Academic literature on the topic 'Force polytope'

Output force or velocity polytopes are usually used as an index of the manipulability of robot. This paper discusses the relationship between the actuator force and the variation of the output force capacity polytope and proposes the output force capacity polytope method for the selection of actuator forces of a three degrees of freedom excavating manipulator with the requirement that the output force on the end effector is a set of all possible forces rather than a single force. In this paper, the method to calculate capacity polytope is introduced with the consideration of gravity effect. With the concept that the required output force space should be within the output capacity polytope, the output force capacity polytope approach for selecting actuator forces is proposed.

A force capacity evaluation for a given posture may provide better understanding of human motor abilities for applications in sport sciences, rehabilitation and ergonomics. From data on posture and maximum isometric joint torques, the upper-limb force feasible set of the hand was predicted by four models called force ellipsoid, scaled force ellipsoid, force polytope and scaled force polytope, which were compared with a measured force polytope. The volume, shape and force prediction errors were assessed. The scaled ellipsoid underestimated the maximal mean force, and the scaled polytope overestimated it. The scaled force ellipsoid underestimated the volume of the measured force distribution, whereas that of the scaled polytope was not significantly different from the measured distribution but exhibited larger variability. All the models characterized well the elongated shape of the measured force distribution. The angles between the main axes of the modelled ellipsoids and polytopes and that of the measured polytope were compared. The values ranged from 7.3° to 14.3°. Over the entire surface of the force ellipsoid, 39.7% of the points had prediction errors less than 50 N; 33.6% had errors between 50 and 100 N; and 26.8% had errors greater than 100 N. For the force polytope, the percentages were 56.2%, 28.3% and 15.4%, respectively.

Linear Parameter Varying models-based Model Predictive Control (LPV-MPC) has stood out in manipulator robots because it presents well-rejection to dynamic uncertainties in flexible joints. However, it has become too weak when the MPC's optimization problem does not include kinematic constraints-based conditions. This paper uses dynamic confined space of velocities (DCSV) to include these conditions as a recursive polytopic constraint, guaranteeing optimal dependency on a simplex scheduling parameter. To this end, the local frame's velocities and torque/force preload of joints (related to violation of kinematic constraints) are associated with different time scale dynamics such that DCSV correlates them as a polytope. So, a classical LPV-MPC will be updated using a dynamic programming approach according to the DCSV-based polytope. As a result, one lemma about DCSV-based recursive polytope and a five-step procedure for two decoupled close-loop schemes with different time scales compose the LPV-MPC proposed method. Numerical validation shows that even for relevant flexibility situations, trajectory tracking performance is improved by tuning finite horizons and optimization problem constraints regarding DCSV's behavior.

SUMMARYThis part of the paper investigates the wrench capabilities of redundantly actuated planar parallel manipulators (PPMs). The wrench capabilities of PPMs are determined by mapping a hypercube from the torque space into a polytope in the wrench space. For redundant PPMs, one actuator output capability constrains the wrench space with a smaller polytope that is contained inside the overall polytope. Performance indices are derived from six study cases. These indices are employed to analyze the wrench workspace for constant orientation of the mobile platform of the non-redundant 3-RRR PPM, and actuation redundant 4-RRR and 3-RRR PPMs, where the underline indicates the actuated joints. A comparison of the results shows that both of the redundantly-actuated PPMs give better wrench capabilities than the non-redundant PPM. However, it is shown that scaled for the operational cost (wrench capabilities divided by total actuation output) the non-redundant 3-RRR PPM provides the highest maximum reachable force, the 3-RRR PPM produces the highest isotropic force, and the 4-RRR yields the highest reachable moment.

Niggli reduction can be viewed as a series of operations in a six-dimensional space derived from the metric tensor. An implicit embedding of the space of Niggli-reduced cells in a higher-dimensional space to facilitate calculation of distances between cells is described. This distance metric is used to create a program,BGAOL, for Bravais lattice determination. Results fromBGAOLare compared with results from other metric based Bravais lattice determination algorithms. This embedding depends on understanding the boundary polytopes of the Niggli-reduced coneNin the six-dimensional spaceG6. This article describes an investigation of the boundary polytopes of the Niggli-reduced coneNin the six-dimensional spaceG6by algebraic analysis and organized random probing of regions near one-, two-, three-, four-, five-, six-, seven- and eightfold boundary polytope intersections. The discussion of valid boundary polytopes is limited to those avoiding the mathematically interesting but crystallographically impossible cases of zero-length cell edges. Combinations of boundary polytopes without a valid intersection in the closure of the Niggli cone or with an intersection that would force a cell edge to zero or without neighboring probe points are eliminated. In all, 216 boundary polytopes are found. There are 15 five-dimensional boundary polytopes of the fullG6Niggli coneN.

SUMMARYThis paper presents a methodology to obtain the wrench capabilities of a kinematically redundant planar parallel manipulator using a wrench polytope approach. A methodology proposed by others for non-redundant and actuation-redundant manipulators is adapted to a kinematically redundant manipulator. Four wrench capabilities are examined: a pure force analysis, the maximum force for a prescribed moment, the maximum reachable force, and the maximum moment with a prescribed force. The proposed methodology, which finds the exact explicit solution for three of the four wrench capabilities, does not use optimization and is very efficient.

En interaction physique Humain-Robot, un robot et un individu effectuent une tâche de collaboration par le biais d'un contact physique, par exemple entre l'effecteur terminal du robot et la main de l'humain. Une attention nécessaire se porte alors sur la sécurité de cette collaboration. Afin que le robot puisse fournir une assistance adaptée, il est primordial de caractériser les limites d'un individu, notamment celles biomécaniques. Les capacités de force du membre supérieur humain correspondent à l'ensemble des efforts qu'il peut exercer au niveau de la main, dans une posture spécifique. La forme de ces ensembles reflète des propriétés individuelles, telles que l'anthropométrie et la force musculaire. De plus, leur surface caractérise les efforts maximaux possibles. Par conséquent, la connaissance des capacités de force d'un individu permet d'aiguiller l'assistance du robot afin de respecter les limites en force de l'humain.Expérimentalement, les capacités de force sont difficiles à mesurer directement. Néanmoins, en conditions isométriques, elles peuvent être décrites partiellement en mesurant des efforts maximaux dans des directions spécifiées. In silico, les modèles musculosquelettiques représentent mathématiquement le squelette, les articulations et les muscles. Ils permettent de simuler les capacités de force dans diverses postures, construites par le biais d'opérations géométriques (somme de Minkowski, projection, intersection) sur des ensembles convexes. Cependant, ces opérations sont coûteuses en temps de calcul. Cette thèse se concentre donc en premier lieu sur une nouvelle approche réduisant le temps de calcul de l'une de ces opérations.Par ailleurs, la modélisation des capacités de force nécessite de faire des hypothèses sur la façon dont les tensions musculaires contribuent aux couples articulaires. Ces hypothèses influencent la forme des capacités de force, notamment leur représentation sous forme de polytope ou d'ellipsoïde. Cette thèse propose donc une unification de ces représentations afin de considérer, de manière géométrique, diverses hypothèses biomécaniques sur les relations entre tensions musculaires. Bien que l'utilisation de modèles musculosquelettiques complexes et détaillés limite la simulation des capacités de force, ce cadre théorique met en évidence une forme universelle pour la représentation des capacités de force d'un individu.Également, une représentation précise des capacités de force d'un individu nécessite la connaissance d'un modèle musculosquelettique personnalisé. Compte tenu de l'approche ensembliste des capacités de force, cette thèse propose une analyse de sensibilité adaptée évaluant l'influence des paramètres musculaires sur les propriétés géométriques des capacités de force. Cette analyse met également en évidence les défis de la personnalisation en regard de l'inter-variabilité entre individus.Enfin, un protocole expérimental a été établi afin de confronter les méthodes de personnalisation in silico à des forces maximales isométriques mesurées dans différentes postures du membre supérieur. La représentation des capacités de force sous forme d'ellipsoïdes, moins coûteuse en temps de calcul, et l'ajout d'hypothèses biomécaniques sur le comportement musculaire amènent à la personnalisation des muscles d'un modèle musculosquelettique, validant in vivo les résultats théoriques proposés dans cette thèse
In physical Human-Robot Interaction, where robots and humans collaborate on shared tasks through physical contact, such as between the robot's end effector and the human's hand, human safety is a primary concern. This necessitates that the collaborative system inherently consider human characteristics to provide appropriate and safe robotic assistance. To achieve this, it is necessary to evaluate the capabilities of the human upper-limb. In biomechanics, these capabilities are defined through force feasible sets at the hand, which represent all the forces a human operator can exert in a given posture. These three-dimensional sets are influenced by individual factors such as anthropometry and muscle strength and the surface of these sets represents the maximum force capabilities of the human upper-limb in all directions. Therefore, force feasible sets are an invaluable tool for guiding robotic assistance, ensuring it respects biomechanical constraints by remaining within the human's exertable force limits.Force feasible sets are challenging to measure directly but can be partially represented in isometric conditions by measuring maximum exerted forces. Musculoskeletal models, which mathematically represent the human skeleton, joints, and muscles, allow for in silico representation of force feasible sets in various postures through geometric operations (Minkowski sum, projection, intersection) on convex sets. However, these operations are computationally expensive. This thesis first focuses on a novel approach to reduce the computational time of one of the most demanding tasks within this framework.Furthermore, existing in silico models often employ various geometric assumptions about how muscle tensions contribute to joint torques, leading to different characterizations of force feasible sets' shapes, including 3D polytopes and ellipsoids. This thesis proposes a unified framework to represent force feasible sets that explicitly incorporates these geometric assumptions. This framework addresses the limitations of current numerical simulations, which struggle to analyze complex scenarios involving more detailed representation of musculoskeletal models and inherently higher computational costs.In this regard, accurate representation of individual force capabilities requires precise parameterization of musculoskeletal model components. Given the set-theoretic nature of force feasible sets, this thesis introduces an adapted sensitivity analysis tailored to assess the influence of parameters on the geometric properties of force feasible sets. This analysis also highlights the challenges of personalizing musculoskeletal models due to biomechanical inter-variability.Finally, an experimental protocol was established to confront in silico personalization processes with experimentally measured maximal isometric force exertions collected across various postures. Through biomechanical assumptions leading to a computationally less expensive representation of force feasible sets as ellipsoids, muscle parameters personalization is achieved, validating in vivo the theoretically-driven results of this thesis

Ce travail propose de nouvelles structures de contrôle pour la téléopération bilatérale à travers des réseaux de communication non dédiés. L'enjeu est donc de concevoir et calculer des structures de commande garantissant la stabilisation et un bon degré de performance en termes de synchronisation (suivi des positions et vitesse) et de transparence (ressenti des forces) sous les retards variables et asymétriques.Nous faisons tout d'abord un tour d'horizon des recherches récentes dans le domaine des systèmes de téléopération et de leurs caractéristiques. Puis, nous considérons des modèles linéaires à plusieurs retards variables pour lesquels nous proposons une approche d'analyse de stabilité par fonctionnelles de Lyapunov-Krasovskii et contrôle robuste H [infinity symbol . Ensuite, trois structures de téléopération seront proposées en temps continu, la comparaison de ces architectures montre que, pour un retard de réseau maximum donné ou calculé, toutes garantissent un suivi de position et vitesse. Les deux dernières, qui utilisent les forces mesurées ou estimées de l'opérateur humain et de l'environnement, garantissent de plus un suivi en force. Au final, la troisième structure (avec proxy) présente la meilleure performance, même si elle demande un peu plus de calcul. Puis, afin d'analyser et d'améliorer les performances de la troisième structure pour des modèles encore plus réalistes, une étude est menée en temps discret, mais aussi sur un modèle non linéaire ou non stationnaire sous perturbations bornées en norme. L'implantation sur la plate-forme est décrite dans un quatrième et dernier chapitre, et puis l'analyse des résultats expérimentaux est alors menée

AbstractArticulated heavy vehicles (AHVs) face yaw instabilities, especially under extensive propulsion or regenerative braking force on the driven axles, risking their directional stability and potentially leading to jackknifing. Hence, safe operating envelopes (SOEs) are essential for allocating propulsion and braking forces among different units. This study proposes a novel approach to ensure yaw stability by reducing longitudinal slip limits of the electric motors (EMs) based on side-slip, enhancing stability and acceleration performance. Validation through simulations and real vehicle tests shows promising results.

AbstractNeural Networks (NNs) have increasingly apparent safety implications commensurate with their proliferation in real-world applications: both unanticipated as well as adversarial misclassifications can result in fatal outcomes. As a consequence, techniques of formal verification have been recognized as crucial to the design and deployment of safe NNs. In this paper, we introduce a new approach to formally verify the most commonly considered safety specifications for ReLU NNs – i.e. polytopic specifications on the input and output of the network. Like some other approaches, ours uses a relaxed convex program to mitigate the combinatorial complexity of the problem. However, unique in our approach is the way we use a convex solver not only as a linear feasibility checker, but also as a means of penalizing the amount of relaxation allowed in solutions. In particular, we encode each ReLU by means of the usual linear constraints, and combine this with a convex objective function that penalizes the discrepancy between the output of each neuron and its relaxation. This convex function is further structured to force the largest relaxations to appear closest to the input layer; this provides the further benefit that the most “problematic” neurons are conditioned as early as possible, when conditioning layer by layer. This paradigm can be leveraged to create a verification algorithm that is not only faster in general than competing approaches, but is also able to verify considerably more safety properties; we evaluated PEREGRiNN on a standard MNIST robustness verification suite to substantiate these claims.

Six-legged robots are reliable locomotive machines with actuation redundancy. This paper analyzes the force and velocity capacities of a six-legged high-payload robot geometrically and numerically. The full-body Jacobian between the body platform and the actuation is first of all computed. A geometric computation approach is then proposed to obtain the robot velocity/force polytopes in the platform operational space. System physical constraints of joint torques and velocities are taken into account so that the task space capacities could be quantitatively given. Besides, several capacity indices are also investigated, including the maximum velocity/force magnitude, the maximum velocity/force along a given direction and the maximum isotropic velocity/force. At last, the robot capacities are numerically analyzed with different supporting legs. The results verify high payload capacity of the robot and clarify the influence of different gait parameters on the task space performance. Our method is proposed in a general and convenient framework, and therefore it is beneficial for the quantitative performance evaluation of any multi-legged walking machine with actuation redundancy.

Robot Capability Analysis (RCA) is a process in which force/motion capabilities of a manipulator are evaluated. It is very useful in both the design and operational phases of robotics. Traditionally, ellipsoids and polytopes are used to both graphically and numerically represent these capabilities. Ellipsoids are computationally efficient but tend to underestimate while polytopes are accurate but computationally intensive. This article proposes a new approach to RCA called the Vector Expansion (VE) method. The VE method offers accurate estimates of robot capabilities in real time and therefore is very suitable in applications like task-based decision making or online path planning. In addition, this method can provide information about the joint that is limiting a robot capability at a given time, thus giving an insight as to how to improve the performance of the robot. This method is then used to estimate capabilities of 4-DOF planar robots and the results discussed and compared with the conventional ellipsoid method. The proposed method is also successfully applied to the 7-DOF Mitsubishi PA10-7C robot.

Boron carbide is a widely used impact-resistant ceramic due to its hardness, low density, and high Hugonio elastic limit, but it is prone to amorphization under high non-hydrostatic loads. Fanchini [1] suggested that the cause of amorphization lies in the (B₁₂)C-C-C boron carbide polytype, namely in the intercosahedral C-C-C chain. Previously, we determined [2] that the substitution of aluminum in the center of the chain is possible, and the most likely configuration is (B₁₂)C^Al^C. In this work, we consider the simulation of uniaxial compression along the intercosahedral chain of (B₁₂)C^Al^C and (B₁₂)C-C-C. For both configurations, we calculate the dependence of uniaxial stress on uniaxial strain and determine the maximum uniaxial stress and elastic strain values. We used a slightly modified method of uniaxial compressing that was described in [3]. The simulation was performed using the Quantum Espresso software package. A 2x2x1 unit cells of (B₁₂)C-C-C hexagonal supercell was constructed along the intercosahedral chain. All central carbon atoms were changed to aluminum and shifted in the same direction. Compression simulations were performed with a step size of 0.01 of the uniaxial elastic strain. Parameters used in the calculation include: kinetic energy cutoff for wavefunctions of 100 Ry, convergence criteria of Ry for the self-consistent field and Ry/Bohr for forces on the atoms, gamma point only for Brillouin zone, and gaussian spreading of Ry. Our results show that the introduction of aluminum into the chain of (B₁₂)C-C-C polytype leads to a decrease in the maximum elastic strain (from 0.24 to 0.17) and the maximum uniaxial stress (from 161 GPa to 94 GPa) that the system can withstand. Consequently, the (B₁₂)C^Al^C configuration has lower mechanical properties compared to the (B₁₂)C-C-C polytype of boron carbide. No mechanism for improving the characteristics of boron carbide was identified.

Abstract In this paper, the vertical carbody dynamics of the railway vehicle excited by random track inputs are investigated. The multi-objective ℋ∞ controllers for carbody weight of the actual, heavy and a mass confined in a polytopic range have been designed with the aim of reducing the wheel forces, heave, pitch and roll body accelerations of the vehicle. Later, the carbody mass is modelled as a free-free Euler Bernoulli beam and the low frequency flexural vibrations of the train body are examined. An omnibus ℋ∞ controller is synthesized to suppress both the rigid and low frequencies flexible modes of the railway vehicle. The performances of the ℋ∞ controllers are verified by using the passive and active suspension responses on the right and left rail track disturbances that are represented by the power spectral density functions authenticated for the stochastic real track data collected from the Qinhuangdao-Shenyang passenger railway line in China. Simulation results showed that all controllers exhibit a very good performance by effectively reducing the car-body accelerations in vicinity of the resonanat frequencies while keeping the wheel-rail forces in the allowable limit.