Due to the complexity of urban and rural drainage systems, although many types of robots have been designed for this purpose, the mainstream pipeline inspection robots are currently dominated by four-wheeled designs. In this study, the shortcomings of four-wheeled pipeline robots were analyzed, including poor passability, difficulties in spatial positioning and orientation, and the limited effectiveness of conventional two-degree-of-freedom observation systems. Based on these issues, the spatial pose mathematical model of the four-wheeled robot inside the pipeline was investigated, along with the spatial geometric constraints and speed characteristics during cornering. This study was intended to reveal the spatial geometric parameter limitations and the kinematic characteristics of the four-wheeled pipeline robot under these constraints, providing corresponding recommendations. To address the issue of the outdated two-degree-of-freedom vision component, a three-degree-of-freedom visual component was designed, and forward kinematics analysis was conducted using Standard-Denavit-Hartenberg parametric modeling, revealing its motion speed and characteristics. Based on this visual component, a new concept of in-pipeline robot vision was proposed, providing new references for the design of four-wheeled pipeline robots.

This theoretical pearl shows how a graphical, relational, point-free, and calculational approach to linear algebra, known as graphical linear algebra, can be used to reason not only about matrices (and matrix algebra, as can be found in the literature) but also vector spaces and more generally linear relations. Linear algebra is usually seen as the study of vector spaces and linear transformations. However, to reason effectively with subspaces in a point-free and calculational manner, both can be generalized to an unifying concept: linear relations, much like relational algebra. While the semantics is relational, the syntax is graphical and uses string diagrams, 2-dimensional formal diagrams, which represent the linear relations. Most importantly, in a number of cases, the relational semantics allows algorithms and properties to be derived calculationally instead of just verified. Our approach is to proceed primarily by examples which involve finding inverses, switching from an implicit basis to an explicit basis (solving a homogeneous linear system), exploring both the exchange lemma and the Zassenhaus’ algorithm.

This paper presents a general approach to synthesizing closed-loop robots for machining and manufacturing of complex quadric surfaces, such as toruses, helicoids, and helical tubes. The proposed approach begins by employing finite screw theory to describe the motion sets generated by prismatic, rotational, and helical joints. Subsequently, generatrices and generating lines are put forward and combined for type synthesis of serial kinematic limbs capable of generating single-DoF translations along spatial curves and two-DoF translations on complex quadric surfaces. Following this manner, the two-DoF translational motion patterns on these complex quadric surfaces are algebraically defined and expressed as finite screw sets. Type synthesis of close-loop robots having the newly defined motion patterns can thus be carried out based upon analytical computations of finite screws. As application of the presented approach, closed-loop robots for machining toruses are synthesized, resulting in four-DoF and five-DoF standard and derived limbs together with their corresponding assembly conditions. Additionally, brief descriptions of robots for machining helicoids and helical tubes are provided, along with a comprehensive list of all the feasible limbs for these kinds of robots. The robots synthesized in this paper have promised applications in machining and manufacturing of spatial curves and surfaces, enabling precise control of machining trajectories ensured by mechanism structures and achieving high precision with low cost.

Simulations of critical phenomena, such as wildfires, epidemics, and ocean dynamics, are indispensable tools for decision-making. Many of these simulations are based on models expressed as Partial Differential Equations (PDEs). PDEs are invaluable inductive inference engines, as their solutions generalize beyond the particular problems they describe. Methods and insights acquired by solving the Navier–Stokes equations for turbulence can be very useful in tackling the Black-Scholes equations in finance. Advances in numerical methods, algorithms, software, and hardware over the last 60 years have enabled simulation frontiers that were unimaginable a couple of decades ago. However, there are increasing concerns that such advances are not sustainable. The energy demands of computers are soaring, while the availability of vast amounts of data and Machine Learning(ML) techniques are challenging classical methods of inference and even the need of PDE based forecasting of complex systems. I believe that the relationship between ML and PDEs needs to be reset. PDEs are not the only answer to modeling and ML is not necessarily a replacement, but a potent companion of human thinking. Algorithmic alloys of scientific computing and ML present a disruptive potential for the reliable and robust forecasting of complex systems. In order to achieve these advances, we argue for a rigorous assessment of their relative merits and drawbacks and the adoption of probabilistic thinking for developing complementary concepts between ML and scientific computing. The convergence of AI and scientific computing opens new horizons for scientific discovery and effective decision-making.

We introduce the framework FreeCHR which formalizes the embedding of Constraint Handling Rules (CHR) into a host language, using the concept of initial algebra semantics from category theory. We hereby establish a high-level implementation scheme for CHR as well as a common formalization for both theory and practice. We propose a lifting of the syntax of CHR via an endofunctor in the category Set and a lifting of the very abstract operational semantics of CHR into FreeCHR, using the free algebra, generated by the endofunctor. We give proofs for soundness and completeness with its original definition. We also propose a first abstract execution algorithm and prove correctness with the operational semantics. Finally, we show the practicability of our approach by giving two possible implementations of this algorithm in Haskell and Python. Under consideration in Theory and Practice of Logic Programming.

This article introduces a dome-type soft tactile sensor that can autonomously adjust its stiffness to evaluate surface contact characteristics, including the elastic modulus, contact force, and the presence of abnormal hardness within soft materials, using a strain gauge as a single sensing element. The strain sensor element is placed at the tip of the dome to measure the deformations during contact that reflect the properties of the contacted object. Using machine learning techniques, the sensor system can accurately predict these characteristics in various materials with an error rate of less than approximately 8%. A hybrid approach that combines experimental and simulation data enables the sensor to be trained effectively, generating sufficient data for accurate predictions without extensive experiments. The high accuracy results of the machine learning models demonstrate that the sensor system can precisely calculate the elastic modulus and depth of the defect. The adaptability and precision of the proposed sensor make it ideal for applications in medical diagnostics and other fields requiring careful interaction with soft materials. Furthermore, its innovative approach can be referenced for exploiting the properties of soft materials to achieve task-specific morphology without redesigning soft sensors or soft robots.

This paper presents a novel simplification calculus for propositional logic derived from Peirce’s existential graphs’ rules of inference and implication graphs. Our rules can be applied to propositional logic formulae in nested form, are equivalence-preserving, guarantee a monotonically decreasing number of variables, clauses and literals, and maximise the preservation of structural problem information. Our techniques can also be seen as higher-level SAT preprocessing, and we show how one of our rules (TWSR) generalises and streamlines most of the known equivalence-preserving SAT preprocessing methods. In addition, we propose a simplification procedure based on the systematic application of two of our rules (EPR and TWSR) which is solver-agnostic and can be used to simplify large Boolean satisfiability problems and propositional formulae in arbitrary form, and we provide a formal analysis of its algorithmic complexity in terms of space and time. Finally, we show how our rules can be further extended with a novel n-ary implication graph to capture all known equivalence-preserving preprocessing procedures.