ct_doc/doc/mainpage.dox - RealtimeRoboticsGroup/test - Gitiles


 /*!
 \mainpage Overview

 @tableofcontents

 \section ct1 Control Toolbox

 This is the ADRL Control Toolbox ('CT'), an open-source C++ library for efficient modelling, control,
 estimation, trajectory optimization and model predictive control.
 The CT is applicable to a broad class of dynamic systems, but features additional modelling tools specially designed for robotics.
 This page outlines its general concept, its major building blocks and highlights selected application examples.

 The library contains several tools to design and evaluate controllers, model dynamical systems and solve optimal control problems.
 The CT was designed with the following features in mind:

  - **Systems and dynamics**:
 	- intuitive modelling of systems governed by ordinary differential- or difference equations.

  - **Trajectory optimization, optimal control and (nonlinear) model predictive control**:
     - intuitive modelling of cost functions and constraints
     - common interfaces for optimal control solvers and nonlinear model predictive control
     - currently supported algorithms:
       - Single Shooting
       - iLQR \cite todorov2005ilqg / SLQ \cite slq:2005
  	  - Gauss-Newton-Multiple-Shooting (GNMS) \cite giftthaler2017family
  	  - Classical Direct Multiple Shooting (DMS) \cite bock1984direct
  	- standardized interfaces for the solvers
  	  - IPOPT (first and second order)
       - SNOPT
       - HPIPM
       - custom Riccati-solver

  - **Performance**:
  	- solve large scale optimal control problems in MPC fashion.

  - **Robot Modelling and rigid body dynamics**:
     - straight-forward interface to a state-of the art rigid body dynamics modelling tool.

  - **Automatic Differentiation**:
     - first- and second order automatic differentiation of arbitrary vector-valued functions including cost functions and constraints
     - automatic differentiation of rigid body dynamics
     - derivative code generation for maximum efficiency

  - **Simplicity**:
     - all algorithm flavors and solver backends are available through simple configuration files.


 The CT is hosted on bitbucket: <a href="https://bitbucket.org/adrlab/ct" target="_blank">https://bitbucket.org/adrlab/ct</a>


 \section ae Robot Application Examples

 The Control Toolbox has been used for Hardware and Simulation control tasks on flying, walking and ground robots.

 \htmlonly
 <iframe width="560" height="315" src="https://www.youtube.com/embed/Y7-1CBqs4x4" frameborder="2" allowfullscreen></iframe>
 <iframe width="560" height="315" src="https://www.youtube.com/embed/vuCSKtP67E4" frameborder="2" allowfullscreen></iframe>
 <iframe width="560" height="315" src="https://www.youtube.com/embed/rWmw-ERGyz4" frameborder="2" allowfullscreen></iframe>
 <iframe width="560" height="315" src="https://www.youtube.com/embed/rVu1L_tPCoM" frameborder="2" allowfullscreen></iframe>
 \endhtmlonly

 For details and more videos see \ref application_examples "Application Examples" and our \ref publications "publications".


 \section teaser What is the CT?

 A common tasks for researchers and practitioners in both the control and the robotics communities
 is to model systems, implement equations of motion and design model-based controllers, estimators,
 planning algorithms, etc.
 Sooner or later, one is confronted with questions of efficient implementation, computing derivative
 information, formulating cost functions and constraints or running controllers in model-predictive
 control fashion.

 The Control Toolbox is specifically designed for these tasks. It is written entirely in C++ and has
 a strong focus on highly efficient code that can be run online (in the loop) on robots or other
 actuated hardware. A major contribution of the CT is are its implementations of optimal control
 algorithms, spanning a range from simple LQR reference implementations to constrained model predictive
 control. The CT supports Automatic Differentiation (Auto-Diff) and allows to generate derivative code
 for arbitrary scalar and vector-valued functions.
 We designed the toolbox with usability in mind, allowing users to apply advanced concepts such as
 nonlinear model predictive control (NMPC) or numerical optimal control easily and with minimal effort.
 While we provide an interface to a state-of-the art Auto-Diff compatible robot modelling software, all
 other modules are independent of the a particular modelling framework, allowing the code to be interfaced
 with existing C/C++ code or libraries.

 The CT has been successfully used in a variety of different projects, including a large number of
 hardware experiments, demonstrations and academic publications.
 Example hardware applications are online trajectory optimization with collision
 avoidance \cite giftthaler2017autodiff, trajectory optimization for Quadrupeds \cite neunert:2017:ral
 and mobile manipulators \cite giftthaler2017efficient as well as NMPC on ground robots \cite neunert2017mpc
 and UAVs \cite neunert16hexrotor. The project originated from research conducted at the Agile \& Dexterous
 Robotics Lab at ETH Zurich, but is continuously extended to cover more fields of applications and algorithms.


 \section scope Scope of the CT

  Software is one of the key building blocks for robotic systems and there is a great effort
  in creating software tools and libraries for robotics.
  However, when it comes to control and especially Numerical Optimal Control, there are not
  many open source tools available that are both easy to use for fast development as well as
  efficient enough for online usage.
  While there exist mature toolboxes for Numerical Optimal Control and Trajectory Optimization,
  they are highly specialized, standalone tools that due not provide sufficient flexibility
  for other applications. Here is where the CT steps in. The CT has been designed from ground
  up to provide the tools needed for fast development and evaluation of control methods while
  being optimized for efficiency allowing for online operation. While the emphasis lies on control,
  the tools provided can also be used for simulation, estimation or optimization applications.

  In contrast to other robotic software, CT is not a rigid integrated application but can be
  seen quite literal as a toolbox: It offers a variety of tools which can be used and combined
  to solve a task at hand. While ease-of-use has been a major criteria during the design and
  application examples are provided, using CT still requires programming and control knowledge.
  However, it frees the users from implementing standard methods that require in-depth experience
  with linear algebra or numerical methods. Furthermore, by using common definitions and types,
  a seamless integration between different components such as systems, controllers or integrators
  is provided, enabling fast prototyping.


 \section design Design and Implementation

 The main focus of CT is efficiency, which is why it is fully implemented in C++.
 Since CT is designed as a toolbox rather than an integrated application, we tried to provide
 maximum flexibility to the users. Therefore, it is not tied to a specific middleware such as
 ROS and dependencies are kept at a minimum. The two essential dependencies for CT are
 <a href="http://eigen.tuxfamily.org" target="_blank">Eigen</a> and
 <a href="http://github.com/ethz-asl/kindr" target="_blank">Kindr</a>
 (which is based on Eigen). This Eigen dependency is intentional since Eigen
 is a defacto standard for linear algebra in C++, as it provides highly efficient implementations
 of standard matrix operations as well as more advanced linear algebra methods.
 Kindr is a header only Kinematics library which builds on top of it and provides data types
 for different rotation representations such as Quaternions, Euler angles or rotation matrices.


 \section modules Structure and Modules of the CT

 The Control Toolbox consists of three main modules. The Core module (ct_core), the Optimal
 Control (ct_optcon) module and the rigid body dynamics (ct_rbd) module.
 There is a clear hierarchy between the modules.
 That means, the modules depend on each other in this order, e.g. you can use the core module
 without the optcon or rbd module.
  - The `core' module (ct_core) module provides general type definitions and mathematical tools.
 For example, it contains most data type definitions, definitions for systems and controllers,
 as well as basic functionality such as numerical integrators for differential equations.
  - The `optimal Control' module (ct_optcon) builds on top of the `core' module and adds
 infrastructure for defining and solving Optimal Control Problems. It contains the functionality
 for defining cost functions, constraints, solver backends and a general MPC wrapper.
  - The `rigid body dynamics' module (ct_rbd) provides tools for modelling Rigid Body Dynamics
 systems and interfaces with ct_core and ct_optcon data types.

 For testing as well as examples, we also provide the 'models' module (ct_models) which contains
 various robot models including a quadruped, a robotic arm, a normal quadrotor and a quadrotor
 with slung load.

 The four different main modules are detailed in the following.


 \subsection ct_core_overview CT Core

  - Definitions of fundamental types for **control** and simulation, such as dynamic systems
  (ct::core::System), states (ct::core::StateVector), controls (ct::core::Controller), or trajectories
  (ct::core::DiscreteTrajectoryBase).
  - **Numeric integration** (ct::core::Integrator) with various ODE solvers including fixed step
  (ct::core::IntegratorEuler, ct::core::IntegratorRK4) and variable step (ct::core::IntegratorRK5Variable,
  ct::core::ODE45) integrators, as well as symplectic (semi-implicit) integrators.
  - Numerical approximation of Trajectory **Sensitivities** (ct::core::Sensitivity , e.g. by forward-integrating
  variational differential equations)
  - Common **feedback controllers** (e.g. ct::core::PIDController)
  - Derivatives/Jacobians of general functions using **Numerical Differentiation** (ct::core::DerivativesNumDiff)
  or **Automatic-Differentiation** with code-generation (ct::core::DerivativesCppadCG) and just-in-time (JIT)
  compilation (ct::core::DerivativesCppadJIT)
  - <a href="../../../ct_core/doc/html/index.html">quick link to ct_core</a>


 \subsection ct_optcon_overview CT Optimal Control

  - Definitions for **Optimal Control Problems** (ct::optcon::OptConProblem) and **Optimal Control Solvers** (ct::optcon::OptConSolver)
  - **CostFunction toolbox** allowing to construct cost functions from file and providing first-order and **second-order approximations**, see ct::optcon::CostFunction.
  - **Constraint toolbox** for formulating constraints of Optimal Control Problems, as well as automatically computing their Jacobians.
  - reference C++ implementations of the **Linear Quadratic Regulator**, infinite-horizon LQR and time-varying LQR (ct::optcon::LQR, ct::optcon::TVLQR)
  - **Riccati-solver** (ct::optcon::GNRiccatiSolver) for unconstrained linear-quadratic optimal control problems, interface to high-performance
  <a href="https://github.com/giaf/hpipm" target="_blank"> third-party Riccati-solvers</a> for constrained linear-quadratic optimal control problems
  - **iterative non-linear Optimal Control** solvers, i.e. Gauss-Newton solvers such as iLQR (ct::optcon::iLQR) and
  Gauss-Newton Multiple Shooting(ct::optcon::GNMS), constrained direct multiple-shooting (ct::optcon::DmsSolver)
  - Non-Linear **Model Predictive Control** (ct::optcon::MPC)
  - Definitions for Nonlinear Programming Problems (**NLPs**, ct::optcon::Nlp) and interfaces to third-party **NLP Solvers**
  (ct::optcon::SnoptSolver and ct::optcon::IpoptSolver)
  - <a href="../../../ct_optcon/doc/html/index.html">quick link to ct_optcon</a>


 \subsection ct_rbd_overview CT Rigid Body Dynamics

  - Standard models for Rigid Body Dynamics
  - Definitions for the state of a Rigid Body System expressed as general coordinates (ct::rbd::RBDState)
  - Routines for different flavors of **Forward** and **Inverse Dynamics** (ct::rbd::Dynamics)
  - Rigid body and end-effector **kinematics** (ct::rbd::Kinematics, note that we do currently not provide inverse kinematics)
  - Operational Space Controllers
  - Basic soft **auto-differentiable contact model** for arbitrary frames (ct::rbd::EEContactModel)
  - **Actuator dynamics** (ct::rbd::ActuatorDynamics)
  - Backend uses <a href="https://bitbucket.org/mfrigerio17/roboticscodegenerator/" target="_blank">RobCoGen</a> \cite frigerioCodeGen,
  a highly efficient Rigid Body Dynamics library
  - <a href="../../../ct_rbd/doc/html/index.html">quick link to ct_rbd</a>


 \subsection ct_models_overview CT Models:

  - Various standard models for testing and evaluation including UAVs (ct::models::Quadrotor), ground robots,
  legged robots (ct::models::HyQ), robot arms (ct::models::HyA), inverted pendulums etc.
  - Means of creating linear approximation of these models
  - <a href="../../../ct_models/doc/html/index.html">quick link to ct_models</a>


 \section source_code Source Code

 The source code is available at <a href="https://bitbucket.org/adrlab/ct" target="_blank">https://bitbucket.org/adrlab/ct</a>

 Furthermore there are examples for ROS interfaces available:
  - <a href="../../../../ct_ros/ct_ros_msgs/doc/html/index.html" target="_blank">ct_ros_msgs</a>
  - <a href="../../../../ct_ros/ct_ros_nodes/doc/html/index.html" target="_blank">ct_ros_nodes</a>


 \section gs How to use the Control Toolbox

 To get started with the control toolbox, please see \ref getting_started "Getting Started".


 \section contact Support

 For any questions, issues or other troubleshooting please either
 - create an issue: https://bitbucket.org/adrlab/ct/issues
 - contact the devs: control-toolbox-dev@googlegroups.com


 \section ct_doc_acknowledgement Acknowledgements

 \subsection contribs Contributors
  - Michael Neunert
  - Markus Giftthaler
  - Markus Stäuble
  - Farbod Farshidian
  - Diego Pardo
  - Timothy Sandy
  - Jan Carius
  - Hamza Merzic

 \subsection lead_overview Project Lead and Maintenance
  - Michael Neunert, neunertm (at) gmail (dot) com
  - Markus Giftthaler, mgiftthaler (at) ethz (dot) ch

 \subsection funding Funding
 This software has been developed at the <a href="http://www.adrl.ethz.ch" target="_blank">Agile & Dexterous Robotics Lab</a>
 at <a href="http://www.ethz.ch/en" target="_blank">ETH Zurich</a>, Switzerland.
 The development has been made possible through financial support from the <a href="http://www.snf.ch/en/" target="_blank">Swiss National Science Foundation (SNF)</a>
 through a SNF Professorship award to Jonas Buchli and the National Competence Centers in Research (NCCR)
 <a href="https://www.nccr-robotics.ch/" target="_blank">Robotics</a> and <a href="http://www.dfab.ch/en/" target="_blank">Digital Fabrication</a>.


 \section licence Licence Information

 The Control Toolbox is released under the
 <a href="https://www.apache.org/licenses/LICENSE-2.0" target="_blank">Apache Licence, Version 2.0</a>.
 Please note the licence and notice files in the source directory.


 \section cite_ct How to cite the CT

 \code
 @misc{adrlCT,
   author = "Giftthaler, Markus and Neunert, Michael and {St\"auble}, Markus and Buchli, Jonas",
   title = "The {Control Toolbox} - An Open-Source {C++} Library for Robotics, Optimal and Model Predictive Control",
   howpublished = "\url{https://adrlab.bitbucket.io/ct}",
   year = "2018",
   note = "arXiv:1801.04290 [cs.RO]"
 }
 \endcode


 \section publications Related Publications

 This toolbox has been used in, or has helped to realize the following academic publications:

 - Markus Giftthaler, Michael Neunert, Markus Stäuble, Jonas Buchli and Moritz Diehl.
 “A Family of iterative Gauss-Newton Shooting Methods for Nonlinear Optimal Control”.
 <a href="https://arxiv.org/abs/1711.11006" target="_blank">arXiv preprint</a>

 - Michael Neunert, Markus Stäuble, Markus Giftthaler, Dario Bellicoso, Jan Carius, Christian Gehring,
 Marco Hutter and Jonas Buchli.
 “Whole Body Model Predictive Control Through Contacts For Quadrupeds”.
 To appear in IEEE Robotics and Automation Letters.
 <a href="https://arxiv.org/abs/1712.02889" target="_blank">arXiv preprint</a>

 - Markus Giftthaler and Jonas Buchli.
 “A Projection Approach to Equality Constrained Iterative Linear Quadratic Optimal Control”.
 2017 IEEE-RAS International Conference on Humanoid Robots, November 15-17, Birmingham, UK.
 <a href="http://ieeexplore.ieee.org/document/8239538/" target="_blank">IEEE Xplore</a>

 - Markus Giftthaler, Michael Neunert, Markus Stäuble, Marco Frigerio, Claudio Semini and Jonas Buchli.
 “Automatic Differentiation of Rigid Body Dynamics for Optimal Control and Estimation”,
 Advanced Robotics, SIMPAR special issue. November 2017.
 <a href="https://arxiv.org/abs/1709.03799" target="_blank">arXiv preprint</a>

 - Michael Neunert, Markus Giftthaler, Marco Frigerio, Claudio Semini and Jonas Buchli.
 “Fast Derivatives of Rigid Body Dynamics for Control, Optimization and Estimation”,
 2016 IEEE International Conference on Simulation, Modelling, and Programming for Autonomous Robots,
 San Francisco. (Best Paper Award).
 <a href="http://ieeexplore.ieee.org/document/7862380/" target="_blank">IEEE Xplore</a>

 - Michael Neunert, Farbod Farshidian, Alexander W. Winkler, Jonas Buchli
 "Trajectory Optimization Through Contacts and Automatic Gait Discovery for Quadrupeds",
 IEEE Robotics and Automation Letters,
 <a href="http://ieeexplore.ieee.org/document/7845678/" target="_blank">IEEE Xplore</a>

 - Michael Neunert, Cédric de Crousaz, Fadri Furrer, Mina Kamel, Farbod Farshidian, Roland Siegwart, Jonas Buchli.
 "Fast nonlinear model predictive control for unified trajectory optimization and tracking",
 2016 IEEE International Conference on Robotics and Automation (ICRA),
 <a href="http://ieeexplore.ieee.org/document/7487274/" target="_blank">IEEE Xplore</a>

 - Markus Giftthaler, Farbod Farshidian, Timothy Sandy, Lukas Stadelmann and Jonas Buchli.
 “Efficient Kinematic Planning for Mobile Manipulators with Non-holonomic Constraints Using Optimal Control”,
 IEEE International Conference on Robotics and Automation, 2017, Singapore.
 <a href="https://arxiv.org/abs/1701.08051" target="_blank">arXiv preprint</a>

 - Markus Giftthaler, Timothy Sandy, Kathrin Dörfler, Ian Brooks, Mark Buckingham, Gonzalo Rey,
 Matthias Kohler, Fabio Gramazio and Jonas Buchli.
 “Mobile Robotic Fabrication at 1:1 scale: the In situ Fabricator”. Construction Robotics, Springer Journal no. 41693
 <a href="https://arxiv.org/abs/1701.03573" target="_blank">arXiv preprint</a>

 - Timothy Sandy, Markus Giftthaler, Kathrin Dörfler, Matthias Kohler and Jonas Buchli.
 “Autonomous Repositioning and Localization of an In situ Fabricator”,
 IEEE International Conference on Robotics and Automation 2016, Stockholm, Sweden.
 <a href="http://ieeexplore.ieee.org/document/7487449/" target="_blank">IEEE Xplore</a>

 - Michael Neunert, Farbod Farshidian, Jonas Buchli (2014). Adaptive Real-time Nonlinear Model Predictive Motion Control.
 In IROS 2014 Workshop on Machine Learning in Planning and Control of Robot Motion
 <a href="http://www.adrl.ethz.ch/archive/p_14_mlpc_mpc_rezero.pdf" target="_blank">preprint</a>

 */

	/*!
	\mainpage Overview

	@tableofcontents

	\section ct1 Control Toolbox

	This is the ADRL Control Toolbox ('CT'), an open-source C++ library for efficient modelling, control,
	estimation, trajectory optimization and model predictive control.
	The CT is applicable to a broad class of dynamic systems, but features additional modelling tools specially designed for robotics.
	This page outlines its general concept, its major building blocks and highlights selected application examples.

	The library contains several tools to design and evaluate controllers, model dynamical systems and solve optimal control problems.
	The CT was designed with the following features in mind:

	- Systems and dynamics:
	- intuitive modelling of systems governed by ordinary differential- or difference equations.

	- Trajectory optimization, optimal control and (nonlinear) model predictive control:
	- intuitive modelling of cost functions and constraints
	- common interfaces for optimal control solvers and nonlinear model predictive control
	- currently supported algorithms:
	- Single Shooting
	- iLQR \cite todorov2005ilqg / SLQ \cite slq:2005
	- Gauss-Newton-Multiple-Shooting (GNMS) \cite giftthaler2017family
	- Classical Direct Multiple Shooting (DMS) \cite bock1984direct
	- standardized interfaces for the solvers
	- IPOPT (first and second order)
	- SNOPT
	- HPIPM
	- custom Riccati-solver

	- Performance:
	- solve large scale optimal control problems in MPC fashion.

	- Robot Modelling and rigid body dynamics:
	- straight-forward interface to a state-of the art rigid body dynamics modelling tool.

	- Automatic Differentiation:
	- first- and second order automatic differentiation of arbitrary vector-valued functions including cost functions and constraints
	- automatic differentiation of rigid body dynamics
	- derivative code generation for maximum efficiency

	- Simplicity:
	- all algorithm flavors and solver backends are available through simple configuration files.


	The CT is hosted on bitbucket: <a href="https://bitbucket.org/adrlab/ct" target="_blank">https://bitbucket.org/adrlab/ct</a>



	\section ae Robot Application Examples

	The Control Toolbox has been used for Hardware and Simulation control tasks on flying, walking and ground robots.

	\htmlonly
	<iframe width="560" height="315" src="https://www.youtube.com/embed/Y7-1CBqs4x4" frameborder="2" allowfullscreen></iframe>
	<iframe width="560" height="315" src="https://www.youtube.com/embed/vuCSKtP67E4" frameborder="2" allowfullscreen></iframe>
	<iframe width="560" height="315" src="https://www.youtube.com/embed/rWmw-ERGyz4" frameborder="2" allowfullscreen></iframe>
	<iframe width="560" height="315" src="https://www.youtube.com/embed/rVu1L_tPCoM" frameborder="2" allowfullscreen></iframe>
	\endhtmlonly

	For details and more videos see \ref application_examples "Application Examples" and our \ref publications "publications".


	\section teaser What is the CT?

	A common tasks for researchers and practitioners in both the control and the robotics communities
	is to model systems, implement equations of motion and design model-based controllers, estimators,
	planning algorithms, etc.
	Sooner or later, one is confronted with questions of efficient implementation, computing derivative
	information, formulating cost functions and constraints or running controllers in model-predictive
	control fashion.

	The Control Toolbox is specifically designed for these tasks. It is written entirely in C++ and has
	a strong focus on highly efficient code that can be run online (in the loop) on robots or other
	actuated hardware. A major contribution of the CT is are its implementations of optimal control
	algorithms, spanning a range from simple LQR reference implementations to constrained model predictive
	control. The CT supports Automatic Differentiation (Auto-Diff) and allows to generate derivative code
	for arbitrary scalar and vector-valued functions.
	We designed the toolbox with usability in mind, allowing users to apply advanced concepts such as
	nonlinear model predictive control (NMPC) or numerical optimal control easily and with minimal effort.
	While we provide an interface to a state-of-the art Auto-Diff compatible robot modelling software, all
	other modules are independent of the a particular modelling framework, allowing the code to be interfaced
	with existing C/C++ code or libraries.

	The CT has been successfully used in a variety of different projects, including a large number of
	hardware experiments, demonstrations and academic publications.
	Example hardware applications are online trajectory optimization with collision
	avoidance \cite giftthaler2017autodiff, trajectory optimization for Quadrupeds \cite neunert:2017:ral
	and mobile manipulators \cite giftthaler2017efficient as well as NMPC on ground robots \cite neunert2017mpc
	and UAVs \cite neunert16hexrotor. The project originated from research conducted at the Agile \& Dexterous
	Robotics Lab at ETH Zurich, but is continuously extended to cover more fields of applications and algorithms.


	\section scope Scope of the CT

	Software is one of the key building blocks for robotic systems and there is a great effort
	in creating software tools and libraries for robotics.
	However, when it comes to control and especially Numerical Optimal Control, there are not
	many open source tools available that are both easy to use for fast development as well as
	efficient enough for online usage.
	While there exist mature toolboxes for Numerical Optimal Control and Trajectory Optimization,
	they are highly specialized, standalone tools that due not provide sufficient flexibility
	for other applications. Here is where the CT steps in. The CT has been designed from ground
	up to provide the tools needed for fast development and evaluation of control methods while
	being optimized for efficiency allowing for online operation. While the emphasis lies on control,
	the tools provided can also be used for simulation, estimation or optimization applications.

	In contrast to other robotic software, CT is not a rigid integrated application but can be
	seen quite literal as a toolbox: It offers a variety of tools which can be used and combined
	to solve a task at hand. While ease-of-use has been a major criteria during the design and
	application examples are provided, using CT still requires programming and control knowledge.
	However, it frees the users from implementing standard methods that require in-depth experience
	with linear algebra or numerical methods. Furthermore, by using common definitions and types,
	a seamless integration between different components such as systems, controllers or integrators
	is provided, enabling fast prototyping.


	\section design Design and Implementation

	The main focus of CT is efficiency, which is why it is fully implemented in C++.
	Since CT is designed as a toolbox rather than an integrated application, we tried to provide
	maximum flexibility to the users. Therefore, it is not tied to a specific middleware such as
	ROS and dependencies are kept at a minimum. The two essential dependencies for CT are
	<a href="http://eigen.tuxfamily.org" target="_blank">Eigen</a> and
	<a href="http://github.com/ethz-asl/kindr" target="_blank">Kindr</a>
	(which is based on Eigen). This Eigen dependency is intentional since Eigen
	is a defacto standard for linear algebra in C++, as it provides highly efficient implementations
	of standard matrix operations as well as more advanced linear algebra methods.
	Kindr is a header only Kinematics library which builds on top of it and provides data types
	for different rotation representations such as Quaternions, Euler angles or rotation matrices.


	\section modules Structure and Modules of the CT

	The Control Toolbox consists of three main modules. The Core module (ct_core), the Optimal
	Control (ct_optcon) module and the rigid body dynamics (ct_rbd) module.
	There is a clear hierarchy between the modules.
	That means, the modules depend on each other in this order, e.g. you can use the core module
	without the optcon or rbd module.
	- The `core' module (ct_core) module provides general type definitions and mathematical tools.
	For example, it contains most data type definitions, definitions for systems and controllers,
	as well as basic functionality such as numerical integrators for differential equations.
	- The `optimal Control' module (ct_optcon) builds on top of the `core' module and adds
	infrastructure for defining and solving Optimal Control Problems. It contains the functionality
	for defining cost functions, constraints, solver backends and a general MPC wrapper.
	- The `rigid body dynamics' module (ct_rbd) provides tools for modelling Rigid Body Dynamics
	systems and interfaces with ct_core and ct_optcon data types.

	For testing as well as examples, we also provide the 'models' module (ct_models) which contains
	various robot models including a quadruped, a robotic arm, a normal quadrotor and a quadrotor
	with slung load.

	The four different main modules are detailed in the following.


	\subsection ct_core_overview CT Core

	- Definitions of fundamental types for control and simulation, such as dynamic systems
	(ct::core::System), states (ct::core::StateVector), controls (ct::core::Controller), or trajectories
	(ct::core::DiscreteTrajectoryBase).
	- Numeric integration (ct::core::Integrator) with various ODE solvers including fixed step
	(ct::core::IntegratorEuler, ct::core::IntegratorRK4) and variable step (ct::core::IntegratorRK5Variable,
	ct::core::ODE45) integrators, as well as symplectic (semi-implicit) integrators.
	- Numerical approximation of Trajectory Sensitivities (ct::core::Sensitivity , e.g. by forward-integrating
	variational differential equations)
	- Common feedback controllers (e.g. ct::core::PIDController)
	- Derivatives/Jacobians of general functions using Numerical Differentiation (ct::core::DerivativesNumDiff)
	or Automatic-Differentiation with code-generation (ct::core::DerivativesCppadCG) and just-in-time (JIT)
	compilation (ct::core::DerivativesCppadJIT)
	- <a href="../../../ct_core/doc/html/index.html">quick link to ct_core</a>


	\subsection ct_optcon_overview CT Optimal Control

	- Definitions for Optimal Control Problems (ct::optcon::OptConProblem) and Optimal Control Solvers (ct::optcon::OptConSolver)
	- CostFunction toolbox allowing to construct cost functions from file and providing first-order and second-order approximations, see ct::optcon::CostFunction.
	- Constraint toolbox for formulating constraints of Optimal Control Problems, as well as automatically computing their Jacobians.
	- reference C++ implementations of the Linear Quadratic Regulator, infinite-horizon LQR and time-varying LQR (ct::optcon::LQR, ct::optcon::TVLQR)
	- Riccati-solver (ct::optcon::GNRiccatiSolver) for unconstrained linear-quadratic optimal control problems, interface to high-performance
	<a href="https://github.com/giaf/hpipm" target="_blank"> third-party Riccati-solvers</a> for constrained linear-quadratic optimal control problems
	- iterative non-linear Optimal Control solvers, i.e. Gauss-Newton solvers such as iLQR (ct::optcon::iLQR) and
	Gauss-Newton Multiple Shooting(ct::optcon::GNMS), constrained direct multiple-shooting (ct::optcon::DmsSolver)
	- Non-Linear Model Predictive Control (ct::optcon::MPC)
	- Definitions for Nonlinear Programming Problems (NLPs, ct::optcon::Nlp) and interfaces to third-party NLP Solvers
	(ct::optcon::SnoptSolver and ct::optcon::IpoptSolver)
	- <a href="../../../ct_optcon/doc/html/index.html">quick link to ct_optcon</a>


	\subsection ct_rbd_overview CT Rigid Body Dynamics

	- Standard models for Rigid Body Dynamics
	- Definitions for the state of a Rigid Body System expressed as general coordinates (ct::rbd::RBDState)
	- Routines for different flavors of Forward and Inverse Dynamics (ct::rbd::Dynamics)
	- Rigid body and end-effector kinematics (ct::rbd::Kinematics, note that we do currently not provide inverse kinematics)
	- Operational Space Controllers
	- Basic soft auto-differentiable contact model for arbitrary frames (ct::rbd::EEContactModel)
	- Actuator dynamics (ct::rbd::ActuatorDynamics)
	- Backend uses <a href="https://bitbucket.org/mfrigerio17/roboticscodegenerator/" target="_blank">RobCoGen</a> \cite frigerioCodeGen,
	a highly efficient Rigid Body Dynamics library
	- <a href="../../../ct_rbd/doc/html/index.html">quick link to ct_rbd</a>


	\subsection ct_models_overview CT Models:

	- Various standard models for testing and evaluation including UAVs (ct::models::Quadrotor), ground robots,
	legged robots (ct::models::HyQ), robot arms (ct::models::HyA), inverted pendulums etc.
	- Means of creating linear approximation of these models
	- <a href="../../../ct_models/doc/html/index.html">quick link to ct_models</a>


	\section source_code Source Code

	The source code is available at <a href="https://bitbucket.org/adrlab/ct" target="_blank">https://bitbucket.org/adrlab/ct</a>

	Furthermore there are examples for ROS interfaces available:
	- <a href="../../../../ct_ros/ct_ros_msgs/doc/html/index.html" target="_blank">ct_ros_msgs</a>
	- <a href="../../../../ct_ros/ct_ros_nodes/doc/html/index.html" target="_blank">ct_ros_nodes</a>


	\section gs How to use the Control Toolbox

	To get started with the control toolbox, please see \ref getting_started "Getting Started".


	\section contact Support

	For any questions, issues or other troubleshooting please either
	- create an issue: https://bitbucket.org/adrlab/ct/issues
	- contact the devs: control-toolbox-dev@googlegroups.com


	\section ct_doc_acknowledgement Acknowledgements

	\subsection contribs Contributors
	- Michael Neunert
	- Markus Giftthaler
	- Markus Stäuble
	- Farbod Farshidian
	- Diego Pardo
	- Timothy Sandy
	- Jan Carius
	- Hamza Merzic

	\subsection lead_overview Project Lead and Maintenance
	- Michael Neunert, neunertm (at) gmail (dot) com
	- Markus Giftthaler, mgiftthaler (at) ethz (dot) ch

	\subsection funding Funding
	This software has been developed at the <a href="http://www.adrl.ethz.ch" target="_blank">Agile & Dexterous Robotics Lab</a>
	at <a href="http://www.ethz.ch/en" target="_blank">ETH Zurich</a>, Switzerland.
	The development has been made possible through financial support from the <a href="http://www.snf.ch/en/" target="_blank">Swiss National Science Foundation (SNF)</a>
	through a SNF Professorship award to Jonas Buchli and the National Competence Centers in Research (NCCR)
	<a href="https://www.nccr-robotics.ch/" target="_blank">Robotics</a> and <a href="http://www.dfab.ch/en/" target="_blank">Digital Fabrication</a>.


	\section licence Licence Information

	The Control Toolbox is released under the
	<a href="https://www.apache.org/licenses/LICENSE-2.0" target="_blank">Apache Licence, Version 2.0</a>.
	Please note the licence and notice files in the source directory.


	\section cite_ct How to cite the CT

	\code
	@misc{adrlCT,
	author = "Giftthaler, Markus and Neunert, Michael and {St\"auble}, Markus and Buchli, Jonas",
	title = "The {Control Toolbox} - An Open-Source {C++} Library for Robotics, Optimal and Model Predictive Control",
	howpublished = "\url{https://adrlab.bitbucket.io/ct}",
	year = "2018",
	note = "arXiv:1801.04290 [cs.RO]"
	}
	\endcode


	\section publications Related Publications

	This toolbox has been used in, or has helped to realize the following academic publications:

	- Markus Giftthaler, Michael Neunert, Markus Stäuble, Jonas Buchli and Moritz Diehl.
	“A Family of iterative Gauss-Newton Shooting Methods for Nonlinear Optimal Control”.
	<a href="https://arxiv.org/abs/1711.11006" target="_blank">arXiv preprint</a>

	- Michael Neunert, Markus Stäuble, Markus Giftthaler, Dario Bellicoso, Jan Carius, Christian Gehring,
	Marco Hutter and Jonas Buchli.
	“Whole Body Model Predictive Control Through Contacts For Quadrupeds”.
	To appear in IEEE Robotics and Automation Letters.
	<a href="https://arxiv.org/abs/1712.02889" target="_blank">arXiv preprint</a>

	- Markus Giftthaler and Jonas Buchli.
	“A Projection Approach to Equality Constrained Iterative Linear Quadratic Optimal Control”.
	2017 IEEE-RAS International Conference on Humanoid Robots, November 15-17, Birmingham, UK.
	<a href="http://ieeexplore.ieee.org/document/8239538/" target="_blank">IEEE Xplore</a>

	- Markus Giftthaler, Michael Neunert, Markus Stäuble, Marco Frigerio, Claudio Semini and Jonas Buchli.
	“Automatic Differentiation of Rigid Body Dynamics for Optimal Control and Estimation”,
	Advanced Robotics, SIMPAR special issue. November 2017.
	<a href="https://arxiv.org/abs/1709.03799" target="_blank">arXiv preprint</a>

	- Michael Neunert, Markus Giftthaler, Marco Frigerio, Claudio Semini and Jonas Buchli.
	“Fast Derivatives of Rigid Body Dynamics for Control, Optimization and Estimation”,
	2016 IEEE International Conference on Simulation, Modelling, and Programming for Autonomous Robots,
	San Francisco. (Best Paper Award).
	<a href="http://ieeexplore.ieee.org/document/7862380/" target="_blank">IEEE Xplore</a>

	- Michael Neunert, Farbod Farshidian, Alexander W. Winkler, Jonas Buchli
	"Trajectory Optimization Through Contacts and Automatic Gait Discovery for Quadrupeds",
	IEEE Robotics and Automation Letters,
	<a href="http://ieeexplore.ieee.org/document/7845678/" target="_blank">IEEE Xplore</a>

	- Michael Neunert, Cédric de Crousaz, Fadri Furrer, Mina Kamel, Farbod Farshidian, Roland Siegwart, Jonas Buchli.
	"Fast nonlinear model predictive control for unified trajectory optimization and tracking",
	2016 IEEE International Conference on Robotics and Automation (ICRA),
	<a href="http://ieeexplore.ieee.org/document/7487274/" target="_blank">IEEE Xplore</a>

	- Markus Giftthaler, Farbod Farshidian, Timothy Sandy, Lukas Stadelmann and Jonas Buchli.
	“Efficient Kinematic Planning for Mobile Manipulators with Non-holonomic Constraints Using Optimal Control”,
	IEEE International Conference on Robotics and Automation, 2017, Singapore.
	<a href="https://arxiv.org/abs/1701.08051" target="_blank">arXiv preprint</a>

	- Markus Giftthaler, Timothy Sandy, Kathrin Dörfler, Ian Brooks, Mark Buckingham, Gonzalo Rey,
	Matthias Kohler, Fabio Gramazio and Jonas Buchli.
	“Mobile Robotic Fabrication at 1:1 scale: the In situ Fabricator”. Construction Robotics, Springer Journal no. 41693
	<a href="https://arxiv.org/abs/1701.03573" target="_blank">arXiv preprint</a>

	- Timothy Sandy, Markus Giftthaler, Kathrin Dörfler, Matthias Kohler and Jonas Buchli.
	“Autonomous Repositioning and Localization of an In situ Fabricator”,
	IEEE International Conference on Robotics and Automation 2016, Stockholm, Sweden.
	<a href="http://ieeexplore.ieee.org/document/7487449/" target="_blank">IEEE Xplore</a>

	- Michael Neunert, Farbod Farshidian, Jonas Buchli (2014). Adaptive Real-time Nonlinear Model Predictive Motion Control.
	In IROS 2014 Workshop on Machine Learning in Planning and Control of Robot Motion
	<a href="http://www.adrl.ethz.ch/archive/p_14_mlpc_mpc_rezero.pdf" target="_blank">preprint</a>

	*/