfaces to the programming languages `Python`, `MATLAB` and `Octave`.
 
 ## General
-- `acados` implements
-  1. fast SQP-type solvers for Nonlinear Programming (NLP) formulations with an Optimal Control Problem (OCP) structure
-  2. efficient integration methods, also called *integrators*, to solve initial value problems with dynamic systems given as an ODE or index-1 DAE.
-  These integrators can efficiently compute first and second-order sensitivities of the results.
+`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](#fields-of-applications).
+
+### Key Features:
+Some key features of `acados` are summarized in the following.
+The [software design](#design-paradigms) 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.
+- **Mo
8000
dular 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 the [`leap-c` project](https://github.com/leap-c/leap-c).
 
 ## Documentation
 - Documentation can be found on [docs.acados.org](https://docs.acados.org/)
@@ -28,3 +42,26 @@ It is written in `C` and offers interfaces to the programming languages `Python`
 ## Installation
 - Instructions can be found at
 [docs.acados.org/installation](https://docs.acados.org/installation)
+
+### 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`](https://web.casadi.org/) symbolic software framework.
+The interfaces allow to conveniently specify commonly used problem formulations via the `AcadosOcp` class and additionally expose the full flexibility of the internal `acados` problem formulation, via multi-phase formulations and `AcadosMultiphaseOcp`.
+
+## Fields of applications
+A non-exhaustive list of projects featuring `acados` is available at [docs.acados.org/list_of_projects](https://docs.acados.org/list_of_projects/index.html).
+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.
diff --git a/docs/index.md b/docs/index.md
@@ -32,21 +32,54 @@ Contributions via pull requests are welcome!
 
 ## About `acados`
 
-`acados` is a software package providing fast and embedded solvers for nonlinear optimal control.
-Problems can be conveniently formulated using the [`CasADi`](https://web.casadi.org/) symbolic framework and the high-level `acados` interfaces.
-
-`acados` provides a collection of computationally efficient building blocks tailored to optimal control structured problems, most prominently optimal control problems (OCP) and moving horizon estimation (MHE) problems.
-Among others, `acados` implements:
-- modules for the integration of ordinary differential equations (ODE) and differential-algebraic equations (DAE),
-- interfaces to state-of-the-art QP solvers like [`HPIPM`](https://github.com/giaf/hpipm), `qpOASES`, [`DAQP`](https://github.com/darnstrom/daqp) and [`OSQP`](https://github.com/osqp/osqp)
-- (partial) condensing routines, provided by `HPIPM`
-- nonlinear programming solvers for optimal control structured problems
-- real-time algorithms, such as the real-time iteration (RTI) and advanced-step real-time iteration (AS-RTI) algorithms
+`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](#fields-of-applications).
+
+`acados` is written in `C`, but control problems can be conveniently formulated using the [`CasADi`](https://web.casadi.org/) 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](#design-paradigms) 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 the [`leap-c` project](https://github.com/leap-c/leap-c).
 
 The back-end of acados uses the high-performance linear algebra package [`BLASFEO`](https://github.com/giaf/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`](https://web.casadi.org/) symbolic software framework.
+The interfaces allow to conveniently specify commonly used problem formulations via the `AcadosOcp` class and additionally expose the full flexibility of the internal `acados` problem formulation, via multi-phase formulations and `AcadosMultiphaseOcp`.
+
+## Fields of applications
+A non-exhaustive list of projects featuring `acados` is available [here](https://docs.acados.org/list_of_projects/index.html).
+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
 
 ```eval_rst