3,529 research outputs found
Fast Second-order Cone Programming for Safe Mission Planning
This paper considers the problem of safe mission planning of dynamic systems
operating under uncertain environments. Much of the prior work on achieving
robust and safe control requires solving second-order cone programs (SOCP).
Unfortunately, existing general purpose SOCP methods are often infeasible for
real-time robotic tasks due to high memory and computational requirements
imposed by existing general optimization methods. The key contribution of this
paper is a fast and memory-efficient algorithm for SOCP that would enable
robust and safe mission planning on-board robots in real-time. Our algorithm
does not have any external dependency, can efficiently utilize warm start
provided in safe planning settings, and in fact leads to significant speed up
over standard optimization packages (like SDPT3) for even standard SOCP
problems. For example, for a standard quadrotor problem, our method leads to
speedup of 1000x over SDPT3 without any deterioration in the solution quality.
Our method is based on two insights: a) SOCPs can be interpreted as
optimizing a function over a polytope with infinite sides, b) a linear function
can be efficiently optimized over this polytope. We combine the above
observations with a novel utilization of Wolfe's algorithm to obtain an
efficient optimization method that can be easily implemented on small embedded
devices. In addition to the above mentioned algorithm, we also design a
two-level sensing method based on Gaussian Process for complex obstacles with
non-linear boundaries such as a cylinder
An Offline-Sampling SMPC Framework with Application to Automated Space Maneuvers
In this paper, a sampling-based Stochastic Model Predictive Control algorithm
is proposed for discrete-time linear systems subject to both parametric
uncertainties and additive disturbances. One of the main drivers for the
development of the proposed control strategy is the need of real-time
implementability of guidance and control strategies for automated rendezvous
and proximity operations between spacecraft. The paper presents considers the
validation of the proposed control algorithm on an experimental testbed,
showing how it may indeed be implemented in a realistic framework. Parametric
uncertainties due to the mass variations during operations, linearization
errors, and disturbances due to external space environment are simultaneously
considered.
The approach enables to suitably tighten the constraints to guarantee robust
recursive feasibility when bounds on the uncertain variables are provided, and
under mild assumptions, asymptotic stability in probability of the origin can
be established. The offline sampling approach in the control design phase is
shown to reduce the computational cost, which usually constitutes the main
limit for the adoption of Stochastic Model Predictive Control schemes,
especially for low-cost on-board hardware. These characteristics are
demonstrated both through simulations and by means of experimental results
OSQP: An Operator Splitting Solver for Quadratic Programs
We present a general-purpose solver for convex quadratic programs based on
the alternating direction method of multipliers, employing a novel operator
splitting technique that requires the solution of a quasi-definite linear
system with the same coefficient matrix at almost every iteration. Our
algorithm is very robust, placing no requirements on the problem data such as
positive definiteness of the objective function or linear independence of the
constraint functions. It can be configured to be division-free once an initial
matrix factorization is carried out, making it suitable for real-time
applications in embedded systems. In addition, our technique is the first
operator splitting method for quadratic programs able to reliably detect primal
and dual infeasible problems from the algorithm iterates. The method also
supports factorization caching and warm starting, making it particularly
efficient when solving parametrized problems arising in finance, control, and
machine learning. Our open-source C implementation OSQP has a small footprint,
is library-free, and has been extensively tested on many problem instances from
a wide variety of application areas. It is typically ten times faster than
competing interior-point methods, and sometimes much more when factorization
caching or warm start is used. OSQP has already shown a large impact with tens
of thousands of users both in academia and in large corporations
Power Management for Energy Systems
The thesis deals with control methods for flexible and efficient power consumption in commercial refrigeration systems that possess thermal storage capabilities, and for facilitation of more environmental sustainable power production technologies such as wind power. We apply economic model predictive control as the overriding control strategy and present novel studies on suitable modeling and problem formulations for the industrial applications, means to handle uncertainty in the control problems, and dedicated optimization routines to solve the problems involved. Along the way, we present careful numerical simulations with simple case studies as well as validated models in realistic scenarios. The thesis consists of a summary report and a collection of 13 research papers written during the period Marts 2010 to February 2013. Four are published in international peer-reviewed scientific journals and 9 are published at international peer-reviewed scientific conferences
Optimized FPGA Implementation of Model Predictive Control for Embedded Systems Using High-Level Synthesis Tool
Model predictive control (MPC) is an optimization-based strategy for high-performance control that is attracting increasing interest. While MPC requires the online solution of an optimization problem, its ability to handle multivariable systems and constraints makes it a very powerful control strategy specially for MPC of embedded systems, which have an ever increasing amount of sensing and computation capabilities. We argue that the implementation of MPC on field programmable gate arrays (FPGAs) using automatic tools is nowadays possible, achieving cost-effective successful applications on fast or resource-constrained systems. The main burden for the implementation of MPC on FPGAs is the challenging design of the necessary algorithms. We outline an approach to achieve a software-supported optimized implementation of MPC on FPGAs using high-level synthesis tools and automatic code generation. The proposed strategy exploits the arithmetic operations necessaries to solve optimization problems to tailor an FPGA design, which allows a tradeoff between energy, memory requirements, cost, and achievable speed. We show the capabilities and the simplicity of use of the proposed methodology on two different examples and illustrate its advantages over a microcontroller implementation
Convex Model Predictive Control for Vehicular Systems
In this work, we present a method to perform Model Predictive Control (MPC)
over systems whose state is an element of for . This is done
without charts or any local linearization, and instead is performed by
operating over the orbitope of rotation matrices. This results in a novel MPC
scheme without the drawbacks associated with conventional linearization
techniques. Instead, second order cone- or semidefinite-constraints on state
variables are the only requirement beyond those of a QP-scheme typical for MPC
of linear systems. Of particular emphasis is the application to aeronautical
and vehicular systems, wherein the method removes many of the transcendental
trigonometric terms associated with these systems' state space equations.
Furthermore, the method is shown to be compatible with many existing variants
of MPC, including obstacle avoidance via Mixed Integer Linear Programming
(MILP)
Optimization with Constraint Learning: A Framework and Survey
Many real-life optimization problems frequently contain one or more
constraints or objectives for which there are no explicit formulas. If data is
however available, these data can be used to learn the constraints. The
benefits of this approach are clearly seen, however there is a need for this
process to be carried out in a structured manner. This paper therefore provides
a framework for Optimization with Constraint Learning (OCL) which we believe
will help to formalize and direct the process of learning constraints from
data. This framework includes the following steps: (i) setup of the conceptual
optimization model, (ii) data gathering and preprocessing, (iii) selection and
training of predictive models, (iv) resolution of the optimization model, and
(v) verification and improvement of the optimization model. We then review the
recent OCL literature in light of this framework, and highlight current trends,
as well as areas for future research
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