Kinematic Limit Research Articles

Selection of Manipulator Configuration for a Portable Robot for Special Tasks

This paper presents method of selection of configuration for manipulators of portable robots for special purposes. On the example of the portable PIAP Patrol robot, the analysis of tasks and related requirements for the functionality of the manipulator was presented. With the use of multi-criteria optimization tools, the selection of the manipulator configuration parameters was carried out, which leads to the maximization of selected working capacities while ensuring that the imposed requirements and mass and kinematic limitations are met. The results of simulation tests were presented and the scope of further work was outlined.

The massless single off-shell scalar box integral — branch cut structure and all-order epsilon expansion

We investigate the single off-shell scalar box integral with massless internal lines in dimensional regularization. A special emphasis is given to higher orders in the dimensional regularization parameter epsilon, its branch cut structure, and kinematic limits. Common representations of the box integral introduce superficial branch cuts, which we eliminate to all orders in the epsilon expansion. In the literature so far a satisfactory solution for this issue only exists up to finite order in the epsilon expansion. However, for certain calculations at NNLO in perturbation theory, higher orders in epsilon of this integral are required. In this paper, we present results to all orders in epsilon in terms of single-valued polylogarithms and explicitly determine the real and imaginary part of the box integral in all kinematic regions.

Three-point energy correlators and the celestial block expansion

We study the three-point energy correlator (EEEC), defined as a matrix element of a product of three energy detectors at different locations on the celestial sphere. Lorentz symmetry implies that the EEEC can be decomposed into special functions called celestial blocks. We compute three-point celestial blocks in an expansion around the collinear limit, where the three detectors approach each other on the celestial sphere. The leading term is a traditional d – 2-dimensional four-point conformal block, and thus the collinear EEEC behaves like a conformally-invariant four-point function in d – 2 dimensions. We obtain the coefficients of the conformal block decomposition for the collinear EEEC at leading nontrivial order in weakly-coupled \U0001d4a9 = 4 SYM and QCD. These data allow us to make certain all-orders predictions for the collinear EEEC in various kinematic limits, including the OPE limit and the double lightcone limit. We also study Ward identities satisfied by the EEEC and compute contact terms in the EEEC in weakly-coupled \U0001d4a9 = 4 SYM. Finally, we study the celestial block expansion of the EEEC in planar \U0001d4a9 = 4 SYM at strong coupling, determining celestial block coefficients to leading and first subleading order at large λ.

A comprehensive proposal for rehabilitation of historic Armenian church belonging to 16th century AD (Diyarbakır, Turkey)

This study presents a comprehensive proposal for the rehabilitation of the ruined Surp Sargis Church located inside the historical city walls of Diyarbakır, namely the Suriçi region. The Suriçi region was home to many ancient civilizations and cultures. This study consists of four major stages; historical research, determination of the original structural features, seismic performance assessment, and a comprehensive proposal for the rehabilitation of the building. In the first stage, the history of the church, from its construction date to the present was examined based on the historical documents, common typology of the period, and old photographs. In the second stage, the plan, facade characteristics, construction system, and material properties of the existing structure were determined and reasons for the deterioration were identified. To determine the architectural features of the analyzed church, other Armenian churches dating back to the 16th century were evaluated in addition to the examination of the old plans, photographs, and repairs. Then, in the third stage, a seismic risk assessment of the church was done through linear, pushover, and kinematic limit analyses. In the final stage, a rehabilitation proposal was presented evaluating all the data obtained from previous stages. The proposed rehabilitation practice also considered local people living around this structure. The main goal of this study is to turn this structure into an active church for religious tourism activities where Armenians living in other places can attend worship and meetings at certain times of the year. Moreover, a social activity area for local people in the surrounding region was also planned. Accordingly, the current paper provides a comprehensive rehabilitation approach that can be applied to similar cultural heritage structures.

Seismic vulnerability assessment through global-and local-scale analyses for a historic masonry building constructed in 1896

The causes of collapse in masonry buildings are different than those of reinforced concrete and steel-framed buildings. This is due to differences in structural behavior as a result of the materials and techniques used in the construction of such buildings. The most significant contribution to this behavioral difference is made by the out-of-plane behavior of masonry buildings. Therefore, in addition to overall collapse, out-of-plane behaviors of the facade walls must also be determined in such buildings. Accordingly, not only global behavior but also local behaviors should be considered while evaluating structural performance. This paper, therefore, presents a seismic performance assessment of a masonry building by global-and local-scale analyses. The examined 3-story building was constructed in 1896 and used for different purposes. Linear, nonlinear, and kinematic limit analysis approaches were used. Shear forces on the walls and inter-story drifts obtained by the linear and nonlinear analyses were analogized with the limit values envisaged in the local building codes, thus the seismic vulnerability of the building was determined. Overturning, vertical bending and lateral bending mechanisms were obtained by local analysis

Seismic performance evaluation and strengthening proposal for a reconstruction project of a historic masonry building demolished in the 1940s

For heritage structures demolished or disappeared over the years, reconstruction projects are prepared based on the original architecture and structural characteristics. Before reconstruction of historic buildings, which represent construction techniques and material characteristics of their era, assessing seismic performance is very important. Otherwise, these valuable heritage buildings may pose a risk of earthquake-induced collapse. However, this important procedure is mostly overlooked in reconstruction practices. Accordingly, the current paper presents a seismic evaluation of a reconstruction project for a historic masonry building built in 1866 and was later demolished in the 1940s. Linear, nonlinear, and kinematic limit analyses were conducted. The seismic performance was determined by comparing the shear force and inter-story drifts as well as overturning and bending behaviors with the limit values given in the code. As the seismic performance level was found to be inadequate, a strengthening proposal was made. It is believed that the evaluation methodology including global and local analyses as well as the strengthening technique presented in the current study would make a valuable contribution to the literature on the reconstruction of disappeared or demolished buildings based on the original construction technique and materials.

Post-restoration seismic performance assessment of a historic hypostyle mosque in Anatolia (13th century AD)

Assessment of structural performance under seismic effects is a very important step for restoration process of historic buildings that represent construction techniques and material characteristics of their era. This process consists of three stages namely, on-site examinations, restoration practices, and seismic analysis, and therefore, requires a multidisciplinary approach. Hypostyle structures are mostly timber-framed buildings with masonry walls on two or three facades. This construction method is a combination of Asia (wooden pillar) and Byzantine (masonry walls) techniques. The primary load-bearing system in these buildings is composed of multiple rows of wooden pillars. This paper presents post-restoration seismic assessment of a historic wooden hypostyle mosque complex constructed in 1273. This mosque complex is an important structure representing wooden hypostyle architecture in the Anatolia region of Turkey and is composed of three separate structures namely, a main mosque building, a minaret, and a tomb. Linear performance analysis, displacement-controlled nonlinear analysis, and kinematic limit analysis for failure mechanisms were conducted for the structures after the restoration. The linear performance analysis results indicated that the structures meet shear strength requirements for DD3 and DD2 earthquakes with recurrence periods of 72 and 475 years, respectively. Furthermore, according to the linear and non-linear analyses, the complex was found to satisfy performance limits for both ground motion levels in terms of inter-story drifts.

Active learning of time-optimal motion for an industrial manipulator with variable payload

Generating optimal motion for robotic systems remains an active field of research, despite its relatively long history. In addition to being optimal with respect to a defined cost, such a motion must respect the electro-mechanical limitations of the system to be of use in real-world applications. Furthermore, in an industrial application where offline planning is not possible due to a priori unknown targets and payloads, the available time budget for computations is often highly limited, making many optimal motion planning approaches unsuitable. This work introduces a supervised learning-based motion planner for industrial manipulators that closely retains the superior performance of an optimal motion planner while requiring a fraction of the computations at runtime. The proposed motion planner implicitly considers the dynamics of the robot and therefore satisfies not only kinematic limits but also those of the actuators. The proposed method is compared to state-of-the-art approaches and demonstrated on a real robot.

Energy-Optimal Coverage Motion Trajectory Generation for Industrial Machines*

Coverage motion of industrial machines are widely used for manufacturing tasks such as milling, polishing, laser cutting, and inspection. Motion smoothness of industrial machines under their kinematic limits are crucial in coverage motion to increase the production efficiency and accuracy. Motion trajectory optimization for typical computer numerical control (CNC) machines plays an important role in achieving smooth motion. In addition, with the current increase in energy costs and environmental concerns, there is a great need to reduce energy consumption by industrial machines which are extensively used in manufacturing industries. This study presents an energy optimization approach for coverage motion of industrial machines, which simultaneously integrates trajectory generation and geometric path optimization. The trajectory along a linear segment is described by the modified S-curve profile with harmonic motion employed for smooth jerk continuity to enhance the motion accuracy. An energy consumption model of the feed drive system is used to achieve energy-optimal. A genetic algorithm is applied for the optimization. Experimental validation of the simulation results is carried out using a two-axis feed drive system. Simulation and experimental results shows that the energy saving of the feed drive system is achieved under machine kinematic limits ensuring smooth motion.

Intelligent feedrate optimization using a physics-based and data-driven digital twin

Intelligent manufacturing machines envisioned for the future must be able to autonomously select process parameters that maximize their speed while adhering to quality specifications. Accordingly, this paper proposes a framework and methodology for using a physics-based and data-driven digital twin of a feed drive to maximize feedrate while respecting kinematic and contour error limits. To correct for inaccuracies introduced by unmodeled dynamics and disturbances, the data-driven model is updated on-the-fly using sensor feedback. Experiments on a 3-axis CNC machine tool prototype are used to demonstrate up to 35% cycle time reduction without violating error tolerances compared to the status quo.

Seismic vulnerability analysis and structural rehabilitation of a historical masonry tower

This paper presents the results of the structural performance assessment of an existing masonry tower and the subsequent repair and strengthening intervention. The study deals with an Italian architectural heritage building in the Cilento National Park (Southern Italy): the bell tower in Torre Orsaia. The tower has been the subject of on-site diagnostic investigations including geometrical surveys, laser scanning surveys, flat jack tests, endoscopic tests, sonic pulse velocity tests, geognostic surveys, and tie-rods tests. The multilevel assessment path proposed by the Italian Guidelines for the assessment and mitigation of the seismic risk of the cultural heritage is followed and the corresponding results are discussed. The global inelastic behavior of the masonry tower is studied through a macro-model approach using the nonlinear static (pushover) analysis. The local collapse mechanisms are studied through a kinematic limit analysis based on rigid block rotation. The repair and strengthening interventions have shown their effectiveness to close the existing cracks, preventing damage to the belfry, and improving the seismic performance of the tower. Both the compatibility, durability, and reversibility of the interventions and their reliability and monitoring are finally highlighted since the bell tower of Torre Orsaia is a historical heritage building.

Формулировка и решение задачи оптимизации формообразования крупногабаритных обшивок двойной кривизны в условиях кинематических ограничений прессового оборудования

Для снижения материальных и временных затрат на разработку и внедрение технологии изготовления обшивок двойной кривизны с использованием процесса обтяжки листовых заготовок разработаны математические модели и методики, позволяющие производить цифровое моделирование процесса формообразования и корректировать его на раннем этапе разработки технологии. При разработке технологии изготовления окантовки двери на самолет SSJ-NEW применялись новые подходы к моделированию процесса формообразования, которые позволили определить наиболее оптимальную стратегию обтяжки крупногабаритной заготовки на пределе кинематических возможностей пресса FET-1500. Разработанная технология позволяет в рамках вычислительного эксперимента провести отработочные итерации с переходом на реальную обтяжку в оптимальных технологических параметрах. To reduce material and time costs for the development and implementation of the technology for the manufacture of double-curvature sheets using the process of stretch-forming sheet workpieces, mathematical models and methods have been developed that allow digital modeling of the forming process and its correction at the early stage of technology development. When developing the technology for manufacturing the door edging on the SSJ-NEW aircraft, new approaches to modeling the forming process were used, which made it possible to determine the most optimal strategy for binding a large-sized workpiece at the limit of the kinematic capabilities of the FET-1500 press. The developed technology allows, within the framework of a computational experiment, to carry out working iterations with the transition to real binding in optimal technological parameters.

Control of Trajectory Tracking for Mobile Manipulator Robot with Kinematic Limitations and Self-Collision Avoidance

In this paper, we propose an optimized differential evolution algorithm based on kinematic limitations and structural complexity constraints to solve the trajectory tracking problem for a mobile manipulator robot. The traditional method mainly involves obtaining the speed of the control variable based on the Jacobian inverse or linearization of the robot’s kinematic model, which cannot avoid the singularity position and/or self-collision phenomena. To address these problems, we directly design an optimized differential evolution algorithm to solve the trajectory planning problem for mobile manipulator robots. First, we analyze various constraints on the actual movement and describe them specifically using various equations or inequalities, including non-holonomic constraints on the mobile platform, the physical limitations of the driving motors, self-collision avoidance restriction, and smoothly traversing the singularity position. Next, we re-define the trajectory tracking of a mobile manipulator robot as an optimization problem under multiple constraints, including the trajectory tracking task and various constraints simultaneously. Then, we propose a new differential evolution (DE) algorithm by optimizing some critical operations to solve the optimization problem, such as improving the population’s distribution, limiting the population distribution range, and adding a success index. Additionally, we design two simple trajectories and two complex trajectories to determine the performance of the optimized DE algorithm in solving the trajectory tracking problem. The results demonstrate that the optimized DE algorithm can effectively realize the high-precision trajectory tracking task of a differential wheeled mobile manipulator robot through the consideration of kinematic limitations and self-collision avoidance.

Task-specific robot base pose optimization for robot-assisted surgeries.

Preoperative planning and intra-operative system setup are crucial steps to successfully integrate robotically assisted surgical systems (RASS) into the operating room. Efficiency in terms of setup planning directly affects the overall procedural costs and increases acceptance of RASS by surgeons and clinical personnel. Due to the kinematic limitations of RASS, selecting an optimal robot base location and surgery access point for the patient is essential to avoid potentially critical complications due to reachability issues. To this end, this work proposes a novel versatile method for RASS setup and planning based on robot capability maps (CMAPs). CMAPs are a common tool to perform workspace analysis in robotics, as they are in general applicable to any robot kinematics. However, CMAPs have not been completely exploited so far for RASS setup and planning. By adapting global CMAPs to surgical procedure-specific tasks and constraints, a novel RASS capability map (RASSCMAP) is generated. Furthermore, RASSCMAPs can be derived to also comply with kinematic access constraints such as access points in laparoscopy. RASSCMAPs are versatile and applicable to any kind of surgical procedure; they can be used on the one hand for aiding in intra-operative experience-based system setup by visualizing online the robot's capability to perform a task. On the other hand, they can be used to find the optimal setup by applying a multi-objective optimization based on a genetic algorithm preoperatively, which is then transfered to the operating room during system setup. To illustrate these applications, the method is evaluated in two different use cases, namely, pedicle screw placement in vertebral fixation procedures and general laparoscopy. The proposed RASSCMAPs help in increasing the overall clinical value of RASS by reducing system setup time and guaranteeing proper robot reachability to successfully perform the intended surgeries.

Face stability analysis of circular tunnels in layered rock masses using the upper bound theorem

An analysis of tunnel face stability generally assumes a single homogeneous rock mass. However, most rock tunnel projects are excavated in stratified rock masses. This paper presents a two-dimensional (2D) analytical model for estimating the face stability of a rock tunnel in the presence of rock mass stratification. The model uses the kinematical limit analysis approach combined with the block calculation technique. A virtual support force is applied to the tunnel face, and then solved using an optimization method based on the upper limit theorem of limit analysis and the nonlinear Hoek–Brown yield criterion. Several design charts are provided to analyze the effects of rock layer thickness on tunnel face stability, tunnel diameter, the arrangement sequence of weak and strong rock layers, and the variation in rock layer parameters at different positions. The results indicate that the thickness of the rock layer, tunnel diameter, and arrangement sequence of weak and strong rock layers significantly affect the tunnel face stability. Variations in the parameters of the lower layer of the tunnel face have a greater effect on tunnel stability than those of the upper layer.

Joint Route Optimization and Multidimensional Resource Management Scheme for Airborne Radar Network in Target Tracking Application

In this article, we investigate the problem of joint route optimization and multidimensional resource management (JRO-MDRM) for an airborne radar network in target tracking application. The mechanism of the proposed JRO-MDRM scheme is to adopt the optimization technique to collaboratively design the flight route, transmit power, dwell time, waveform bandwidth, and pulselength of each airborne radar node subject to the system kinematic limitations and several resource budgets, with the aim of simultaneously enhancing the target tracking accuracy and low probability of intercept (LPI) performance of the overall system. The predicted Bayesian Cramér–Rao lower bound and the probability of intercept are calculated and employed as the metrics to gauge the target tracking performance and LPI performance, respectively. It is shown that the resulting optimization problem is nonlinear and nonconvex, and the corresponding working parameters are coupled in both objective functions, which is generally intractable. By incorporating the particle swarm optimization and cyclic minimization approaches, an efficient four-step solution algorithm is proposed to deal with the above problem. Extensive numerical results are provided to demonstrate the correctness and advantages of our developed scheme compared with other existing benchmarks.

Seismic vulnerability assessment of a masonry structure and an FRP-strengthening proposal

This paper reports an approach to seismic performance evaluation for masonry structures using linear, nonlinear, and kinematic limit analyses. Considering the analysis results, a retrofitting proposal using fiber-reinforced polymer composites was made. All examinations and strengthening interventions were carried out for a masonry restaurant building currently in use. First, a structural model of the building was prepared based on the current seismic codes. In the second stage, the seismic performance of the building was determined using global and local analysis approaches. The shear force and relative story drift ratios were compared using the limit values given in the seismic code. In addition, local failure mechanisms were determined. Accordingly, the structural strength of the building was found to be insufficient. Therefore, a fiber-reinforced polymer -strengthened design proposal was presented. In order to determine the effectiveness of the proposed strengthening, linear and nonlinear analyses were made based on the strengthened state. In this study, the analysis methods used to assess the seismic performance of a masonry building and strengthening proposal can make significant contributions to construction engineers and architects for the rehabilitation of masonry structures.

Stability Analysis of Inhomogeneous Slopes in Unsaturated Soils Optimized by a Genetic Algorithm

Most theoretical analysis for the assessment of the stability of soil slopes is commonly performed under completely dry or saturated and homogeneous conditions, the effect of suction and soil inhomogeneity are generally ignored in stability assessments. This paper presents an analytical framework to investigate the stability of three-dimensional (3D) inhomogeneous slopes in unsaturated soils under one-dimensional steady flow. Based on the kinematic limit analysis method, a 3D rotational failure mechanism is adopted, and three possible failure mechanisms of soil slopes (e.g., toe, face, and base failure) are considered. A closed-form solution for the factor of safety is derived by the energy balance equation, which takes the effects of the suction stress, effective unit weight, and inhomogeneity of soil simultaneously into account. To improve optimize efficiency, a genetic algorithm (GA), which has the advantages of high efficiency and good accuracy, is applied to search for the minimum of the factor of safety of the slope. This methodology is well validated through comparison with existing solutions and numerical simulation. Parameter analyses are performed to investigate the effects of different parameters on slope stability. The results of the present study indicate that the stability of the slope will be underestimated if the suction stress and the change in effective unit soil weight are not considered. The inhomogeneity of soil can reduce the stability of slopes.

One-loop central-emission vertex for two gluons in mathcal{N} = 4 super Yang-Mills theory

A necessary ingredient for extending the BFKL equation to next-to-next-to-leading logarithmic (NNLL) accuracy is the one-loop central emission vertex (CEV) for two gluons which are not strongly ordered in rapidity. Here we consider the one-loop six-gluon amplitude in mathcal{N} = 4 super Yang-Mills (SYM) theory in a central next-to-multi-Regge kinematic (NMRK) limit, we show that its dispersive part factorises in terms of the two-gluon CEV, and we use it to extract the one-loop two-gluon CEV for any helicity configuration within this theory. This is a component of the two-gluon CEV in QCD. Although computed in the NMRK limit, both the colour structure and the kinematic dependence of the two-gluon CEV capture much of the complexity of the six-gluon amplitudes in general kinematics. In fact, the transcendental functions of the latter can be conveniently written in terms of impact factors, trajectories, single-emission CEVs and a remainder, which is a function of the conformally invariant cross ratios which characterise the six-gluon amplitudes in planar mathcal{N} = 4 SYM. Finally, as expected, in the MRK limit the two-gluon CEV neatly factorises in terms of two single-emission CEVs.

Emission of high-energy alpha particles in nuclear reactions of 48Ca and 56Fe ions on 181Ta and 238U targets

The results of experiments on measuring the energy spectra of alpha particles in reactions with heavy ions are presented. The measurements were performed using the high-resolution magnetic analyzer MAVR with beams of 48Ca (280 MeV) and 56Fe (320 and 400 MeV) on 181Ta and 238U targets at an angle of 0°. A strong dependence of the double differential cross sections for production of alpha particles on the atomic number of the target nucleus was observed, which indicates that fast alpha particles are mainly emitted from the target nucleus; this conclusion was also confirmed by calculations within the time-dependent Schrödinger equation approach. An analysis of the obtained experimental data was carried out within the model of moving sources modified to consider the kinematic limits for two-body and three-body exit channels.