895 research outputs found
A Family of Iterative Gauss-Newton Shooting Methods for Nonlinear Optimal Control
This paper introduces a family of iterative algorithms for unconstrained
nonlinear optimal control. We generalize the well-known iLQR algorithm to
different multiple-shooting variants, combining advantages like
straight-forward initialization and a closed-loop forward integration. All
algorithms have similar computational complexity, i.e. linear complexity in the
time horizon, and can be derived in the same computational framework. We
compare the full-step variants of our algorithms and present several simulation
examples, including a high-dimensional underactuated robot subject to contact
switches. Simulation results show that our multiple-shooting algorithms can
achieve faster convergence, better local contraction rates and much shorter
runtimes than classical iLQR, which makes them a superior choice for nonlinear
model predictive control applications.Comment: 8 page
Refraction-corrected ray-based inversion for three-dimensional ultrasound tomography of the breast
Ultrasound Tomography has seen a revival of interest in the past decade,
especially for breast imaging, due to improvements in both ultrasound and
computing hardware. In particular, three-dimensional ultrasound tomography, a
fully tomographic method in which the medium to be imaged is surrounded by
ultrasound transducers, has become feasible. In this paper, a comprehensive
derivation and study of a robust framework for large-scale bent-ray ultrasound
tomography in 3D for a hemispherical detector array is presented. Two
ray-tracing approaches are derived and compared. More significantly, the
problem of linking the rays between emitters and receivers, which is
challenging in 3D due to the high number of degrees of freedom for the
trajectory of rays, is analysed both as a minimisation and as a root-finding
problem. The ray-linking problem is parameterised for a convex detection
surface and three robust, accurate, and efficient ray-linking algorithms are
formulated and demonstrated. To stabilise these methods, novel
adaptive-smoothing approaches are proposed that control the conditioning of the
update matrices to ensure accurate linking. The nonlinear UST problem of
estimating the sound speed was recast as a series of linearised subproblems,
each solved using the above algorithms and within a steepest descent scheme.
The whole imaging algorithm was demonstrated to be robust and accurate on
realistic data simulated using a full-wave acoustic model and an anatomical
breast phantom, and incorporating the errors due to time-of-flight picking that
would be present with measured data. This method can used to provide a
low-artefact, quantitatively accurate, 3D sound speed maps. In addition to
being useful in their own right, such 3D sound speed maps can be used to
initialise full-wave inversion methods, or as an input to photoacoustic
tomography reconstructions
The Control Toolbox - An Open-Source C++ Library for Robotics, Optimal and Model Predictive Control
We introduce the Control Toolbox (CT), an open-source C++ library for
efficient modeling, control, estimation, trajectory optimization and Model
Predictive Control. The CT is applicable to a broad class of dynamic systems
but features interfaces to modeling tools specifically designed for robotic
applications. This paper outlines the general concept of the toolbox, its main
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 for intuitive
modeling of systems governed by ordinary differential or difference equations.
It supports rapid prototyping of cost functions and constraints and provides
standard interfaces for different optimal control solvers. To date, we support
Single Shooting, the iterative Linear-Quadratic Regulator, Gauss-Newton
Multiple Shooting and classical Direct Multiple Shooting. We provide interfaces
to general purpose NLP solvers and Riccati-based linear-quadratic optimal
control solvers. The CT was designed to solve large-scale optimal control and
estimation problems efficiently and allows for online control of dynamic
systems. Some of the key features to enable fast run-time performance are full
compatibility with Automatic Differentiation, derivative code generation, and
multi-threading. Still, the CT is designed as a modular framework whose
building blocks can also be used for other control and estimation applications
such as inverse dynamics control, extended Kalman filters or kinematic
planning
A Simple and Efficient Algorithm for Nonlinear Model Predictive Control
We present PANOC, a new algorithm for solving optimal control problems
arising in nonlinear model predictive control (NMPC). A usual approach to this
type of problems is sequential quadratic programming (SQP), which requires the
solution of a quadratic program at every iteration and, consequently, inner
iterative procedures. As a result, when the problem is ill-conditioned or the
prediction horizon is large, each outer iteration becomes computationally very
expensive. We propose a line-search algorithm that combines forward-backward
iterations (FB) and Newton-type steps over the recently introduced
forward-backward envelope (FBE), a continuous, real-valued, exact merit
function for the original problem. The curvature information of Newton-type
methods enables asymptotic superlinear rates under mild assumptions at the
limit point, and the proposed algorithm is based on very simple operations:
access to first-order information of the cost and dynamics and low-cost direct
linear algebra. No inner iterative procedure nor Hessian evaluation is
required, making our approach computationally simpler than SQP methods. The
low-memory requirements and simple implementation make our method particularly
suited for embedded NMPC applications
FATROP : A Fast Constrained Optimal Control Problem Solver for Robot Trajectory Optimization and Control
Trajectory optimization is a powerful tool for robot motion planning and
control. State-of-the-art general-purpose nonlinear programming solvers are
versatile, handle constraints in an effective way and provide a high numerical
robustness, but they are slow because they do not fully exploit the optimal
control problem structure at hand. Existing structure-exploiting solvers are
fast but they often lack techniques to deal with nonlinearity or rely on
penalty methods to enforce (equality or inequality) path constraints. This
works presents FATROP: a trajectory optimization solver that is fast and
benefits from the salient features of general-purpose nonlinear optimization
solvers. The speed-up is mainly achieved through the use of a specialized
linear solver, based on a Riccati recursion that is generalized to also support
stagewise equality constraints. To demonstrate the algorithm's potential, it is
benchmarked on a set of robot problems that are challenging from a numerical
perspective, including problems with a minimum-time objective and no-collision
constraints. The solver is shown to solve problems for trajectory generation of
a quadrotor, a robot manipulator and a truck-trailer problem in a few tens of
milliseconds. The algorithm's C++-code implementation accompanies this work as
open source software, released under the GNU Lesser General Public License
(LGPL). This software framework may encourage and enable the robotics community
to use trajectory optimization in more challenging applications
Crocoddyl: An Efficient and Versatile Framework for Multi-Contact Optimal Control
We introduce Crocoddyl (Contact RObot COntrol by Differential DYnamic Library), an open-source framework tailored for efficient multi-contact optimal control. Crocoddyl efficiently computes the state trajectory and the control policy for a given predefined sequence of contacts. Its efficiency is due to the use of sparse analytical derivatives, exploitation of the problem structure, and data sharing. It employs differential geometry to properly describe the state of any geometrical system, e.g. floating-base systems. We have unified dynamics, costs, and constraints into a single concept-action-for greater efficiency and easy prototyping. Additionally, we propose a novel multiple-shooting method called Feasibility-prone Differential Dynamic Programming (FDDP). Our novel method shows a greater globalization strategy compared to classical Differential Dynamic Programming (DDP) algorithms, and it has similar numerical behavior to state-of-the-art multiple-shooting methods. However, our method does not increase the computational complexity typically encountered by adding extra variables to describe the gaps in the dynamics. Concretely, we propose two modifications to the classical DDP algorithm. First, the backward pass accepts infeasible state-control trajectories. Second, the rollout keeps the gaps open during the early "exploratory" iterations (as expected in multiple-shooting methods). We showcase the performance of our framework using different tasks. With our method, we can compute highly-dynamic maneuvers for legged robots (e.g. jumping, front-flip) in the order of milliseconds
Contact-Implicit Trajectory Optimization Based on a Variable Smooth Contact Model and Successive Convexification
In this paper, we propose a contact-implicit trajectory optimization (CITO)
method based on a variable smooth contact model (VSCM) and successive
convexification (SCvx). The VSCM facilitates the convergence of gradient-based
optimization without compromising physical fidelity. On the other hand, the
proposed SCvx-based approach combines the advantages of direct and shooting
methods for CITO. For evaluations, we consider non-prehensile manipulation
tasks. The proposed method is compared to a version based on iterative linear
quadratic regulator (iLQR) on a planar example. The results demonstrate that
both methods can find physically-consistent motions that complete the tasks
without a meaningful initial guess owing to the VSCM. The proposed SCvx-based
method outperforms the iLQR-based method in terms of convergence, computation
time, and the quality of motions found. Finally, the proposed SCvx-based method
is tested on a standard robot platform and shown to perform efficiently for a
real-world application.Comment: Accepted for publication in ICRA 201
Solution of Ordinary Differential Equations in Gradient-Based Multidisciplinary Design Optimization
A gradient-based approach to multidisciplinary design optimization enables efficient scalability to large numbers of design variables. However, the need for derivatives causes difficulties when integrating ordinary differential equations (ODEs) in models. To simplify this, we propose the use of the general linear methods framework, which unifies all Runge-Kutta and linear multistep methods. This approach enables rapid implementation of integration methods without the need to differentiate each one, even in a gradient-based optimization context. We also develop a new parallel time integration algorithm that enables vectorization across time steps. We present a set of benchmarking results using a stiff ODE, a non-stiff nonlinear ODE, and an orbital dynamics ODE, and compare integration methods. In a modular gradient-based multidisciplinary design optimization context, we find that the new parallel time integration algorithm with high-order implicit methods, especially Gauss-Legendre collocation, is the best choice for a broad range of problems
Improving Tatonnement Methods of Solving Heterogeneous Agent Models
This paper modifies standard block Gauss-Seidel iterations used by tatonnement methods for solving large scale deterministic heterogeneous agent models. The composite method between first- and second-order tatonnement methods is shown to considerably improve convergence both in terms of speed as well as robustness relative to conventional first-order tatonnement methods. In addition, the relative advantage of the modified algorithm increases in the size and complexity of the economic model. Therefore, the algorithm allows significant reductions in computational time when solving large models. The algorithm is particularly attractive since it is easy to implement â it only augments conventional and intuitive tatonnement iterations with standard numerical methods.
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