Redundant Constraints Research Articles

Projection continuation for minimal coordinate set formulation and singularity detection of redundantly constrained system dynamics

The formulation of (possibly redundantly) constrained system dynamics using coordinate projection onto a subspace locally tangent to the constraint manifold is revisited using the QR factorization of the constraint Jacobian matrix, using column pivoting to identify a suitable subspace, possibly detect any singular configurations that may arise, and extract it. The evolution of the QR factorization is integrated along with that of the constraint Jacobian matrix as the solution evolves, generalizing to redundant constraints a recently proposed true continuation algorithm that tracks the evolution of the subspace of independent coordinates. The resulting subspace does not visibly affect the quality of the solution, as it is merely a recombination of that resulting from the blind application of the QR factorization but avoids the artificial algorithmic irregularities or discontinuities in the generalized velocities that could otherwise result from arbitrary reparameterizations of the coordinate set, and identifies and discriminates any further possible motions that arise at singular configurations. The characteristics of the proposed subspace evolution approach are exemplified by solving simple problems with incremental levels of redundancy and singularity orders.

Introspective perception for mobile robots

Perception algorithms that provide estimates of their uncertainty are crucial to the development of autonomous robots that can operate in challenging and uncontrolled environments. Such perception algorithms provide the means for having risk-aware robots that reason about the probability of successfully completing a task when planning. There exist perception algorithms that come with models of their uncertainty; however, these models are often developed with assumptions, such as perfect data associations, that do not hold in the real world. Hence the resultant estimated uncertainty is a weak lower bound. To tackle this problem we present introspective perception — a novel approach for predicting accurate estimates of the uncertainty of perception algorithms deployed on mobile robots. By exploiting sensing redundancy and consistency constraints naturally present in the data collected by a mobile robot, introspective perception learns an empirical model of the error distribution of perception algorithms in the deployment environment and in an autonomously supervised manner. In this paper, we present the general theory of introspective perception and demonstrate successful implementations for two different perception tasks. We provide empirical results on challenging real-robot data for introspective stereo depth estimation and introspective visual simultaneous localization and mapping and show that they learn to predict their uncertainty with high accuracy and leverage this information to significantly reduce state estimation errors for an autonomous mobile robot.

Optimizing public transport transfers by integrating timetable coordination and vehicle scheduling

Transfer optimization in public transport (PT) networks can be achieved through coordinated timetabling and vehicle scheduling. Traditionally, the coordinated timetabling problem is solved first before proceeding to the vehicle scheduling problem. The integration of these two problems can help further reduce the total operation cost and improve the level of service, especially when timetables of different PT lines are well-coordinated at transfer stations. This work addresses the integrated PT timetable coordination and vehicle scheduling problem while ensuring that each PT line is dispatched with an even headway. We first separately formulate two integer linear programming models for the timetable coordination and vehicle scheduling problems. Next, the two models are integrated into a bi-objective integer linear programming model for the integrated timetable coordination and vehicle scheduling problem. For small size PT networks, the model can be solved by using an ɛ-constraint method, together with off-the-shelfoptimization solvers. For large-size problems, two constraint-reduction procedures are developed to reduce the number of redundant constraints so as to reduce the computation complexity and improve the solution process. Finally, the models and solution method are applied to a numerical example and a real-world bus rapid transit (BRT) network in Chengdu, China. Computation results show that the solution generated by the sequential optimization approach is usually dominated by the Pareto-optimal solutions generated by the integrated optimization approach. Our findings suggest that it is not a wise decision to use the solution generated by the sequential optimization approach or the solution with the minimum fleet size generated by the integrated optimization approach. For practical implementation, it is recommended to choose the solution that has a fleet size of one more vehicle than the minimum fleet size.

Predicting Online Item-Choice Behavior: A Shape-Restricted Regression Approach

This paper examines the relationship between user pageview (PV) histories and their itemchoice behavior on an e-commerce website. We focus on PV sequences, which represent time series of the number of PVs for each user–item pair. We propose a shape-restricted optimization model that accurately estimates item-choice probabilities for all possible PV sequences. This model imposes monotonicity constraints on item-choice probabilities by exploiting partial orders for PV sequences, according to the recency and frequency of a user’s previous PVs. To improve the computational efficiency of our optimization model, we devise efficient algorithms for eliminating all redundant constraints according to the transitivity of the partial orders. Experimental results using real-world clickstream data demonstrate that our method achieves higher prediction performance than that of a state-of-the-art optimization model and common machine learning methods.

An algorithm of dynamic temporal constraints for the mission series in deep space detectors

Deep space exploration activities can effectively promote the development and application of space technology, which holds significant scientific and strategic value. The multi-mission and long-period detector is executed in deep space, and numerous temporal constraints are generated by mission planning. Moreover, scheduled missions may face external uncertainties, hindering their smooth execution. Therefore, temporal constraint processing strategies that possess dynamic adjustment capabilities play a crucial role in ensuring the successful execution of deep space detectors. Existing methods primarily concentrate on investigating fixed mission series, with limited efficiency in planning. Specifically, these methods do not rigorously enforce temporal constraints and lack the capability to handle the disruptions caused by emergencies, which hinder the smooth execution of planned missions. In this paper, we propose a dynamic temporal constraints algorithm, aiming to efficiently plan missions subject to temporal constraints and let it possess a certain degree of dynamic adjust capability. The simulation results demonstrate the effective simplification of redundant temporal constraints in mission networks by the proposed algorithm. In comparison to the classical algorithm, the computation time exhibits a clear advantage. Furthermore, the proposed algorithm possesses the capability to perform local, small-scale dynamic adjustments in response to emergencies that may disrupt the normal execution of missions. Consequently, this research establishes a robust basis for addressing temporal constraints in deep space detectors.

A fast linearized AC power flow-constrained robust unit commitment approach with customized redundant constraint identification method

The large-scale integration of renewable energy resources in the power system challenges its economic and secure operation. Particularly, the increasing penetration of renewable energy will result in insufficient system voltage regulation and reactive power support capabilities, and may cause high risks of nodal voltage and branch flow violations. Therefore, to hedge the operational risks under the worst realization of uncertainties of renewable energy sources, a two-stage robust unit commitment (UC) model is developed. Meanwhile, the convexified AC power flow model is incorporated in the robust UC model to more accurately characterize the real-time operating status of power systems. On this basis, an AC power flow-constrained robust unit commitment (ACRUC) model is formulated. A circular linearization method is then adopted to handle the quadratic constraints in the original AC power flow model, transforming them into tractable linear constraints. Furthermore, to reduce the computational complexity caused by the large-scale newly-added constraints after the linearization process, a customized redundant constraint identification (RCI) method is developed, in which two different modes (i.e., cold and warm start modes) are designed considering the difference in base case system operating condition for linearizing branch losses. Then, the redundant network security constraints could be identified by solving a series of relatively simple optimization subproblems. Numerical results on the modified NERL-118 test system indicate that the proposed model could accurately depict actual operation and scheduling conditions, and also verify that the proposed customized RCI method could effectively reduce the problem scale and improve the solution efficiency.

Numerical study on the structural performance of the continuous concrete slabs reinforced with hybrid BFRP/steel bars

AbstractThis study is mainly focused on the behavior of continuous concrete slabs reinforced with hybrid bars. Moment redistribution is a specific phenomenon in statically indeterminate structures due to the existence of redundant constraints and non‐uniform flexural stiffness of the reinforced concrete (RC) members. In this paper, a numerical one‐factor‐at‐a‐time parametric study was conducted using ABAQUS software to intensely understand the impact of several parameters on the performance of the hybrid RC continuous slabs. The investigated parameters were reinforcement type and ratio, FRP‐to‐steel ratio, and arrangement of reinforcement. The analysis results showed that the difference between sagging and hogging axial stiffness is the most influential parameter on the moment redistribution of hybrid‐RC continuous slabs. In addition, increasing the amount of reinforcement ratio at the mid‐span section is more effective in enhancing the load capacity of the slabs than over middle support section. Based on the obtained numerical results, some modifications to the Tarek et al. equations were proposed to be valid for hybrid‐RC continuous slabs. The presented modifications yielded good agreement with the numerical results predicting the moment redistribution of continuous concrete slabs with hybrid reinforcement.

RAFA: Redundancies-assisted Algebraic Fault Analysis and its implementation on SPN block ciphers

Algebraic Fault Analysis (AFA) is a cryptanalysis for block ciphers proposed by Courtois et al., which incorporates algebraic cryptanalysis to overcome the complexity of manual analysis within the context of Differential Fault Analysis (DFA). The effectiveness of AFA on lightweight block ciphers has been demonstrated. However, the complexity of the algebraic systems prevents it from attacking heavyweight block ciphers efficiently. In this paper, we propose a novel cryptanalysis called Redundancies-assisted Algebraic Fault Analysis (RAFA) to facilitate the solution of algebraic systems in the setting of heavyweight block ciphers. The core idea of RAFA is to expedite SAT solvers by modifying the algebraic systems, which is accomplished via two methods. The first method introduces redundant constraints, which is proposed for the first time in the context of algebraic cryptanalysis. The second one is a sophisticated linearization of the nonlinear Algebraic Normal Form (ANF). It takes RAFA for about 9.68 hours to attack AES-128. To the best of our knowledge, this is the first work that uses a general SAT solver to attack AES with only a single injection of byte-fault. Moreover, RAFA can attack AES-128 in 50.92 and 27.54 minutes for nibble- and bit-based fault model, respectively. In comparison, the traditional DFA algorithm implemented by pure C takes 4 ~ 5 hours under all three fault models investigated in this work. Moreover, in order to show the generality of RAFA, we also apply it to other heavyweight block ciphers. The best results show that RAFA could recover the key of Serpent-256 and SPEEDY-r-192 in 20.7 and 1.5 hours using only three faults, respectively. In comparison, AFA could not break these two ciphers even when 30 bits and 50 bits of their keys are known, respectively. Furthermore, no DFA work on Serpent or SPEEDY is known using comparable fault models.

The Chebyshev center as an alternative to the analytic center in the feasibility pump

As a heuristic for obtaining feasible points of mixed integer linear problems, the feasibility pump (FP) generates two sequences of points: one of feasible solutions for the relaxed linear problem; and another of integer points obtained by rounding the linear solutions. In a previous work, the present authors proposed a variant of FP, named analytic center FP, which obtains integer solutions by rounding points in the segment between the linear solution and the analytic center of the polyhedron of the relaxed problem. This work introduces a new FP variant that replaces the analytic center with the Chebyshev center. Two of the benefits of using the Chebyshev center are: (i) it requires the solution of a linear optimization problem (unlike the analytic center, which involves a convex nonlinear optimization problem for its exact solution); and (ii) it is invariant to redundant constraints (unlike the analytic center, which may not be well centered within the polyhedron for problems with highly rank-deficient matrices). The computational results obtained with a set of more than 200 MIPLIB2003 and MIPLIB2010 instances show that the Chebyshev center FP is competitive and can serve as an alternative to other FP variants.

A low‐drift and real‐time localisation and mapping method for handheld hemispherical view LiDAR‐IMU integration system

AbstractThis paper proposes a simultaneous localisation and mapping (SLAM) framework that uses a handheld hemispherical view LiDAR‐IMU integration system. Inspired by the specific characteristic of the hemispherical view LiDAR, a ground segmentation module based on seed points is designed. The ground points are then downsampled to eliminate redundant vertical constraints. The IMU data and the pre‐processed point cloud are used to perform state estimation via a tightly coupled iterative extended Kalman filter (iEKF) to obtain the pose estimation. The automatically detected loop closures provide closed‐loop constraints for the odometry, and a factor graph ensures the global consistency of the map. Data from diverse scenes are collected via a prototype system. Both qualitative and quantitative experiments are carried out to verify the framework's performance. According to the experimental results, our framework achieves low‐drift, high‐coverage and real‐time performance, outperforming the state‐of‐the‐art LiDAR SLAM methods in our handheld hemispherical view LiDAR‐IMU test sites. For the research community's benefit, the dataset is publicly provided for other researchers to compare against.

A constraint programming model for the scheduling and workspace layout design of a dual-arm multi-tool assembly robot

The generation of a robot program can be seen as a collection of sub-problems, where many combinations of some of these sub-problems are well studied. The performance of a robot program is strongly conditioned by the location of the tasks. However, the scope of previous methods does not include workspace layout design, likely missing high-quality solutions. In industrial applications, designing robot workspace layout is part of the commissioning. We broaden the scope and show how to model a dual-arm multi-tool robot assembly problem. Our model includes more robot programming sub-problems than previous methods, as well as workspace layout design. We propose a constraint programming formulation in MiniZinc that includes elements from scheduling and routing, extended with variable task locations. We evaluate the model on realistic assembly problems and workspaces, utilizing the dual-arm YuMi robot from ABB Ltd. We also evaluate redundant constraints and various formulations for avoiding arm-to-arm collisions. The best model variant quickly finds high-quality solutions for all problem instances. This demonstrates the potential of our approach as a valuable tool for a robot programmer.

A general formulation for simulating the dynamic deployment of thick origami

The deployment of origami is usually a rapid and complicated dynamic process. However, little has been done to simulate the entire deployment process of thick origami which is a typical over-constrained mechanical system. Based on the constrained Hamilton’s equations in conjunction with the natural coordinate formulation, a general formulation capable of tracing the dynamic deployment of thick origami is established. Particular efforts are paid to dealing with the problems including geometric description, redundant constraint, large rotational angle, and possible bifurcation paths. The proposed formulation is applied to three thick origami structures: thick Miura-ori, thick diamond origami, and thick waterbomb origami. The results show that the dynamic characteristics during the deployment can be successfully obtained, and the numerical accuracy is also validated by the ADAMS simulation and prototype experiments. Furthermore, parametric analyses are performed to investigate the effects of actuating positions and geometric parameters on deployment behaviors. The proposed formulation provides a clear view of the deployment process for thick origami structures, which will benefit the optimal design in practical applications.

Kinematic calibration of over-constrained robot with geometric error and internal deformation

In the over-constrained robot with geometric errors, internal forces would occur and lead to deformation due to redundant constraints and common constraints. In current kinematic calibration approaches, since the deformation, geometric errors and pose errors cannot be described in a unified framework, the error propagation fails to be solved intuitively and generically. In this article, a general calibration framework of over-constrained robots is proposed to unify geometric errors and internal deformation through the least action principle. In the framework, considering the interaction between errors and deformation, the difference map between geometric errors and pose errors is explicitly and analytically revealed. The mapping matrix can degenerate to be consistent with the previous research under non-over-constrained robots. In addition, the error forward propagation method and the error identification algorithm are proposed to solve the error nonlinear propagation and the ill-posed identification equations, respectively. Finally, the calibration simulation and experiment results of a 5-DOF over-constrained hybrid robot show that the proposed method can accurately predict the pose of the end-effector under geometric errors robustly and effectively.

Experimental investigations on structural improvement of morphing mechanism for nose cone of aerospace vehicle adopting a bionic redundant constraint strategy

Experimental investigations on structural improvement of morphing mechanism for nose cone of aerospace vehicle adopting a bionic redundant constraint strategy

On the Coordination of Transmission-Distribution Grids: A Dynamic Feasible Region Method

Recently, the turnover of energy services between transmission-distribution grids has continued to increase, arousing widespread attention to the efficient coordination between transmission system operator (TSO) and distribution system operator (DSO). The existing literature has characterized the feasible region of distribution networks via equivalent projection methods, which is conducive to the participation of DSO in TSO scheduling. However, the redundant constraints of DSO and the processing of temporal-coupled constraints remain challenging in realistic cases. To achieve an effective interaction between TSO and DSO with least information, we develop a TSO-DSO coordination framework with temporal-coupled constraints embedded, i.e., the concept of dynamic feasible region (DFR). We theoretically derive the polyhedral form of a DFR, which can be characterized as a constraint set formed by the extreme points of the dual space of the DSO optimization program. A novel outer progressive approximation (OPA)-based algorithm is designed to effectively add feasibility cuts until convergence is achieved. To reduce the redundant constraints in the DSO operation model, the enhanced umbrella constraint identification (E-UCI) method is employed. Case studies based on i) a real-world distribution grid in China and IEEE 30-bus system, ii) a Caracas 141-bus distribution network and IEEE 118-bus transmission grid are adopted to validate the effectiveness and computational efficiency of our proposed method.

Extracting Umbrella Constraint-Based Representation of Local Electricity Markets

The coordination between local and wholesale markets has been widely regarded as an effective means to improve the utilization of demand side resources. Existing literature has begun to explore the feasible region for incorporating local electricity markets into the wholesale level via projection algorithms. However, it remains challenging to deal with the complex constraints of inner spatiotemporal coupling. To achieve efficient interaction between local and wholesale markets, this paper proposes a local electricity market representation method based on umbrella constraints extraction. In contrast to the existing projection methods, we theoretically derive the closed form of a projection-based feasible region, which can be characterized as a constraint set formed by the extreme points of the dual space of the proposed diagnostic methods. A local market is equivalently formulated as a condensed model represented by its temporal-coupled feasible region (TCFR). To reduce the redundant constraints of TCFR, an umbrella constraint identification method is developed for the minimal representation of the problem. Case studies based on a modified IEEE 33-bus feeder and a realistic distribution grid in Venezuela demonstrate the effectiveness and computational efficiency of our proposed method.

Encoding words into interval type-2 fuzzy sets: The retained region approach

The first step of implementing computing with words using a perceptual computer is to establish an encoder to transform words into interval type-2 fuzzy sets. In this paper, a novel approach named the retained region approach is introduced for encoding words into interval type-2 fuzzy sets. In the retained region approach, the data part is redesigned relative to the existing approaches, and a new fuzzy set part is established in accordance with the principle of justifiable granularity. The different means and standard deviations of the embedded type-1 fuzzy sets associated with a word are recognized as the origins of its inter-uncertainty, and the relations between them are taken into account in the construction of interval type-2 fuzzy sets. Importantly, the retained region approach is a versatile approach that does not impose redundant constraints on the selection of embedded type-1 fuzzy sets, and the capacity of the retained region can be flexibly adjusted along the two dimensions of the mean and the standard deviation. Finally, the performance of the retained region approach is illustrated by several simulations and comparisons with existing approaches.

Cost-Driven Screening of Network Constraints for the Unit Commitment Problem

In an attempt to speed up the solution of the unit commitment (UC) problem, both machine-learning and optimization-based methods have been proposed to lighten the full UC formulation by removing as many superfluous line-flow constraints as possible. While the elimination strategies based on machine learning are fast and typically delete more constraints, they may be over-optimistic and result in infeasible UC solutions. For their part, optimization-based methods seek to identify redundant constraints in the full UC formulation by exploring the feasibility region of an LP-relaxation. In doing so, these methods only get rid of line-flow constraints whose removal leaves the feasibility region of the original UC problem unchanged. In this paper, we propose a procedure to substantially increase the line-flow constraints that are filtered out by optimization-based methods without jeopardizing their appealing ability of preserving feasibility. Our approach is based on tightening the LP-relaxation that the optimization-based method uses with a valid inequality related to the objective function of the UC problem and hence, of an economic nature. The result is that the so strengthened optimization-based method identifies not only redundant line-flow constraints but also inactive ones, thus leading to more reduced UC formulations.

A DX-Like Ternary/Pair-Map, Its Eco-Entropy Scheme, and Managerial Diversity of Nature versus Artifacts Type on Sandwich Theory

The problem means to pursue sustainable eco-entropy as redundancy (constraints) or marginal profit, value, and diversity. Therefore, this paper will discuss the following problem of realizing the DX-like microcosm of the ternary/pair-map with allowance (buffer), its eco-entropy scheme, and managerial diversity of nature versus artifacts’ body, on the sandwich theory. First, an outline of ternary sandwich (SW)/pair-map is geometrically prepared, along with the introduction and discussion of the eco-entropy concept, based on three types of energy, economy, and information structure without buffer. Subsequently, a managerial problem of body’s diversity is proposed and formulated, based on topics within the spectrum of the 3M & I world. Next, the relaxation problem of ternary SW/pair-map with allowance (buffer/delay), will be remarked as the case of demand-equals-supply (without buffer), and re-named as an allowed buffer type of ternary SW, or a 2-center case of demand versus supply (with buffer). Finally, the better realization problem will be formulated by the class of eigenvalue or progressive type, under certain indications of the eco-entropy class concept, and also, a systematic unification of ternary SW/pair-map is geometrically realized at 3D type. This approach towards human-friendly and sustainable nature versus artifacts’ body, may be incorporated into such the practical object of bodies (on vector space) as enterprise, economic structures, and Sustainable Development Goals (SDGs), in the near future.

Transitive Reduction Approach to Large-Scale Parallel Machine Rescheduling Problem With Controllable Processing Times, Precedence Constraints and Random Machine Breakdown

This paper studied a novel parallel machine rescheduling problem with controllable processing times under machine breakdown and precedence constraints. This problem is strongly <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {NP}$ </tex-math></inline-formula> -hard, and we modeled it as a mixed-integer problem (MIP). The primal problem is decomposed into the discrete subproblem and the continuous one. We treat the discrete with the dispatching rule and analyze the continuous in the terms of mathematical programming. Pros and cons from the analysis lead us to implement the commercial solver. The proposed method is capable of efficiency and nonzero initial state. We introduce transitive reduction to cull the redundant constraints out of its directed acyclic graph (DAG) representation. Transitive reduction extends the efficiency from the dispatching rule to the solver. The proposed method can do the predictive scheduling and pick up the partial solution left by the machine breakdown in the reactive session. As a result, the complete method solves the rescheduling problem with efficiency, and allows for large cases. At last, the computational results showed that this technique significantly brought down the time and RAM consumption in using the solver. This technique allows the scheduler to solve big instances with computational economy and efficiency.