1,721,025 research outputs found
Is time-optimal speed planning under jerk constraints a convex problem?
Full text linkWe consider the speed planning problem for a vehicle moving along an assigned trajectory, under maximum speed, tangential and lateral acceleration, and jerk constraints. The problem is a nonconvex one, where nonconvexity is due to jerk constraints. We propose a convex relaxation, and we present various theoretical properties. In particular, we show that the relaxation is exact under some assumptions. Also, we rewrite the relaxation as a Second Order Cone Programming (SOCP) problem. This has a relevant practical impact, since solvers for SOCP problems are quite efficient and allow solving large instances within tenths of a second. We performed many numerical tests, and in all of them the relaxation turned out to be exact. For this reason, we conjecture that the convex relaxation is always exact, although we could not give a formal proof of this fact. (c) 2024 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)
A convex optimization approach for equivariant control systems
No full textA system is called equivariant if it is invariant with respect to a set of coordinate transformations associated to the elements of a multiplicative group. One established fact of the theory of equivariant systems is that various control problems can be solved by a generic controller if and only if they can be solved with a controller that satisfies the same invariance properties of the system. In this note, we show that this is true for all control tasks that can be obtained as a solution of an equivariant convex optimization problem and present some applications related to state and output feedback stabilization and decentralized control
Multi-optimization of eta3-splines for autonomous parking
No full textThis paper proposes a multi-optimization approach to the autonomous parking of car-like vehicles. It uses a polynomial curve primitive - the η 3-spline - to build up intrinsically feasible path maneuvers over which to minimize with a weighted sum method the total length of parking paths and the moduli of the maximum path curvature and curvature derivative. The approach takes into account the mandatory constraint of obstacle avoidance and maximal steering angle and the constraint of maximal curvature derivative which is a selectable limit to ensure the desired smoothness of the parking paths. Simulation results are included for a garage parking example. © 2011 IEEE
A Sequential Algorithm for Jerk Limited Speed Planning
No full textIn this article, we discuss a sequential algorithm for the computation of a minimum-time speed profile over a given path, under velocity, acceleration, and jerk constraints. Such a problem arises in industrial contexts, such as automated warehouses, where LGVs need to perform assigned tasks as fast as possible in order to increase productivity. It can be reformulated as an optimization problem with a convex objective function, linear velocity and acceleration constraints, and nonconvex jerk constraints, which, thus, represent the main source of the difficulty. While existing nonlinear programming (NLP) solvers can be employed for the solution of this problem, it turns out that the performance and robustness of such solvers can be enhanced by the sequential line-search algorithm proposed in this article. At each iteration, a feasible direction, with respect to the current feasible solution, is computed, and a step along such direction is taken in order to compute the next iterate. The computation of the feasible direction is based on the solution of a linearized version of the problem, and the solution of the linearized problem, through an approach that strongly exploits its special structure, represents the main contribution of this work. The efficiency of the proposed approach with respect to existing NLP solvers is proven through different computational experiments
Structured identification for network reconstruction of RC-models
No full textResistive–capacitive (RC) networks are used to model various processes in engineering, physics or biology. We consider the problem of recovering the network connection structure from measured input–output data. We address this problem as a structured identification one, that is, we assume to have a state-space model of the system (identified with standard techniques, such as subspace methods) and find a coordinate transformation that puts the identified system in a form that reveals the nodes connection structure. We characterize the solution set, that is, the set of all possible RC-networks that can be associated to the input–output data. We present a possible solution algorithm and show some computational experiments
Generalized Bang-Bang Control for Multivariable Feedforward Regulation
No full textIn control engineering, effective implementations
require to take into account the constraints for both the
inputs and the outputs of the controlled system. A feedforward
regulation problem is then set out to achieve a minimum-time
rest-to-rest output transition for square MIMO (multi-input
multi-output) linear time-invariant systems. The found
time-optimal solution extends the well-known bang-bang control
to a generalized bang-bang control in which some amplitude
constraints on the outputs are active. A straightforward
sufficient condition to have a solution is provided. The structure
of the time-optimal input-output pair is also investigated.
A feasibility linear programming approach to compute an
approximate solution is proposed. An example highlights the
found results
Leak Detection and Classification in Pharmaceutical Freeze-Dryers: An Identification-Based Approach
No full textFreeze-drying is a standard procedure in pharmaceutical industry, used to stabilize, store and increase the shelf life of drug products. In this process, the product has to be brought to a very low pressure and the lyophilization chamber has to be perfectly sealed. Even small external leaks can contaminate the entire drug batch. Since a single batch may contain thousands of product vials, freeze-dryer leakages are one of the most critical problems of the entire production chain of lyophilized drugs. We describe a simple mathematical model for lyophilizer leaks and address the problem of identifying and separating internal and external leaks. We propose a leak identification method based on the use of multiple leak detection tests. By using the real data of a pharmaceutical lyophilizer, we show that the proposed method allows to identify internal and external leaks and to estimate their evolution in time
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