Greg Horn

Bio: Greg Horn is an academic researcher from University of Freiburg. The author has contributed to research in topics: Wind power & Crosswind. The author has an hindex of 6, co-authored 6 publications receiving 955 citations. Previous affiliations of Greg Horn include Katholieke Universiteit Leuven.

CasADi: a software framework for nonlinear optimization and optimal control

Abstract: We present CasADi, an open-source software framework for numerical optimization. CasADi is a general-purpose tool that can be used to model and solve optimization problems with a large degree of flexibility, larger than what is associated with popular algebraic modeling languages such as AMPL, GAMS, JuMP or Pyomo. Of special interest are problems constrained by differential equations, i.e. optimal control problems. CasADi is written in self-contained C++, but is most conveniently used via full-featured interfaces to Python, MATLAB or Octave. Since its inception in late 2009, it has been used successfully for academic teaching as well as in applications from multiple fields, including process control, robotics and aerospace. This article gives an up-to-date and accessible introduction to the CasADi framework, which has undergone numerous design improvements over the last 7 years.

Nonlinear Model Predictive Control of a Human-sized Quadrotor

Abstract: This paper discusses the design, implementation and deployment of an attitude controller for a quadrotor based on nonlinear model predictive control on a low-power embedded system equipped with a Cortex A9 CPU running at 800 MHz. Due to the limited computational power of the available hardware, a modified interior-point solver for the so-called partially tightened Real-Time Iteration is used. The algorithm splits the prediction horizon in two sections. A Riccati-like recursion is exploited that relies on a single linearization of the complementarity conditions per sampling-time for the terminal section. In this way, it is possible to achieve a speedup of a factor 3 with respect to a standard real-time iteration formulation for the application under consideration. Simulation results that show the improvement in performance obtained by using NMPC over standard control techniques are discussed and experimental results using the proposed implementation are presented.

Effect of the Electrical Energy Conversion on Optimal Cycles for Pumping Airborne Wind Energy

Abstract: Airborne wind energy harvesting offers an alternative to traditional wind turbines by flying crosswind cycles with a tethered airfoil. By reeling in and out the tether periodically, net electrical power can be generated. When looking for the optimal cycle to fly, one should optimize for maximal electrical power generation. However, the conversion from mechanical to electrical power was not yet included in the models. In this paper, it is shown that by including an electrical energy conversion model into cycle optimization, the electrical output of the system increases and the acquired system can be used in a broader range of wind speeds. The approach is illustrated with experimentally verified models.

A quaternion-based model for optimal control of the SkySails airborne wind energy system

Abstract: Airborne wind energy systems are capable of extracting energy from higher wind speeds at higher altitudes. The configuration considered in this paper is based on a tethered kite flown in a pumping orbit. This pumping cycle generates energy by winching out at high tether forces and driving a generator while flying figures-of-eight, or lemniscates, as crosswind pattern. Then, the tether is reeled in while keeping the kite at a neutral position, thus leaving a net amount of generated energy. In order to achieve an economic operation, optimization of pumping cycles is of great interest. In this paper, first the principles of airborne wind energy will be briefly revisited. The first contribution is a singularity-free model for the tethered kite dynamics in quaternion representation, where the model is derived from first principles. The second contribution is an optimal control formulation and numerical results for complete pumping cycles. Based on the developed model, the setup of the optimal control problem (OCP) is described in detail along with its numerical solution based on the direct multiple shooting method in the CasADi optimization environment. Optimization results for a pumping cycle consisting of six lemniscates show that the approach is capable to find an optimal orbit in a few minutes of computation time. For this optimal orbit, the power output is increased by a factor of two compared to a sophisticated initial guess for the considered test scenario.

A quaternion-based model for optimal control of an airborne wind energy system

Abstract: Airborne wind energy systems are capable of extracting energy from higher wind speeds at higher altitudes. The configuration considered in this paper is based on a tethered kite flown in a pumping orbit. This pumping cycle generates energy by winching out at high tether forces and driving a generator while flying figures-of-eight, or lemniscates, as crosswind pattern. Then, the tether is reeled in while keeping the kite at a neutral position, thus leaving a net amount of generated energy. In order to achieve an economic operation, optimization of pumping cycles is of great interest. In this paper, first the principles of airborne wind energy will be briefly revisited. The first contribution is a singularity-free model for the tethered kite dynamics in quaternion representation, where the model is derived from first principles. The second contribution is an optimal control formulation and numerical results for complete pumping cycles. Based on the developed model, the setup of the optimal control problem (OCP) is described in detail along with its numerical solution based on the direct multiple shooting method in the CasADi optimization environment. Optimization results for a pumping cycle consisting of six lemniscates show that the approach is capable to find an optimal orbit in a few minutes of computation time. For this optimal orbit, the power output is increased by a factor of two compared to a sophisticated initial guess for the considered test scenario.

CasADi: a software framework for nonlinear optimization and optimal control

Abstract: We present CasADi, an open-source software framework for numerical optimization. CasADi is a general-purpose tool that can be used to model and solve optimization problems with a large degree of flexibility, larger than what is associated with popular algebraic modeling languages such as AMPL, GAMS, JuMP or Pyomo. Of special interest are problems constrained by differential equations, i.e. optimal control problems. CasADi is written in self-contained C++, but is most conveniently used via full-featured interfaces to Python, MATLAB or Octave. Since its inception in late 2009, it has been used successfully for academic teaching as well as in applications from multiple fields, including process control, robotics and aerospace. This article gives an up-to-date and accessible introduction to the CasADi framework, which has undergone numerous design improvements over the last 7 years.

Enabling New Flexibility in the SUNDIALS Suite of Nonlinear and Differential/Algebraic Equation Solvers.

Abstract: In recent years, the SUite of Nonlinear and DIfferential/ALgebraic equation Solvers (SUNDIALS) has been redesigned to better enable the use of application-specific and third-party algebraic solvers and data structures. Throughout this work, we have adhered to specific guiding principles that minimized the impact to current users while providing maximum flexibility for later evolution of solvers and data structures. The redesign was done through creation of new classes for linear and nonlinear solvers, enhancements to the vector class, and the creation of modern Fortran interfaces that leverage interoperability features of the Fortran 2003 standard. The vast majority of this work has been performed "behind-the-scenes," with minimal changes to the user interface and no reduction in solver capabilities or performance. However, these changes now allow advanced users to create highly customized solvers that exploit their problem structure, enabling SUNDIALS use on extreme-scale, heterogeneous computational architectures.

Neural Ordinary Differential Equations

Abstract: We introduce a new family of deep neural network models. Instead of specifying a discrete sequence of hidden layers, we parameterize the derivative of the hidden state using a neural network. The output of the network is computed using a black-box differential equation solver. These continuous-depth models have constant memory cost, adapt their evaluation strategy to each input, and can explicitly trade numerical precision for speed. We demonstrate these properties in continuous-depth residual networks and continuous-time latent variable models. We also construct continuous normalizing flows, a generative model that can train by maximum likelihood, without partitioning or ordering the data dimensions. For training, we show how to scalably backpropagate through any ODE solver, without access to its internal operations. This allows end-to-end training of ODEs within larger models.

Mini Cheetah: A Platform for Pushing the Limits of Dynamic Quadruped Control

Abstract: Mini Cheetah is a small and inexpensive, yet powerful and mechanically robust quadruped robot, intended to enable rapid development of control systems for legged robots. The robot uses custom backdriveable modular actuators, which enable high-bandwidth force control, high force density, and robustness to impacts. Standing around 0.3 m tall and weighing 9 kg, Mini Cheetah can easily be handled by a single operator. We have demonstrated dynamic trot, trot-run, bounding, and pronking gaits on the robot to speeds of up to 2.45 meters per second using Convex Model-Predictive Control (cMPC). In addition to locomotion, we have used the robot to execute 360° backflips, with trajectories generated using offline nonlinear optimization.