Articles de revues : « Contrôle de trajectoire optimal »

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Daneault, Serge. « La poursuite d’une bonne mort est-elle une utopie ? » Articles 20, n^o 1 (8 mai 2008) : 27–33. http://dx.doi.org/10.7202/017944ar.

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Résumé La préoccupation de la bonne mort se situe dans la mouvance intellectuelle de ce nouveau millénaire caractérisé par une désillusion généralisée à l’égard de la science et de la technologie et un vacuum spirituel. La réalité de la mort n’est pas forcément le reflet de ce qui se passe dans les milieux de soins palliatifs. La majorité des décès surviennent dans les unités de soins actifs des hôpitaux de courte durée ou dans les centres hospitaliers de soins prolongés, endroits où il est possible que le soulagement de la souffrance ne soit pas optimal. Les caractéristiques de la bonne mort sont surtout axées sur le contrôle et l’autonomie, valeurs éminemment individuelles. L’utilisation de ces critères pour évaluer les trajectoires de soins de fin de vie fait moins l’unanimité que la nécessité d’assurer à tous l’accès à des soins palliatifs de qualité.

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Podobryaev, A. V. « Symmetric Extremal Trajectories in Left-Invariant Optimal Control Problems ». Nelineinaya Dinamika 15, n^o 4 (2019) : 569–75. http://dx.doi.org/10.20537/nd190416.

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SAIDI, IMEN, et NAHLA TOUATI. « APPRENTISSAGE DE COMMANDE POUR LE SUIVI DE TRAJECTOIRE D'UN PENDULE INVERSÉ À ROUE D'INERTIE NON LINÉAIRE ». REVUE ROUMAINE DES SCIENCES TECHNIQUES — SÉRIE ÉLECTROTECHNIQUE ET ÉNERGÉTIQUE 68, n^o 4 (23 décembre 2023) : 424–30. http://dx.doi.org/10.59277/rrst-ee.2023.4.17.

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Cet article propose le contrôle d'apprentissage itératif pour les systèmes sous-actionnés non linéaires. Pour améliorer la vitesse de convergence du contrôle d'apprentissage itératif pour de tels systèmes et réduire la fluctuation de l'erreur du système, un algorithme de contrôle d'apprentissage itératif en boucle fermée de type D à gain variable exponentiel a été choisi. L'analyse de simulation MATLAB a ensuite été réalisée sur un système sous-actionné, non linéaire et instable, à savoir le pendule inversé à roue d'inertie. Les résultats de la simulation montrent que l'algorithme est efficace. De bonnes performances de suivi ont été obtenues. Le système converge vers des cycles limites stables après quelques itérations, garantissant des erreurs fluides et une vitesse de convergence satisfaisante.

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Foehn, Philipp, Angel Romero et Davide Scaramuzza. « Time-optimal planning for quadrotor waypoint flight ». Science Robotics 6, n^o 56 (21 juillet 2021) : eabh1221. http://dx.doi.org/10.1126/scirobotics.abh1221.

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Quadrotors are among the most agile flying robots. However, planning time-optimal trajectories at the actuation limit through multiple waypoints remains an open problem. This is crucial for applications such as inspection, delivery, search and rescue, and drone racing. Early works used polynomial trajectory formulations, which do not exploit the full actuator potential because of their inherent smoothness. Recent works resorted to numerical optimization but require waypoints to be allocated as costs or constraints at specific discrete times. However, this time allocation is a priori unknown and renders previous works incapable of producing truly time-optimal trajectories. To generate truly time-optimal trajectories, we propose a solution to the time allocation problem while exploiting the full quadrotor’s actuator potential. We achieve this by introducing a formulation of progress along the trajectory, which enables the simultaneous optimization of the time allocation and the trajectory itself. We compare our method against related approaches and validate it in real-world flights in one of the world’s largest motion-capture systems, where we outperform human expert drone pilots in a drone-racing task.

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Simon, Dan, et Can Isik. « Optimal trigonometric robot joint trajectories ». Robotica 9, n^o 4 (décembre 1991) : 379–86. http://dx.doi.org/10.1017/s0263574700000552.

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SUMMARYInterpolation of a robot joint trajectory is realized using trigonometric splines. This original application has several advantages over existing methods (e.g. those using algebraic splines). For example, the computational expense is lower, more constraints can be imposed on the trajectory, obstacle avoidance can be implemented in real time, and smoother trajectories are obtained. Some of the spline parameters can be chosen to minimize an objective function (e.g. minimum jerk or minimum energy). If jerk is minimized, the optimization has a closed form solution. This paper introduces a trajectory interpolation algorithm, discusses a method for path optimization, and includes examples.

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Liu, Ke, Guanzheng Wen, Yao Fu et Honglin Wang. « A Hierarchical Lane-Changing Trajectory Planning Method Based on the Least Action Principle ». Actuators 13, n^o 1 (26 décembre 2023) : 10. http://dx.doi.org/10.3390/act13010010.

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This paper presents a hierarchical lane-changing trajectory planner based on the least action principle for autonomous driving. Our approach aims to achieve reliable real-time avoidance of static and moving obstacles in multi-vehicle interaction scenarios on structured urban roads. Unlike previous studies that rely on subjective weight allocation and single weighting methods, we propose a novel trajectory planning strategy that decomposes the process into two stages: candidate trajectory generation and optimal trajectory decision-making. The candidate trajectory generation employs a path-velocity decomposition method, using B-spline curves to generate a multi-objective optimal lane-changing candidate path. Collision checking eliminates paths at risk of collision with static obstacles. Dynamic programming (DP) and quadratic programming (QP) are then used to plan the velocity of safe paths, generating candidate lane-changing trajectories based on curvature checking. The optimal trajectory decision-making process follows the decision mechanism of excellent drivers. We introduce a comprehensive evaluation function, the average action, which considers safety, comfort, and efficiency based on the least action principle. Feasible trajectories are ranked based on their average action, and the trajectory with the minimum average action and no collision risk with moving obstacles is selected as the tracking target. The effectiveness of the proposed method is validated through two common lane-changing scenarios. The results demonstrate that our approach enables smooth, efficient, and safe lane-changing while effectively tracking the planned velocity and path. This method offers a solution to local trajectory planning problems in complex environments and holds promising prospects in the field of autonomous driving.

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Yin, Haolin, Baoquan Li, Hai Zhu et Lintao Shi. « Kinodynamic RRT* Based UAV Optimal State Motion Planning with Collision Risk Awareness ». Information Technology and Control 52, n^o 3 (26 septembre 2023) : 665–79. http://dx.doi.org/10.5755/j01.itc.52.3.33583.

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In this paper, an autonomous navigation strategy is proposed for unmanned aerial vehicles (UAVs) based on consideration of dynamic sampling and field of view (FOV). Compare to search-based motion planning, sampling-based kinodynamic planning schemes can often find feasible trajectories in complex environments. Specifically, a global trajectory is first generated with physical information, and an expansion algorithm is constructed regarding to kinodynamic rapidly-exploring random tree* (KRRT*). Then, a KRRT* expansion strategy is designed to find local collision-free trajectories. In trajectory optimization, bending radius, collision risk function, and yaw angle penalty term are defined by taking into account onboard sensor FOV and potentialrisk. Then, smooth and dynamic feasible terms are penalized based on initial trajectory generation. Trajectories are refined by time reallocation, and weights are solved by optimization. Effectiveness of the proposed strategy is demonstrated by both simulation and experiment.

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Al Younes, Younes, et Martin Barczyk. « Nonlinear Model Predictive Horizon for Optimal Trajectory Generation ». Robotics 10, n^o 3 (14 juillet 2021) : 90. http://dx.doi.org/10.3390/robotics10030090.

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This paper presents a trajectory generation method for a nonlinear system under closed-loop control (here a quadrotor drone) motivated by the Nonlinear Model Predictive Control (NMPC) method. Unlike NMPC, the proposed method employs a closed-loop system dynamics model within the optimization problem to efficiently generate reference trajectories in real time. We call this approach the Nonlinear Model Predictive Horizon (NMPH). The closed-loop model used within NMPH employs a feedback linearization control law design to decrease the nonconvexity of the optimization problem and thus achieve faster convergence. For robust trajectory planning in a dynamically changing environment, static and dynamic obstacle constraints are supported within the NMPH algorithm. Our algorithm is applied to a quadrotor system to generate optimal reference trajectories in 3D, and several simulation scenarios are provided to validate the features and evaluate the performance of the proposed methodology.

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Peralta-Caprachin, Henry, Raul Angeles-Orahulio et Ernesto Paiva-Peredo. « Design and Position Control of a Robot with 5 Degrees of Freedom ». International Journal of Mechanical Engineering and Robotics Research 13, n^o 2 (2024) : 241–48. http://dx.doi.org/10.18178/ijmerr.13.2.241-248.

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In recent decades, robotics and artificial intelligence have gained significant importance for their involvement in various industrial processes currently at their peak. Nevertheless, advanced robots are not designed explicitly for lemon supply. This research aims to develop a manipulator robot with 5 degrees of freedom and control its trajectories for lemon supply purposes. To achieve this goal, kinematic and dynamic calculations of the manipulator robot were performed, along with the development of programming code in Matlab to determine its trajectories, positions, speeds, and accelerations. In addition, the Proportional Integral Derivative (PID) tuner was used to obtain the optimal controller parameters and ensure accurate joint trajectory generation.

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Zhao, Jiangying, Yongbiao Hu, Chengshuo Liu, Mingrui Tian et Xiaohua Xia. « Spline-Based Optimal Trajectory Generation for Autonomous Excavator ». Machines 10, n^o 7 (3 juillet 2022) : 538. http://dx.doi.org/10.3390/machines10070538.

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In this paper, we propose a novel trajectory generation method for autonomous excavator teach-and-plan applications. Rather than controlling the excavator to precisely follow the teaching path, the proposed method transforms the arbitrary slow and jerky trajectory of human excavation into a topologically equivalent path that is guaranteed to be fast, smooth and dynamically feasible. This method optimizes trajectories in both time and jerk aspects. A spline is used to connect these waypoints, which are topologically equivalent to the human teaching path. Then the trajectory is reparametrized to obtain the minimum time-jerk trajectory with the kinodynamic constraints. The optimal time-jerk trajectory generation method is both formulated using nonlinear programming and conducted iteratively. The framework proposed in this paper was integrated into a complete autonomous excavation platform and was validated to achieve aggressive excavation in a field environment.

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Zennir, Youcef, et Pierre Couturier. « Approche distribuée de l'apprentissage. Application au contrôle de la trajectoire d'un robot hexapode ». Journal Européen des Systèmes Automatisés 39, n^o 8 (30 octobre 2005) : 965–93. http://dx.doi.org/10.3166/jesa.39.965-993.

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Chen, Heping, Ning Xi, Weihua Sheng et Yifan Chen. « General Framework of Optimal Tool Trajectory Planning for Free-Form Surfaces in Surface Manufacturing ». Journal of Manufacturing Science and Engineering 127, n^o 1 (1 février 2005) : 49–59. http://dx.doi.org/10.1115/1.1828057.

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Surface manufacturing is a process of adding material to or removing material from the surfaces of a part. Spray painting, spray forming, rapid tooling, spray coating, and polishing are some of the typical applications of surface manufacturing, where industrial robots are usually used. Tool planning for industrial robots in surface manufacturing is a challenging research topic. Typical teaching methods are not affordable any more because products are subject to a shorter product life, frequent design changes, small lot sizes, and small in-process inventory restrictions. An automatic tool trajectory planning process is hence desirable for tool trajectory planning of industrial robots. Based on the computer-aided design model of a part, the tool model, task constraints, and optimization criteria, a general framework of optimal tool trajectory planning in surface manufacturing is developed. Optimal tool trajectories are generated by approximately solving a multiobjective optimization problem. To test if the generated trajectory satisfies the given constraints, a trajectory verification model is developed. Simulations are performed to determine if the given constraints are satisfied. Simulation results show that the optimal tool trajectory planning framework can be applied to generate trajectories for a variety of applications in surface manufacturing. This general framework can also be extended to other applications such as dimensional inspection and demining.

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Belta, Calin, et Sadra Sadraddini. « Formal Methods for Control Synthesis : An Optimization Perspective ». Annual Review of Control, Robotics, and Autonomous Systems 2, n^o 1 (3 mai 2019) : 115–40. http://dx.doi.org/10.1146/annurev-control-053018-023717.

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In control theory, complicated dynamics such as systems of (nonlinear) differential equations are controlled mostly to achieve stability. This fundamental property, which can be with respect to a desired operating point or a prescribed trajectory, is often linked with optimality, which requires minimizing a certain cost along the trajectories of a stable system. In formal verification (model checking), simple systems, such as finite-state transition graphs that model computer programs or digital circuits, are checked against rich specifications given as formulas of temporal logics. The formal synthesis problem, in which the goal is to synthesize or control a finite system from a temporal logic specification, has recently received increased interest. In this article, we review some recent results on the connection between optimal control and formal synthesis. Specifically, we focus on the following problem: Given a cost and a correctness temporal logic specification for a dynamical system, generate an optimal control strategy that satisfies the specification. We first provide a short overview of automata-based methods, in which the dynamics of the system are mapped to a finite abstraction that is then controlled using an automaton corresponding to the specification. We then provide a detailed overview of a class of methods that rely on mapping the specification and the dynamics to constraints of an optimization problem. We discuss advantages and limitations of these two types of approaches and suggest directions for future research.

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Saint-Martin, Jean, Lise Cardin et Lisa Walther. « Marie-Thérèse Eyquem ou l’émancipation sous contrôle des pratiques corporelles féminines (1942-1961) ». Revista Brasileira de História da Educação 23, n^o 1 (6 juillet 2023) : e268. http://dx.doi.org/10.4025/rbhe.v23.2023.e286.

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Entre 1942, année où elle est nommée chargée de mission de l’éducation physique et des sports féminins auprès et 1961 où elle devient Inspectrice de la Jeunesse et des Sports, Marie-Thérèse Eyquem multiplie les initiatives pour sensibiliser les jeunes françaises aux buts hygiéniques et esthétiques des exercices physiques. L’objet de cet article vise à interroger cet engagement continu durant deux décennies et ses effets sur les transformations de l’éducation physique féminine. Il s’agira alors de mesurer à la fois l’importance des sources d’inspiration de cette actrice et l’évolution de sa trajectoire intellectuelle pour tenter d’expliquer en quoi l’émancipation sous contrôle des femmes qu’elle ne cesse de promouvoir s’appuie pour partie sur une liberté surveillée du corps féminin.

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Shiller, Zvi. « Time-Energy Optimal Control of Articulated Systems With Geometric Path Constraints ». Journal of Dynamic Systems, Measurement, and Control 118, n^o 1 (1 mars 1996) : 139–43. http://dx.doi.org/10.1115/1.2801134.

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The motions of articulated systems along specified paths are optimized to minimize a time-energy cost function. The optimization problem is formulated is a reduced two-dimensional state space and solved using the Pontryagin maximum principle. The optimal control is shown to be smooth, as opposed to the typically discontinuous time optimal control. The numerical solution is obtained with a gradient search that iterates over the initial value of one co-state. Optimal trajectories are demonstrated numerically for a two-link planar manipulator and experimentally for the UCLA Direct Drive Arm. The smoother time-energy optimal trajectory is shown to result in smaller tracking errors than the time optimal trajectory.

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Dumlao, Samuel Matthew G., et Keiichi N. Ishihara. « Dynamic Cost-Optimal Assessment of Complementary Diurnal Electricity Storage Capacity in High PV Penetration Grid ». Energies 14, n^o 15 (25 juillet 2021) : 4496. http://dx.doi.org/10.3390/en14154496.

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Solar Photovoltaics (PV) is seen as one of the renewable energy technologies that could help reduce the world’s dependence on fossil fuels. However, since it is dependent on the sun, it can only generate electricity in the daytime, and this restriction is exacerbated in electricity grids with high PV penetration, where solar energy must be curtailed due to the mismatch between supply and demand. This study conducts a techno-economic analysis to present the cost-optimal storage growth trajectory that could support the dynamic integration of solar PV within a planning horizon. A methodology for cost-optimal assessment that incorporates hourly simulation, Monte Carlo random sampling, and a proposed financial assessment is presented. This approach was tested in Japan’s southernmost region since it is continuously increasing its solar capacity and is at the precipice of high PV curtailment scenario. The results show the existence of a cost-optimal storage capacity growth trajectory that balances the cost penalty from curtailment and the additional investment cost from storage. This optimal trajectory reduces the impact of curtailment on the energy generation cost to manageable levels and utilizes more solar energy potential that further reduces CO2 emissions. The results also show that the solar capacity growth rate and storage cost significantly impact the optimal trajectory. The incorporation of the Monte Carlo method significantly reduced the computational requirement of the analysis enabling the exploration of several growth trajectories, and the proposed financial assessment enabled the time-bound optimization of these trajectories. The approach could be used to calculate the optimal growth trajectories in other nations or regions, provided that historical hourly temperature, irradiance, and demand data are available.

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Peaucelle, Héloïse. « Ressources spatiales d’un ancrage commercial en exil ». Mondes arabes N° 4, n^o 2 (13 décembre 2023) : 67–90. http://dx.doi.org/10.3917/machr2.004.0067.

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En s’intéressant à l’étude du travail migrant et réfugié, cet article analyse les pratiques d’établissement des entreprises syriennes qui fleurissent à Irbid depuis 2011 et leurs dynamiques territoriales. J’interroge les cadres juridiques de la migration syrienne en Jordanie au regard de ceux de l’investissement pour les Syriens. À partir d’une enquête ethnographique, je montre les difficultés rencontrées par les entrepreneurs syriens face au contrôle jordanien qui s’exprime notamment au travers de l’État-rentier. Pour pallier les différentes contraintes, les entrepreneurs mobilisent alors des ressources spatiales qu’ils constituent au cours de leur trajectoire migratoire, pour s’ancrer à Irbid et interagir avec les espaces urbains qu’ils investissent par la suite.

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Cavagnari, Giulia, Antonio Marigonda et Benedetto Piccoli. « Averaged time-optimal control problem in the space of positive Borel measures ». ESAIM : Control, Optimisation and Calculus of Variations 24, n^o 2 (26 janvier 2018) : 721–40. http://dx.doi.org/10.1051/cocv/2017060.

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We introduce a time-optimal control theory in the space ℳ+ (ℝd) of positive and finite Borel measures. We prove some natural results, such as a dynamic programming principle, the existence of optimal trajectories, regularity results and an HJB equation for the value function in this infinite-dimensional setting. The main tool used is the superposition principle (by Ambrosio–Gigli–Savaré) which allows to represent the trajectory in the space of measures as weighted superposition of classical characteristic curves in ℝd.

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Gil de Lamadrid, James, et Jill Zimmerman†. « Avoidance of obstacles with unknown trajectories : locally optimal paths and path complexity, Part I ». Robotica 11, n^o 4 (juillet 1993) : 299–308. http://dx.doi.org/10.1017/s0263574700016556.

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SUMMARYWe consider the problem of moving a point robot through a two dimensional workspace containing polygonal obstacles moving on unknown trajectories. We propose to use sensor information to predict the trajectories of the obstacles, and interleave path planning and execution. In this paper, we present preliminary work in which we propose our basic algorithm and define a locally minimum velocity path as an optimal robot trajectory, given only local information about obstacle trajectories. In the sequel (part II) to this paper we will show that the complexity of a path planning problem can be characterized by how frequently the robot must change directions to approximate the locally minimum velocity path.

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de Lamadrid, James Gil, et Jill Zimmermanf. « Avoidance of obstacles with unknown trajectories : locally optimal paths and path complexity, Part II ». Robotica 11, n^o 5 (septembre 1993) : 403–12. http://dx.doi.org/10.1017/s0263574700016957.

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SUMMARYContinuing the work presented in part I, ‡ we consider the problem of moving a point robot through a two dimensional workspace containing polygonal obstacles moving on unknown trajectories. We propose to use sensor information to predict the trajectories of the obstacles, and interleave path planning and execution. We define a locally minimum velocity path as an optimal robot trajectory, given only local information about obstacle trajectories. We show that the complexity of a path planning problem can be characterized by how frequently the robot must change directions to approximate the locally minimum velocity path. Our results apply to both robots with and without maximum velocity limits.

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Takalani, Rofhiwa Lutendo Edward, et Lesedi Masisi. « Development of An Optimal Port Crane Trajectory for Reduced Energy Consumption ». Energies 16, n^o 20 (20 octobre 2023) : 7172. http://dx.doi.org/10.3390/en16207172.

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This paper is concerned with the development of an optimal load-handling trajectory for port cranes. The objective is to minimize load cycle time and reduce energy consumption. Energetic macroscopic representation formalism is used to model a port crane load-handling mechanism. The crane model developed includes the mathematical model, the crane’s local control system, and a MATLAB/Simulink model for simulation. The particle swarm optimization algorithm is used to find the set of pareto optimal crane trajectories given the variation in crane size, ship size, and wind speed. Experimental validation of the crane model is conducted by comparing it with a real-world crane. Simulation results show that the optimal crane load trajectory is 38% faster and more productive than the nonoptimal crane load trajectory. Furthermore, the results show that the optimal trajectory reduces the cranes’ peak power and energy consumption by 36% when compared with the nonoptimal trajectory.

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Timchenko, Victor. « OPTIMIZATION OF PROGRAMMED TRAJECTORIES OF MOVING OBJECTʼS STABILIZATION BASED ON CONTROL SYSTEMS OF VARIABLE STRUCTURE ». International Scientific Technical Journal "Problems of Control and Informatics 67, n^o 3 (1 juin 2022) : 61–76. http://dx.doi.org/10.34229/2786-6505-2022-3-5.

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The article considers optimal systems that provide dynamic systems with highcontrol quality indicators: speed, accuracy, and low energy consumption. An approach to the synthesis of robust-optimal systems based on the use of feedbackwith a variable structure is being developed and includes the following mainstages: planning of the programmed optimal trajectory; determination of moments of switching of control functions in feedback loops of the object; synthesis of control functions in the corresponding feedback loops of a multidimensional object. The application of the proposed order of synthesis of systems witha variable structure for various types of objects based on the preliminary construction of optimal programmed trajectories of stabilization of dynamic processes allows optimizing the stabilization processes of nonlinear non-stationarysystems of high order. Optimal programmed stabilization trajectories are formedfrom segments established relative to the corresponding derivative of the motioncoordinate, based on polynomial forms for given boundary conditions and theoptimality criterion, taking into account limited control values, and are solvedfor the time of moments of switching of control and the time of the end of thetransition process based on a system of algebraic equations. Control synthesis iscarried out taking into account the initial values based on the equations of thebalance of forces and moments efforts on the moving object and their derivatives. The optimal trajectory and control are formed in such a way that, duringthe synthesis of an additional robust control circuit (with feedback from theoutput of the object) to compensate for the incomplete certainty of the mathematical model and uncontrolled (unmeasured) disturbances and noises, sufficiently limited areas of changing the coordinates of the moving object relative to given values. In the future, this allows the construction of sufficientlyeffective and practical in the implementation of robust-optimal control systems, for example, marine mobile objects, quadcopters, that function in conditions of considerable uncertainty.

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Bianchi, Domenico, Alessandro Borri, Federico Cappuzzo et Stefano Di Gennaro. « Quadrotor Trajectory Control Based on Energy-Optimal Reference Generator ». Drones 8, n^o 1 (22 janvier 2024) : 29. http://dx.doi.org/10.3390/drones8010029.

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Inspired by the limited battery life of multi-rotor unmanned aerial vehicles (UAVs), this research investigated hierarchical real-time control of UAVs with the generation of energy-optimal reference trajectories. The goal was to design a reference generator and controller based on optimal-control theory that would guarantee energy consumption close to optimal with lower computational cost. First, a least-squares-estimation-(LSE) algorithm identified the parameters of the UAV mathematical model. Then, by considering a precise electrical model for the brushless DC motors and rest-to-rest maneuvers, the extraction of clear rules to compute the optimal mission time and generate ’energetic trajectories’ was performed. These rules emerged from analyzing the optimal-control strategy results that minimized the consumption over many simulations. Afterward, a hierarchical controller tracked those desired energetic trajectories identified as sub-optimal. Numerical experiments compared the results regarding trajectory tracking, energy performance index, and battery state of charge (SOC). A co-simulation framework consisting of commercial software tools, Simcenter Amesim for the physical modeling of the UAV, and Matlab-Simulink executed numerical simulations of the implemented controller.

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Alayrac, Pierre. « Concurrence sur la concurrence. La résistible économicisation des pratiques et de l’administration du contrôle des marchés à la Commission européenne (1958-2003) ». Revue Française de Socio-Économie 31, n^o 2 (13 décembre 2023) : 69–88. http://dx.doi.org/10.3917/rfse.031.0069.

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La littérature sur la politique européenne de concurrence présente un hiatus. À ses débuts, elle aurait d’abord été marquée par une approche très légaliste de la régulation des luttes économiques, avant une évolution brutale vers une analyse plus économique au tournant des années 2000. Cet article entend proposer un trait d’union entre ces deux épisodes en étudiant la trajectoire heurtée d’économicisation de l’administration européenne de la concurrence et ses conditions de possibilité.

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Rondé, Patrick. « Inertie : un comportement optimal en fin de trajectoire technologique ». Économie appliquée 54, n^o 1 (2001) : 201–24. http://dx.doi.org/10.3406/ecoap.2001.1757.

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Un point central de la dynamique industrielle concerne les phénomènes d’irréversibilité qui peuvent bloquer le système économique dans des alternatives sous-optimales du fait de l’inertie des agents face aux signaux économiques. L’objet de l’article est de comprendre l’origine de l’excès d’inertie à l’aide d’un modèle décisionnel où l’on détermine le schéma optimal des dépenses de R&D dans une situation d’incertitude technologique et concurrentielle et sous l’hypothèse d’une fin de trajectoire technologique. Le rôle central des externalités technologiques est alors mis en évidence en tant qu’élément déterminant du choix inertie versus recherche de nouvelles alternatives. Une discussion portant sur le secteur de l’agrochimie illustre les comportements mis en évidence dans le modèle théorique.

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Jouybari, Behnoush Rezaeian, Kambiz Ghaemi Osgouie et Ali Meghdari. « Optimization of kinematic redundancy and workspace analysis of a dual-arm cam-lock robot ». Robotica 34, n^o 1 (5 juin 2014) : 23–42. http://dx.doi.org/10.1017/s0263574714000423.

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SUMMARYIn this paper, the problem of obtaining the optimal trajectory of a Dual-Arm Cam-Lock (DACL) robot is addressed. The DACL robot is a reconfigurable manipulator consisting of two cooperative arms, which may act separately. These may also be cam-locked in each other in some links and thus lose some degrees of freedom while gaining higher structural stiffness. This will also decrease their workspace volume. It is aimed to obtain the optimal configuration of the robot and the optimal joint trajectories to minimize the consumed energy for following a specific task space path. The Pontryagin's Minimum Principle is utilized with a shooting method to resolve kinematic redundancy. Numerical examples are investigated to show optimal trajectories in different cam-locked configurations, and the final decision is made based on a selection table of the computed performance indices.

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Gao, Xueshan, Yu Mu et Yongzhuo Gao. « Optimal trajectory planning for robotic manipulators using improved teaching-learning-based optimization algorithm ». Industrial Robot : An International Journal 43, n^o 3 (16 mai 2016) : 308–16. http://dx.doi.org/10.1108/ir-08-2015-0167.

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Purpose The purpose of this paper is to propose a method of optimal trajectory planning for robotic manipulators that applies an improved teaching-learning-based optimization (ITLBO) algorithm. Design/methodology/approach The ITLBO algorithm possesses better ability to escape from the local optimum by integrating the original TLBO with variable neighborhood search. The trajectory of robotic manipulators complying with the kinematical constraints is constructed by fifth-order B-spline curves. The objective function to be minimized is execution time of the trajectory. Findings Experimental results with a 6-DOF robotic manipulator applied to surface polishing of metallic workpiece verify the effectiveness of the method. Originality/value The presented ITLBO algorithm is more efficient than the original TLBO algorithm and its variants. It can be applied to any robotic manipulators to generate time-optimal trajectories.

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Deshayes, Clément. « De la révolution à la guerre au Soudan. Fragmentation politique, concurrence pour le contrôle de l’État et généralisation du conflit ». Politique africaine 173, n^o 1 (22 mai 2024) : 69–92. http://dx.doi.org/10.3917/polaf.173.0069.

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Le Soudan connaît une guerre depuis le 15 avril 2023 qui oppose deux forces armées. Cet article vise à replacer cet affrontement dans une histoire plus longue en analysant le glissement de la révolution de décembre 2018 vers la guerre et en décrivant les principales dynamiques de ce conflit. En s’appuyant sur des enquêtes de terrain antérieures à la guerre, cet article montre que l’enjeu de la guerre s’inscrit dans la poursuite de la concurrence pour le contrôle de l’appareil étatique et dans la trajectoire historique de gestion de la violence au travers de dispositifs miliciens. La généralisation du conflit a entraîné une diffusion de l’armement de la population et accentué la fragmentation politique et sécuritaire entamée durant la période de transition.

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Tahraoui, R. « Contrôle Optimal dans les Équations Elliptiques ». SIAM Journal on Control and Optimization 30, n^o 3 (mai 1992) : 495–521. http://dx.doi.org/10.1137/0330030.

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Cecchin, Alekos. « Finite state N-agent and mean field control problems ». ESAIM : Control, Optimisation and Calculus of Variations 27 (2021) : 31. http://dx.doi.org/10.1051/cocv/2021032.

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We examine mean field control problems on a finite state space, in continuous time and over a finite time horizon. We characterize the value function of the mean field control problem as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation in the simplex. In absence of any convexity assumption, we exploit this characterization to prove convergence, as N grows, of the value functions of the centralized N-agent optimal control problem to the limit mean field control problem value function, with a convergence rate of order [see formula in PDF]. Then, assuming convexity, we show that the limit value function is smooth and establish propagation of chaos, i.e. convergence of the N-agent optimal trajectories to the unique limiting optimal trajectory, with an explicit rate.

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Zavadskiy, Sergey V., Dmitrii A. Ovsyannikov et Dmitrii D. Melnikov. « Optimization approach to the design of nonlinear control system controllers ». Vestnik of Saint Petersburg University. Applied Mathematics. Computer Science. Control Processes 19, n^o 1 (2023) : 109–19. http://dx.doi.org/10.21638/11701/spbu10.2023.109.

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The optimization approach is applied to the synthesis and optimization of nonlinear real-time feedback optimal control system of a certain Maglev platform. To optimize the nonlinear control law, the integral functional criteria is minimized, which evaluates the quality of the dynamics of not one trajectory, but an ensemble of nonlinear trajectories of the system. The considered ensemble of trajectories covers the entire area of the engineering gap between the platform and the guide rails. In this area the magnetic forces provide highly nonlinear effects due to the considered design features of the object. At the same time, it is required to provide the stabilization within the entire engineering gap. It makes this statement to be a multi-input nonlinear control problem. The components of the feedback control law vector have a polynomial form of the state-space variables. As a result of computational optimization of trajectories ensemble, a class of Pareto-optimal polynomial regulators is constructed for considered control object. In the presented set, each Pareto-optimal point corresponds to a specific designed controller and investigated functional criteria which evaluates the entire ensemble of perturbed nonlinear trajectories. This allows a research engineer to choose various nonlinear regulators and achieve a compromise between stabilization accuracy and energy costs.

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Frankowska, Helene, Elsa M. Marchini et Marco Mazzola. « Distance estimates for state constrained trajectories of infinite dimensional differential inclusions ». ESAIM : Control, Optimisation and Calculus of Variations 24, n^o 3 (2018) : 1207–29. http://dx.doi.org/10.1051/cocv/2017032.

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This paper concerns estimates on the distance between a trajectory of a differential inclusion and the set of feasible trajectories of the same inclusion, feasible meaning confined to a given set of constraints. We apply these estimates to investigate Lipschitz continuity of the value functions arising in optimal control, and to variational inclusions, useful for proving non degenerate necessary optimality conditions. The main feature of our analysis is the infinite dimensional framework, which can be applied to models involving PDEs.

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Lisowski, Józef. « Optimality of Safe Game and Non-Game Control of Marine Objects ». Electronics 12, n^o 17 (28 août 2023) : 3637. http://dx.doi.org/10.3390/electronics12173637.

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The article presents a model of the process of safe and optimal control of an autonomous surface object in a group of encountered objects. An algorithm for determining the optimal and safe trajectory based on a multi-object game model was proposed, and an algorithm for determining the optimal trajectory was proposed for comparative analysis, not taking into account the maneuverability of other objects. Simulation studies of the algorithms made it possible to assess the optimality of the trajectories for various acceptable object strategies. An analysis of the characteristics of the sensitivity of the safe control—assessed with the risk of collision, both on the inaccuracy of navigation data and on the number of possible strategies of objects, was carried out.

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Eisler, G. R., R. D. Robinett, D. J. Segalman et J. D. Feddema. « Approximate Optimal Trajectories for Flexible-Link Manipulator Slewing Using Recursive Quadratic Programming ». Journal of Dynamic Systems, Measurement, and Control 115, n^o 3 (1 septembre 1993) : 405–10. http://dx.doi.org/10.1115/1.2899116.

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The method of recursive quadratic programming, coupled with a homotopy method, has been used to generate approximate minimum-time and minimum tracking-error tip trajectories for two-link flexible manipulator movements in the horizontal plane. The manipulator is modeled with an efficient finite-element scheme for a multi-link, multi-joint system with bending only in the horizontal-plane. Constraints on the trajectory include boundary conditions on link tip position, final joint velocities, accelerations and torque inputs to complete a rest-to-rest maneuver, straight-line tip tracking between boundary positions, and motor torque limits. Trajectory comparisons demonstrate the impact of torque input smoothness on structural mode excitation. Applied torques retain much of the qualitative character of rigid-body slewing motion with alterations for energy dissipation.

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Wang, L. T., et B. Ravani. « Dynamic Load Carrying Capacity of Mechanical Manipulators—Part II : Computational Procedure and Applications ». Journal of Dynamic Systems, Measurement, and Control 110, n^o 1 (1 mars 1988) : 53–61. http://dx.doi.org/10.1115/1.3152648.

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A computational procedure is presented for obtaining numerical solutions to the trajectory optimization problem associated with synthesizing robot dynamic trajectories with maximum load carrying capacities. The applications of the procedure and the problem formulations given in Part I of this paper to synthesizing time-optimal robot motions and classification of multi-degree-of-freedom robot manipulators are also investigated.

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McCormick, J., et R. Horowitz. « Time Optimal Seek Trajectories for a Dual Stage Optical Disk Drive Actuator ». Journal of Dynamic Systems, Measurement, and Control 113, n^o 3 (1 septembre 1991) : 534–36. http://dx.doi.org/10.1115/1.2896446.

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A closed-form solution for the time optimal control of a dual actuator disk drive system that takes into account the physical constraint limiting the relative motion of the fine and coarse actuator has been derived. The result is useful for determining track seeking strategies for high performance optical disks. The application of the necessary conditions to a simplified model of the compound actuator is presented and a solution derived.

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Lu, Ping, Sergio Sandoval et Christopher Davami. « Fast and Robust Optimization of Full Trajectory from Entry Through Powered Descent ». Journal of Guidance, Control, and Dynamics 47, n^o 2 (février 2024) : 203–16. http://dx.doi.org/10.2514/1.g007564.

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A high-mass Mars entry, descent, and landing (EDL) mission for cargo delivery or human exploration faces the challenge of a high propellant mass fraction requirement for powered descent. This work develops a novel method and the associated algorithm that utilize existing entry and propellant-optimal powered descent guidance algorithms for fast and robust optimization of the end-to-end EDL trajectory for achieving the overall optimized propellant efficiency. A bilevel optimization formulation aided by a predictive logic based on the optimal powered descent algorithm to determine the near-optimal transition from entry to powered descent allows the end-to-end trajectory to be optimized in a relatively simple manner. No new major software or algorithms are required other than the existing guidance algorithms. A solution to the bilevel optimization problem is shown to exist, and the convergence of the bilevel optimization algorithm is guaranteed under certain mild assumptions. The algorithm developed in this paper is able to find consistently an end-to-end near-optimal EDL trajectory in just over 10 s on a desktop computer, while general-purpose modern trajectory optimization software can take thousands of seconds. The effectiveness and robustness of the algorithm are demonstrated by successfully optimizing thousands of complete EDL trajectories efficiently and reliably from dispersed initial entry conditions.

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Dobiš, Michal, Martin Dekan, Peter Beňo, František Duchoň et Andrej Babinec. « Evaluation Criteria for Trajectories of Robotic Arms ». Robotics 11, n^o 1 (15 février 2022) : 29. http://dx.doi.org/10.3390/robotics11010029.

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This paper presents a complex trajectory evaluation framework with a high potential for use in many industrial applications. The framework focuses on the evaluation of robotic arm trajectories containing only robot states defined in joint space without any time parametrization (velocities or accelerations). The solution presented in this article consists of multiple criteria, mainly based on well-known trajectory metrics. These were slightly modified to allow their application to this type of trajectory. Our framework provides the methodology on how to accurately compare paths generated by randomized-based path planners, with respect to the numerous industrial optimization criteria. Therefore, the selection of the optimal path planner or its configuration for specific applications is much easier. The designed criteria were thoroughly experimentally evaluated using a real industrial robot. The results of these experiments confirmed the correlation between the predicted robot behavior and the behavior of the robot during the trajectory execution.

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Xu, Zequan, Wei Wang, Yixiang Chi, Kun Li et Leiying He. « Optimal Trajectory Planning for Manipulators with Efficiency and Smoothness Constraint ». Electronics 12, n^o 13 (3 juillet 2023) : 2928. http://dx.doi.org/10.3390/electronics12132928.

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Path planning to generate an appropriate time sequence of positions for a complex trajectory is an open challenge in robotics. This paper proposes an optimization method with the integration of an improved ant colony algorithm and a high-order spline interpolation technique. The optimization process can be modelled as the travelling salesman problem. The greatest features of this method include: (1) automatic generation for complex trajectory and a new idea of selecting the nearest start point instead of using the traditional way of human operation; (2) an optimized motion sequence of the manipulator with the shortest length of the free-load path improves efficiency by nearly 65% and (3) trajectories both in Cartesian space and joint space are interpolated with good smoothness to reduce shocks and vibrations. Simulations and experiments are conducted to demonstrate the good properties of this method.

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Cancès, Eric, Claude le Bris et Mathieu Pilot. « Contrôle optimal bilinéaire d'une équation de Schrödinger ». Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 330, n^o 7 (avril 2000) : 567–71. http://dx.doi.org/10.1016/s0764-4442(00)00227-5.

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Khoroshavin, V. S., et V. S. Grudinin. « Synthesis of Programmed Motion Based on Special Optimal Control ». Mekhatronika, Avtomatizatsiya, Upravlenie 22, n^o 8 (20 août 2021) : 395–403. http://dx.doi.org/10.17587/mau.22.395-403.

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A method is proposed for the synthesis of a closed-loop system with controls that ensure the movement of an object with minimal deviations from a given trajectory of the output coordinate and its higher derivatives and a transition to this set. To solve the problem, the Pontryagin maximum principle is used to study special situations without analysis of auxiliary variables, supplemented by the apparatus of general position conditions for nonlinear systems in an extended coordinate space, taking into account the object, a functional that is nonlinear regarding deviations of the output coordinate and the explicit occurrence of time. The combined use of these methods allows us, firstly, to find special trajectories of coordinates that are higher derivatives of the output coordinate, and after excluding time, a special phase trajectory is found, which is a switching line for reaching the final state, a given programmed motion along which in a closed system is carried out by special control. Secondly, access to a special phase trajectory from the initial state is carried out for linear objects by relay control, and for nonlinear objects, under certain boundary conditions, relay control is supplemented by a special control of the speed problem. Examples of control of programmed motion with oscillatory and aperiodic processes of a given duration for linear and nonlinear objects are given. Taking into account the nature of equilibrium states, determined by the methods of the qualitative theory of differential equations, and restrictions on control and coordinates, topologies of trajectories are obtained for the implementation of a continuous special control or sliding mode. New algorithms and structures of control systems are obtained. The results are accompanied by modeling, illustrating the effectiveness of algorithms and structures of control systems according to the proposed synthesis method and confirming analytical materials. The results of the work can be used to control linear and nonlinear objects in mechatronics, robotics, thermal processes and other industries.

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Park, Kyung-Jo. « Fourier-based optimal excitation trajectories for the dynamic identification of robots ». Robotica 24, n^o 5 (28 mars 2006) : 625–33. http://dx.doi.org/10.1017/s0263574706002712.

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This paper describes a new approach to the parameterization of robot excitation trajectories for optimal robot identification. The trajectory parameterization is based on a combined Fourier series and polynomial functions. The coefficients of the Fourier series are optimized for minimal sensitivity of the identification to measurement disturbances, which is measured as the d-optimality criterion, taking into account motion constraints in joint and Cartesian space. This parameterization satisfies both the guarantees of convergence by adding terms and the matching of the boundary conditions. Application of the method for the identification of the CRS A465 industrial robot proves the validity of the proposed approach.

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Al Younes, Younes Al, et Martin Barczyk. « Adaptive Nonlinear Model Predictive Horizon Using Deep Reinforcement Learning for Optimal Trajectory Planning ». Drones 6, n^o 11 (27 octobre 2022) : 323. http://dx.doi.org/10.3390/drones6110323.

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This paper presents an adaptive trajectory planning approach for nonlinear dynamical systems based on deep reinforcement learning (DRL). This methodology is applied to the authors’ recently published optimization-based trajectory planning approach named nonlinear model predictive horizon (NMPH). The resulting design, which we call `adaptive NMPH’, generates optimal trajectories for an autonomous vehicle based on the system’s states and its environment. This is done by tuning the NMPH’s parameters online using two different actor-critic DRL-based algorithms, deep deterministic policy gradient (DDPG) and soft actor-critic (SAC). Both adaptive NMPH variants are trained and evaluated on an aerial drone inside a high-fidelity simulation environment. The results demonstrate the learning curves, sample complexity, and stability of the DRL-based adaptation scheme and show the superior performance of adaptive NMPH relative to our earlier designs.

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Alekseeva, I. V., O. I. Lysenko et O. M. Tachinina. « Necessary optimality conditions of control of stochastic compound dynamic system in case of full in-formation about state vector. » Mathematical machines and systems 4 (2020) : 136–47. http://dx.doi.org/10.34121/1028-9763-2020-4-136-147.

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Stochastic Compound Dynamic Systems (CDS) are complex technical systems that are created through the use of precision mechanics in combination with modern telecommunications and computer technologies. Incertitude in these CDS shows up under the influence of external and internal stochastic perturbations. The constituent elements of CDS are combined into a single system because these elements perform a single complex mission. The information exchange is wireless, there is no mechanical connection between the elements of the CDS. The paper considers groups of unmanned aerial vehicles (UAVs), which are equipped with sensors or multisensors that are able to perform a mobile sensor network. The trajectories of individual elements of the mobile sensor network are trajectories formed under the influence of stochastic perturbations. This fact means that the nature of the mobile sensor network can be classified as a stochastic compound dynamic system and for the mathematical description and optimization of the movement of this system is adequate to use models and methods for optimizing stochastic CDS. The model of CDS motion is considered to be a branching trajectory or, as they say, a branched trajectory. A stochastic mathematical model of the motion of a mobile sensor network, which performs the combined mission of surveying an emergency zone, can be classified as a model of the motion of a stochastic compound dynamic system. This approach is an adequate for mathematical model creation to the mobile sensor network physical condition, for its operation in the zone of natural disaster by natural or anthropogenic origin. This paper is devoted to solving a theoretical problem related to the formulation and proof of the necessary conditions for stochastic CDS moving optimal control along a branched trajectory with an arbitrary branching scheme.

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Lisowski, Józef Andrzej. « Maximum Principle in Autonomous Multi-Object Safe Trajectory Optimization ». Electronics 13, n^o 6 (20 mars 2024) : 1144. http://dx.doi.org/10.3390/electronics13061144.

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The following article presents the task of optimizing the control of an autonomous object within a group of other passing objects using Pontryagin’s bounded maximum principle. The basis of this principle is a multidimensional nonlinear model of the control process, with state constraints reflecting the motion of passing objects. The analytical synthesis of optimal multi-object control became the basis for the algorithm for determining the optimal and safe object trajectory. Simulation tests of the algorithm on the example of real navigation situations with various numbers of objects illustrate their safe trajectories in changing environmental conditions. The optimal object trajectory obtained using Pontryagin’s maximum principle was compared with the trajectory calculated using the Bellman dynamic programming method. The analysis of the research allowed for the formulation of valuable conclusions and a plan for further research in the field of autonomous vehicle control optimization. The maximum principle algorithm allows one to take into account a larger number of objects whose data are derived from ARPA anti-collision radar systems.

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Yan, Zhenzhuo, Hongwei Ji et Qing Chang. « Energy Consumption Minimization of Quadruped Robot Based on Reinforcement Learning of DDPG Algorithm ». Actuators 13, n^o 1 (2 janvier 2024) : 18. http://dx.doi.org/10.3390/act13010018.

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Energy consumption is one of the most critical factors in determining the kinematic performance of quadruped robots. However, existing research methods often encounter challenges in quickly and efficiently reducing the energy consumption associated with quadrupedal robotic locomotion. In this paper, the deep deterministic policy gradient (DDPG) algorithm was used to optimize the energy consumption of the Cyber Dog quadruped robot. Firstly, the kinematic and energy consumption models of the robot were established. Secondly, energy consumption was optimized by reinforcement learning using the DDPG algorithm. The optimized plantar trajectory was then compared with two common plantar trajectories in simulation experiments, with the same period and the number of synchronizations but varying velocities. Lastly, real experiments were conducted using a prototype machine to validate the simulation data. The analysis results show that, under the same conditions, the proposed method can reduce energy consumption by 7~9% compared with the existing optimal trajectory methods.

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Ardema, Mark D., Jeffrey V. Bowles et Thomas Whittaker. « Optimal trajectories for hypersonic launch vehicles ». Dynamics and Control 4, n^o 4 (octobre 1994) : 337–47. http://dx.doi.org/10.1007/bf01974139.

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Ghosh, Bijoy K., et Bhagya Athukorallage. « Minimum energy optimal external torque control of human binocular vision ». Control Theory and Technology 18, n^o 4 (23 novembre 2020) : 431–58. http://dx.doi.org/10.1007/s11768-020-00015-x.

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AbstractIn this paper, we consider eyes from the human binocular system, that simultaneously gaze on stationary point targets in space, while optimally skipping from one target to the next, by rotating their individual gaze directions. The head is assumed fixed on the torso and the rotating gaze directions of the two eyes are assumed restricted to pass through a point in the visual space. It is further assumed that, individually the rotations of the two eyes satisfy the well known Listing’s law. We formulate and study a combined optimal gaze rotation for the two eyes, by constructing a single Riemannian metric, on the associated parameter space. The goal is to optimally rotate so that the convergent gaze changes between two pre-specified target points in a finite time interval [0, 1]. The cost function we choose is the total energy, measured by the $$L^2$$ L 2 norm, of the six external torques on the binocular system. The torque functions are synthesized by solving an associated ‘two-point boundary value problem’. The paper demonstrates, via simulation, the shape of the optimal gaze trajectory of the focused point of the binocular system. The Euclidean distance between the initial and the final point is compared to the arc-length of the optimal trajectory. The consumed energy, is computed for different eye movement chores and discussed in the paper. Via simulation we observe that certain eye movement maneuvers are energy efficient and demonstrate that the optimal external torque is a linear function in time. We also explore and conclude that splitting an arbitrary optimal eye movement into optimal vergence and version components is not energy efficient although this is how the human oculomotor control seems to operate. Optimal gaze trajectories and optimal external torque functions reported in this paper is new.

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Bujold, Audrey, et Sylvie Lévesque. « La paradoxalité de la reconnaissance de l’expérience de coercition reproductive : une analyse qualitative ». Aporia 14, n^o 2 (22 novembre 2022) : 59–71. http://dx.doi.org/10.18192/aporia.v14i2.6459.

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La coercition reproductive fait référence aux comportements de contrôle et de force infligés afin d'orienter la trajectoire reproductive des femmes. Les conséquences inhérentes sont multiples : grossesses inopportunes, recours accentué aux contraceptifs d’urgence et avortements, dépression.... Malgré ces effets importants, les femmes qui en sont victimes éprouvent souvent de la difficulté à reconnaitre leur expérience comme telle, ce qui contribue à limiter leur recherche de soutien. À travers la théorie du parcours de vie, cette analyse qualitative réalisée auprès de 13 femmes ayant vécu de la coercition reproductive présente comment la reconnaissance d'une telle expérience se déploie à l'intersection de diverses trajectoires de vie. Nos résultats suggèrent que le processus de reconnaissance est intrinsèquement paradoxal, et revêt un caractère à la fois subjectif, intersubjectif, sociohistorique et évolutif. Contrastant nos résultats avec la reconnaissance honnéthienne, des pistes critiques sont formulées en ce qui concerne notamment le déficit de ressources herméneutiques.

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Chen, Chun-Ta, et Hua-Wei Chi. « Singularity-free trajectory planning of platform-type parallel manipulators for minimum actuating effort and reactions ». Robotica 26, n^o 3 (mai 2008) : 371–84. http://dx.doi.org/10.1017/s0263574707004043.

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SUMMARYDue to the existence of singular configurations within the workspace for a platform- type parallel manipulator (PPM), the actuating force demands increase drastically as the PPM approaches or crosses singular points. Therefore, in this report, a numerical technique is presented to plan a singularity-free trajectory of the PPM for minimum actuating effort and reactions. By using the parametric trajectory representation, the singularity-free trajectory planning problem can be cast to the determination of undetermined control points, after which a particle swarm optimization algorithm is employed to find the optimal control points. This algorithm ensures that the obtained trajectories can avoid singular points within the workspace and that the PPM has the minimum actuating effort and reactions. Simulations and discussions are presented to demonstrate the effectiveness of the algorithm.

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