The Control Toolbox ('CT'), is a C++ library for modelling, control, estimation, trajectory optimization and model predictive control. The CT is applicable to a broad class of dynamic systems, but features additional 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 numerically 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
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 [3], trajectory optimization for Quadrupeds [8] and mobile manipulators [4] as well as NMPC on ground robots [9] and UAVs [6]. 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.
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.
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 Eigen and Kindr (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.
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.
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)
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)
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 third-party Riccati-solvers 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)
The Control Toolbox is released under the BSD-2 clause license. Please note the licence and notice files in the source directory.
How to cite the CT
@INPROCEEDINGS{adrlCT,
author = "Giftthaler, Markus and Neunert, Michael and {St\"auble}, Markus and Buchli, Jonas",
booktitle={2018 IEEE International Conference on Simulation, Modeling, and Programming for Autonomous Robots (SIMPAR)},
title = "The {Control Toolbox} - An Open-Source {C++} Library for Robotics, Optimal and Model Predictive Control",
year={2018},
pages={123-129},
doi={10.1109/SIMPAR.2018.8376281},
month={May},
number={},
volume={},
}
Related Publications
This toolbox has been used in, or has helped to realize the following academic publications:
Markus Giftthaler, Michael Neunert, Markus Stäuble and Jonas Buchli. “The Control Toolbox - An Open-Source C++ Library for Robotics, Optimal and Model Predictive Control”. IEEE Simpar 2018 (Best Student Paper Award). arXiv preprint
Markus Giftthaler, Michael Neunert, Markus Stäuble, Jonas Buchli and Moritz Diehl. “A Family of iterative Gauss-Newton Shooting Methods for Nonlinear Optimal Control”. IROS 2018. arXiv preprint
Jan Carius, René Ranftl, Vladlen Koltun and Marco Hutter. "Trajectory Optimization with Implicit Hard Contacts." IEEE Robotics and Automation Letters 3, no. 4 (2018): 3316-3323.
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”. IEEE Robotics and Automation Letters, 2017. arXiv preprint
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. IEEE Xplore
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. arXiv preprint
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). IEEE Xplore
Michael Neunert, Farbod Farshidian, Alexander W. Winkler, Jonas Buchli "Trajectory Optimization Through Contacts and Automatic Gait Discovery for Quadrupeds", IEEE Robotics and Automation Letters, IEEE Xplore
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), IEEE Xplore
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. arXiv preprint
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 arXiv preprint
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. IEEE Xplore
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 preprint
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