Redundant Constraints Research Articles

Physics-informed neural networks for inversion of river flow and geometry with shallow water model

The river flow transports sediment, resulting in the formation of alternating sandbars in the riverbed. The underlying physics is characterized by the interaction between flow and river geometry, necessitating an understanding of their inseparable relationship. However, the dynamics of river flow with alternating sandbars are hard to understand due to the difficulty of measuring flow depth and riverbed geometry during floods with current technology. This study implements an innovative approach utilizing physics-informed neural networks (PINNs) to estimate important hydraulic variables in rivers that are difficult to measure directly. The method uses sparse yet obtainable flow velocity and water level data. The governing equations of motion, continuity, and the constant discharge condition based on the mass conservation principle are integrated into the neural network as physical constraints. This approach enables the completion of sparse velocity fields and the inversion of flow depth, riverbed elevation, and roughness coefficients without requiring direct training data for these variables. Validation was performed using model experiment data and numerical simulations derived from these experiments. Results indicate that the accuracy of the estimations is relatively robust to the number of training data points, provided their spatial resolution is finer than the wavelength of the sandbars. The inclusion of mass conservation as a redundant constraint significantly improved the convergence and accuracy of the model. This PINNs-based approach, using measurable data, offers a new way to quantify complex river flows on alternating sandbars without significant updates to conventional methods, providing new insights into river physics.

Certifiably optimal rotation and pose estimation based on the Cayley map

We present novel, convex relaxations for rotation and pose estimation problems that can a posteriori guarantee global optimality for practical measurement noise levels. Some such relaxations exist in the literature for specific problem setups that assume the matrix von Mises-Fisher distribution (a.k.a., matrix Langevin distribution or chordal distance) for isotropic rotational uncertainty. However, another common way to represent uncertainty for rotations and poses is to define anisotropic noise in the associated Lie algebra. Starting from a noise model based on the Cayley map, we define our estimation problems, convert them to Quadratically Constrained Quadratic Programs (QCQPs), then relax them to Semidefinite Programs (SDPs), which can be solved using standard interior-point optimization methods; global optimality follows from Lagrangian strong duality. We first show how to carry out basic rotation and pose averaging. We then turn to the more complex problem of trajectory estimation, which involves many pose variables with both individual and inter-pose measurements (or motion priors). Our contribution is to formulate SDP relaxations for all these problems based on the Cayley map (including the identification of redundant constraints) and to show them working in practical settings. We hope our results can add to the catalogue of useful estimation problems whose solutions can be a posteriori guaranteed to be globally optimal.

A constraint programming approach for resource-constrained flexible assembly flow shop scheduling problem with batch direct delivery

Production and distribution are both crucial components of supply chains. Integrated production and distribution scheduling (IPDS) in the context of flexible assembly flow shop scheduling and batch delivery problems is often overlooked. A realistic problem inspired by the production and distribution processes of a dishwasher factory can be modeled as a resource-constrained flexible assembly flow shop scheduling problem with batch direct delivery (RCFAFSP-BDD). In this problem, order requirements are decomposed into several production tasks processed at different stages of the workshop, and are then delivered in batches via a third-party logistics provider to regional distributors at various locations. Auxiliary resource restrictions, hierarchical coupling constraints, machine eligibility restrictions and sequence-dependent setup times, are incorporated into the problem as operational constraints. To the best of our knowledge, this is the first attempt to solve this problem. This work formulates a mixed-integer linear programming (MIP) model to minimize total costs, including tardiness, inventory, and delivery costs. Given the problem’s strong NP-hard nature, the focus is on developing an efficient solution approach using constraint programming (CP). A CP model is proposed and enhanced with multiple redundant constraints. To reduce runtime, two branching strategies are designed for the CP model. Numerical experiments with varying instance scales reveal that the proposed CP model outperforms the MIP model in accuracy and efficiency within the given time limit. The redundant constraints and search strategy can reduce CP model runtime by up to 263.83%. Compared to manual scheduling at the studied factory, the CP model can cut costs by up to 26.59% for real data, offering viable alternatives for factory planners.

Vibration damping method of cantilever structure considering redundant constraint of monocrystalline blade casting mold shell

Excessive vibrations of the mold shell during the manufacturing process of monocrystalline blades lead to dendirite and frekle defects in directional solidification. The dynamics of the casting lifting device-mold shell system is analysed theoretically to reveal the influence of key parameters such as excitation force, damping and stiffness on the monocrystalline blade casting. The effect of redundant constraint onto the system is analysed via the developed vibration model. A lifting device-mold shell system test bench is developed, a slide-support arm device is designed to provide redundant constraint. A self-developed high-precision sensor is used to test the vibration signals, and the effectiveness of the damping method is verified. The experimental results show that the redundant constraint can reduce the undesired vibration of mold shell by more than 77 %, which ensures the casting quality of monocrystalline blades. The proposed vibration damping method can provide a reference for the vibration damping of the cantilever machine.

Adaptive backstepping controller based on a novel framework for dynamic solution of an ankle rehabilitation spherical parallel robot

AbstractThis research offers an adaptive model-based methodology for autonomous control of 3-RRR spherical parallel manipulator (RSPM) based on a novel modeling framework. RSPM is an overconstrained parallel mechanism that has a variety of applications in medical procedures such as ankle rehabilitation because of its precision and accuracy. However, obtaining a complete explicit dynamic model of these mechanisms for tracking purposes has been a problematic challenge due to their inherent singularities, coupling effects of the limbs, and redundant constraints imposed by the intermediate joints. This paper presents a novel algorithm to obtain the analytical kinematic solutions of RSPMs based on the closed-loop vector method, which includes constraint analysis. By incorporating constrained kinematics into the dynamic model, a comprehensive explicit dynamic solution of the non-overconstrained version 3-RCC of RSPM is developed in task space, based on screw theory and the linear homogeneous property of algebraic equations on the manipulator twist. Based on the proposed computational framework, a robust self-tuning backstepping control (STBC) strategy is applied to the robot to overcome the effect of external disturbances and time-varying uncertainties. Furthermore, an observer-based compensation (OBC) method is presented for dealing with the nonlinear hysteresis loops of the ankle during trajectory tracking purposes. The closed-loop stability of the whole system including STBC and OBC is theoretically performed by Lyapunov methods. The proposed methodologies are validated by realistic co-simulations in different scenarios. For instant, in the presence of external disturbances, the maximum tracking error norm of STBC is 37.5% less than the sliding mode approach.

A network search space reduction method for robust coordinated energy storage and transmission expansion planning

AbstractThe development of renewable energy will increase the demand for flexible resources in power systems due to the strong uncertainties. To allocate resources and cope with these uncertainties, it is beneficial to apply robust coordinated energy storage and transmission expansion planning (ES&TEP). The large candidate line set can significantly increase the computational complexity of robust optimization models. However, there is currently no suitable network search space reduction (NSSR) method to address this problem. This paper designs a NSSR method based on redundancy constraint identification that only requires information on component power ranges rather than fixed power curves, which can be well adapted to robust optimization. Additionally, this method requires only basic numerical calculations and ensures convergence within a finite number of iterations. The classical stochastic robust ES&TEP model and the column and constraint generation (C&CG) algorithm are used to validate the effectiveness of the NSSR method. In the case studies, the numerical results confirm the rationality and effectiveness of the approach proposed in this paper. By selecting appropriate parameters, the candidate line set can be reduced by over 70% and the computational efficiency can be improved by an order of magnitude.

WaveNets: physics-informed neural networks for full-field recovery of rotational flow beneath large-amplitude periodic water waves

AbstractWe formulate physics-informed neural networks (PINNs) for full-field reconstruction of rotational flow beneath nonlinear periodic water waves using a small amount of measurement data, coined WaveNets. The WaveNets have two NNs to, respectively, predict the water surface, and velocity/pressure fields. The Euler equation and other prior knowledge of the wave problem are included in WaveNets loss function. We also propose a novel method to dynamically update the sampling points in residual evaluation as the free surface is gradually formed during model training. High-fidelity data sets are obtained using the numerical continuation method which is able to solve nonlinear waves close to the largest height. Model training and validation results in cases of both one-layer and two-layer rotational flows show that WaveNets can reconstruct wave surface and flow field with few data either on the surface or in the flow. Accuracy in vorticity estimate can be improved by adding a redundant physical constraint according to the prior information on the vorticity distribution.

Non-probability sampling network based on anomaly pedestrian trajectory discrimination for pedestrian trajectory prediction

Pedestrian trajectory prediction in first-person view is an important support for achieving fully automated driving in cities. However, existing pedestrian trajectory prediction methods still have significant shortcomings in terms of pedestrian trajectory diversity, dynamic scene constraints, and dependence on long-term trajectory prediction. We proposes a non-probability sampling network based on pedestrian trajectory anomaly recognition (ADsampler) to predict multiple possible future pedestrian trajectories. First, by incorporating pose and optical flow information, ADsampler models the multi-dimensional motion characteristics of pedestrians based on observed trajectory information and discriminates trajectory states. The sampling range in the Gaussian latent space is determined based on the recognition results. Next, velocity and yaw information of the car are introduced to model the car's motion state. A subtraction fusion network is employed to remove redundant image feature constraints in highly dynamic scenes. Finally, ADsampler utilizes a novel trajectory decoding network that combines the position encoding capability of GRU with the long-term dependency capturing ability of Transformer to decode and predict the fused features. we evaluate our model on crowded videos in the public datasets JAAD, PIE, ETH and UCY. Experiments demonstrate that the proposed method outperforms state-of-the-art approaches in prediction accuracy.

Energy-efficient scheduling model and method for assembly blocking permutation flow-shop in industrial robotics field

Implementing green and sustainable development strategies has become essential for industrial robot manufacturing companies to fulfill their societal obligations. By enhancing assembly efficiency and minimizing energy consumption in workshops, these enterprises can differentiate themselves in the fiercely competitive market landscape and ultimately bolster their financial gains. Consequently, this study focuses on examining the collaborative assembly challenges associated with three crucial parts: the body, electrical cabinet, and pipeline pack, within the industrial robot manufacturing process. Considering the energy consumption during both active and idle periods of the industrial robot workshop assembly system, this paper presents a multi-stage energy-efficient scheduling model to minimize the total energy consumption. Two classes of heuristic algorithms are proposed to address this model. Our contribution is the restructuring of the existing complex mathematical programming model, based on the structural properties of scheduling sub-problems across multiple stages. This reformation not only effectively reduces the variable scale and eliminates redundant constraints, but also enables the Gurobi solver to tackle large-scale problems. Extensive experimental results indicate that compared to traditional workshop experience, the constructed green scheduling model and algorithm can provide more precise guidance for the assembly process in the workshop. Regarding total energy consumption, the assembly plans obtained through our designed model and algorithm exhibit approximately 3% lower energy consumption than conventional workshop experience-based approaches.

Assembly law of multi-ring hybrid origami mechanism and calculation method of the degree of freedom

This paper proposes a method for calculating the degrees of freedom of multi-loop hybrid folding mechanisms, which is used to calculate the degrees of freedom of multi-loop hybrid folding mechanisms, redefines the problem of not being able to determine whether the folding units are in series and parallel during the assembly process, summaries the two cases of redundant constraints, gives the calculation principle of multi-loop hybrid folding mechanisms, calculates the degrees of freedom for The calculation of degrees of freedom for the assembly of a variety of different crease folding units is carried out to verify the accuracy and feasibility of the degree of freedom calculation rule proposed in this paper. The control of the hand claw is improved and the number of drives added to the envelope type paper folding hand claw to capture space debris is reduced, greatly improving the reliability and stability of the paper-folding hand claw in space capture work, which is of great significance to the problem of calculating degrees of freedom after the assembly of paper folding units and the analysis of degrees of freedom of complex paper folding mechanisms and their design.

A Problem based on Lagrange Relaxation Approach & Solving Optimization on Bi-level Model Programming Problem

Abstract: In this paper, a salutation method based on Lagrange relaxation for discrete-continuous bi-level problems, with binary variables in the leading problem, considering the optimistic approach in bi-level programming. Linearized taking advantage of the structure of the leading problem, an algorithm is solving two-dimensional bi-level linear programming problems, classification of constrains, algorithm removes all redundant constraints, cycling and solution of problem.

Ecological Approach and Departure‐Driving Strategy Optimized by Using Syncretic Learning with Trapezoidal Collocation Algorithm for the Plug‐In Hybrid Electric Vehicles

The eco‐driving strategy is of great significance in driving cost for plug‐in hybrid electric vehicles in driving trips, especially at signalized intersections. To address the issue of further energy saving, this study proposes an ecological approach and departure‐driving strategy by using syncretic learning with trapezoidal collocation algorithm. First, a syncretic learning‐based speed predictor is built by merging back propagation neural networks and radial basis function neural networks. Second, the syncretic learning‐based speed predictor and trapezoidal collocation algorithm are combined to optimize the speed trajectory. Third, the torque between the engine and the motor is distributed by the dynamic programming algorithm. Then, model predictive control optimizes torque output in the control time domain. Finally, the driving interval optimization method is designed to avoid mixed‐integer programming problems and redundant constraints, which make vehicles cross intersections without stopping. The numerical verification results show that the trapezoidal collocation algorithm with syncretic learning has more advantages than other methods in speed trajectory planning. Compared with the original trajectory, the driving time through the intersection is reduced and the total driving cost is lowered by 19.82%. Validation results confirm the effectiveness of the proposed strategy in energy consumption management at signalized intersections.

Overcoming Confounding Bias in Causal Discovery using Minimum Redundancy and Maximum Relevancy Constraint

Overcoming Confounding Bias in Causal Discovery using Minimum Redundancy and Maximum Relevancy Constraint

Grammar-aware test case trimming for efficient hybrid fuzzing

In recent years, hybrid fuzzing has garnered significant attention by combining the benefits of both fuzzing and concolic execution. However, existing hybrid fuzzing techniques face problems such as the performance overhead of concolic execution and low code coverage in real-world programs. In this study, we observed that concolic execution often falls into repetitive loop structures when analyzing inputs generated by fuzzing, leading to the construction of redundant constraint expressions, which severely impacts its efficiency. Based on this observation, we design a test case trimming approach to remove input fields related to repetitive loop structures. We propose a lightweight taint analysis technique to infer input’s grammatical structure and construct a hierarchical grammar tree. Then, through delta debugging, we identify nodes that do not affect the code coverage and remove the corresponding input fields. We implement a prototype ScissorFuzz. Experimental results show that our approach brings an average of 8.2% improvement in code coverage and triggers 115 more crashes compared to the state-of-the-art hybrid fuzzing technique QSYM. By eliminating redundant fields, our approach reduces the resource and time overhead associated with concolic execution during input processing, thereby enhancing the efficiency of hybrid fuzzing.

Optimal Design of Robotic Character Kinematics

The kinematic motion of a robotic character is defined by its mechanical joints and actuators that restrict the relative motion of its rigid components. Designing robots that perform a given target motion as closely as possible with a fixed number of actuated degrees of freedom is challenging, especially for robots that form kinematic loops. In this paper, we propose a technique that simultaneously solves for optimal design and control parameters for a robotic character whose design is parameterized with configurable joints. At the technical core of our technique is an efficient solution strategy that uses dynamic programming to solve for optimal state, control, and design parameters, together with a strategy to remove redundant constraints that commonly exist in general robot assemblies with kinematic loops. We demonstrate the efficacy of our approach by either editing the design of an existing robotic character, or by optimizing the design of a new character to perform a desired motion.

UAV-Assisted Wireless Charging Incentive Mechanism Design Based on Contract Theory

In wireless sensor networks, terminal devices with restricted cost and size have limited battery life. Meanwhile, these energy-constrained devices are not easy to access, especially when the terminal devices are located in severe environments. To recharge the energy-constrained devices and extend their network service time, unmanned aerial vehicles (UAVs) equipped with wireless power chargers are leased by the third-party control center. To incent the participation of UAVs with different charging capabilities and ensure the strategy-proofness of the incentive mechanism, a hidden information based contract theory model, specifically adverse selection, is introduced. By leveraging individual rationality and incentive compatibility, a contract theory based optimization problem is then formulated. After reducing redundant constraints, the optimal contract items are derived by Lagrangian multiplier. Finally, numerical simulation results are implemented to compare the prepared algorithm with three other baselines, which validates the effectiveness of our proposed incentive mechanism.

Tri-Space Operational Control of Redundant Multilink and Hybrid Cable-Driven Parallel Robots Using an Iterative-Learning-Based Reactive Approach

Cable-driven parallel robots (CDPRs) are a type of parallel mechanism in which cables are used as actuators. Due to the two levels of redundancy and numerous constraints within the CDPR actuation, joint and operational spaces (together known as the tri-space), tracking a given trajectory in the operational space while satisfying constraints in tri-space simultaneously is challenging. To the best of the authors’ knowledge, there does not exist any tri-space control framework, which is robust, effective, and directly applicable to several architectures of redundantly actuated CDPRs. This article proposes a tri-space control framework that combines reactive control (RC) and iterative-learning control (ILC) to perform repetitive tasks in the operational space. The framework allows the tracking of operational space trajectories online with feasible cable forces while avoiding undesirable situations such as cable-link interference, joint interference, and loss of manipulability. On the other hand, by finding an optimal parameter in the null space using a novel parameterization of a null-space vector, the performance can be improved through ILC when the task is repeatedly executed. Simulation and hardware results on various multilink cable-driven robots (MCDRs) and hybrid cable-driven robots (HCDRs) show that the proposed tri-space control framework can be conveniently and effectively applied to the real-time control of different CDPRs.

Resilient supply chain network design under uncertain environment

Modern supply chain operates in a highly uncertain environment caused by natural disasters and market changes. Such a fact has motivated academics and practitioners to pay more attention to the supply chain resilience. This paper reports on designing a resilient supply chain under uncertain environment by an uncertain programming method. The desired resilience level against disruption is achieved with less redundancy by controlling them in the presented models. And parameter uncertainty caused by the limited historical data is also addressed using uncertainty theory. To cope with the problem's complexity, we convert the proposed models into their deterministic formulations, which can easily be solved by cplex solver. The results from sensitivity analysis demonstrate the necessity of including uncertainty during the planning phase of supply chain network design. The performance of resilience constraint and the positive effect of sticker redundancy constraint in improving service level are also investigated fully.

Numerical and experimental investigation on the synthesis of extended Kalman filters for cable-driven parallel robots modeled through DAEs

Cable-driven parallel robots are parallel robots where light-weight cables replace rigid bodies to move an end-effector. Their peculiar design allows obtaining large workspaces, high-dynamic handlings, ease of reconfigurability and, in general, low-cost architecture. Knowing the full state variables of a cable robot may be essential to implement advanced control and monitoring strategies and imposes the development of state observers. In this work a general approach to develop nonlinear state observers based on an extended Kalman filter (EKF) is proposed and validated both numerically and experimentally by referring to a cable-suspended parallel robot. The state observer is based on a system model obtained by converting a set of differential algebraic equations into ordinary differential equations through different formulations: the penalty formulation, the Udwadia–Kalaba formulation, and the Udwadia–Kalaba–Phohomsiri formulation, which have been chosen since they can handle the presence of redundant constraints as often happens in cable-driven parallel robots. In the numerical investigation, the EKF is validated simulating encoders heavily affected by quantization errors to demonstrate the filtering capabilities of EKF. In the experimental investigation, a very challenging validation is proposed: only two sensors measuring the rotations of two motors are used to estimate the actual position and velocity of the end-effector. This result cannot be achieved by sole forward kinematics and clearly proves the effectiveness of the proposed observer.

Motion Performance Study of 2UPR-1RPS/2R Hybrid Robot Based on Kinematics, Dynamics, and Stiffness Modeling

Abstract The unique structural characteristics of hybrid robots, such as few degrees-of-freedom (DOF) and redundant constraints, lead to a series of challenges in the establishment of theoretical models. However, these theoretical models are indispensable parts of motion control. Therefore, this paper focuses on establishing the kinematics, dynamics, and stiffness models for an Exechon-like hybrid robot, which are then used for error compensation and velocity planning to improve the robot’s motion performance. First, the kinematic model is derived through intermediate parameters and the kinematics equivalent chains. By analyzing the parasitic motion due to few DOF, the redundant equations in the model are eliminated to obtain the solution of inverse kinematics. Second, based on the beam element, the optimal equivalent configuration of the moving platform which connects the parallel part and serial part is determined, and then an entire equivalent structure of the robot is formed. It helps establish the stiffness model by using the matrix structure analysis method. Next, the dynamic model is established by combining the Newton–Euler method with co-deformation theory to solve the underdetermined dynamic equations caused by redundant constraints. Finally, the compensation method is designed based on the stiffness model and kinematic model to improve the end positioning accuracy of the robot; the velocity planning algorithm is designed based on the dynamic model and kinematic model to enhance the smoothness of the robot motion. The methods proposed in this paper are also of referential significance to other Exechon-like hybrid robots.