Given partially ordered sets (posets) $(P, \leq _P\!)$ and $(P^{\prime}, \leq _{P^{\prime}}\!)$, we say that $P^{\prime}$ contains a copy of $P$ if for some injective function $f\,:\, P\rightarrow P^{\prime}$ and for any $X, Y\in P$, $X\leq _P Y$ if and only if $f(X)\leq _{P^{\prime}} f(Y)$. For any posets $P$ and $Q$, the poset Ramsey number $R(P,Q)$ is the least positive integer $N$ such that no matter how the elements of an $N$-dimensional Boolean lattice are coloured in blue and red, there is either a copy of $P$ with all blue elements or a copy of $Q$ with all red elements. We focus on a poset Ramsey number $R(P, Q_n)$ for a fixed poset $P$ and an $n$-dimensional Boolean lattice $Q_n$, as $n$ grows large. We show a sharp jump in behaviour of this number as a function of $n$ depending on whether or not $P$ contains a copy of either a poset $V$, that is a poset on elements $A, B, C$ such that $B\gt C$, $A\gt C$, and $A$ and $B$ incomparable, or a poset $\Lambda$, its symmetric counterpart. Specifically, we prove that if $P$ contains a copy of $V$ or $\Lambda$ then $R(P, Q_n) \geq n +\frac{1}{15} \frac{n}{\log n}$. Otherwise $R(P, Q_n) \leq n + c(P)$ for a constant $c(P)$. This gives the first non-marginal improvement of a lower bound on poset Ramsey numbers and as a consequence gives $R(Q_2, Q_n) = n + \Theta \left(\frac{n}{\log n}\right)$.

In this paper, we study the estimation of a scale parameter from a sample of lifetimes of coherent systems with a fixed structure. We assume that the components are independent and identically distributed having a common distribution which belongs to a scale parameter family. Some results are obtained as well for dependent (exchangeable) components. To this end, we will use the representations for the distribution function of a coherent system based on signatures. We prove that the efficiency of the estimators depends on the structure of the system and on the scale parameter family. In the dependence case, it also depends on the baseline copula function.

Robots and inertial measurement units (IMUs) are typically calibrated independently. IMUs are placed in purpose-built, expensive automated test rigs. Robot poses are typically measured using highly accurate (and thus expensive) tracking systems. In this paper, we present a quick, easy, and inexpensive new approach to calibrate both simultaneously, simply by attaching the IMU anywhere on the robot’s end-effector and moving the robot continuously through space. Our approach provides a fast and inexpensive alternative to both robot and IMU calibration, without any external measurement systems. We accomplish this using continuous-time batch estimation, providing statistically optimal solutions. Under Gaussian assumptions, we show that this becomes a nonlinear least-squares problem and analyze the structure of the associated Jacobian. Our methods are validated both numerically and experimentally and compared to standard individual robot and IMU calibration methods.

Fin Ray soft grippers, as a notable passive compliant structures, can be easily actuated by external devices to adapt their shape to conform to a grasped object. Their unique ability is aided by their V-shaped structure and morphable material utilized by the Fin Ray finger. Thus, when the internal structure changes, the adaptability and grasping abilities also change. However, related works focus on the effects of changing key parameters on the grasping performance based on the Festo structure, and few works have explored the effects of changing the internal structure. To close the research gap, four different Fin Ray structures are presented in this article, and a parameter determination process was carried out by maximizing their adaptability by investigating the key parameters of each structure through finite element analysis. Then, the force responses of four selected Fin Ray structures are analyzed and experimentally validated. The results show that the No Internal Filling structure obtained by omitting the crossbeams is ideal for grasping delicate targets with the best adaptability and the minimum resultant force. The cross structure attained by adding vertical beams connected to crossbeams decreases the adaptability of the Fin Ray finger but significantly increases the contact force. The unsymmetric design of the branched structure significantly enhances the final contact force while improving the passive adaptation to objects. Thus, the application of the Fin Ray finger ranges from adaptive delicate grasping tasks to high-force manipulation tasks.

Ocean wave climate has a significant impact on near-shore and off-shore human activities, and its characterization can help in the design of ocean structures such as wave energy converters and sea dikes. Therefore, engineers need long time series of ocean wave parameters. Numerical models are a valuable source of ocean wave data; however, they are computationally expensive. Consequently, statistical and data-driven approaches have gained increasing interest in recent decades. This work investigates the spatiotemporal relationship between North Atlantic wind and significant wave height ($ {H}_s $) at an off-shore location in the Bay of Biscay, using a two-stage deep learning model. The first step uses convolutional neural networks to extract the spatial features that contribute to $ {H}_s $. Then, long short-term memory is used to learn the long-term temporal dependencies between wind and waves.

Day by day, biped robots’ usage is increasing enormously in all industrial and non-industrial applications due to their ability to move in any unstructured environment compared to wheeled robots. Keeping this in mind, worldwide, many researchers are working on various aspects of biped robots, such as gait generation, dynamic balance margin, and the design of controllers. The main aim of this review article is to discuss the main challenges encountered in the biped gait generation and design of various controllers while moving on different terrain conditions such as flat, ascending and descending slopes or stairs, avoiding obstacles/ditches, uneven terrain, and an unknown environment. As per the authors’ knowledge, no single study has been carried out in one place related to the gait generation and design of controllers for each joint of the biped robot on various terrains. This review will help researchers working in this field better understand the concepts of gait generation, dynamic balance margin, and the design of controllers while moving on various terrains. Moreover, the current article will also cover the different soft computing techniques used to tune the gains of the controllers. In this article, the authors have reviewed a vast compilation of research work on the gait generation of the biped robot on various terrains. Further, the authors have proposed taxonomies on various design issues identified while generating the gait in different aspects. The authors reviewed approximately 296 articles and discovered that all researchers attempted to generate the dynamically balanced biped gait on various terrains.

Random walks on graphs are an essential primitive for many randomised algorithms and stochastic processes. It is natural to ask how much can be gained by running $k$ multiple random walks independently and in parallel. Although the cover time of multiple walks has been investigated for many natural networks, the problem of finding a general characterisation of multiple cover times for worst-case start vertices (posed by Alon, Avin, Koucký, Kozma, Lotker and Tuttle in 2008) remains an open problem. First, we improve and tighten various bounds on the stationary cover time when $k$ random walks start from vertices sampled from the stationary distribution. For example, we prove an unconditional lower bound of $\Omega ((n/k) \log n)$ on the stationary cover time, holding for any $n$-vertex graph $G$ and any $1 \leq k =o(n\log n )$. Secondly, we establish the stationary cover times of multiple walks on several fundamental networks up to constant factors. Thirdly, we present a framework characterising worst-case cover times in terms of stationary cover times and a novel, relaxed notion of mixing time for multiple walks called the partial mixing time. Roughly speaking, the partial mixing time only requires a specific portion of all random walks to be mixed. Using these new concepts, we can establish (or recover) the worst-case cover times for many networks including expanders, preferential attachment graphs, grids, binary trees and hypercubes.

This paper presents a study on the design and modeling of a novel pneumatic self-repairing soft actuator. The self-repairing soft actuator is composed of driving element, heating element, and repairing element. The driving element completes the deformation of the self-repairing soft actuator. The heating element and the repairing element complete the self-repairing function of the self-repairing soft actuator. A model used to optimize the structure is established, and the structure of the self-repairing soft actuator is determined through finite element analysis and experiment. The self-repairing time model of the soft actuator is established. The influences of different factors on the self-repairing effect and the self-repairing time are analyzed. The self-repairing scheme of the soft actuator is determined. Experiments show that the shortest time for the self-repairing soft actuator to complete the self-repairing process is 83 min. When the self-repairing soft actuator works normally, the bending angle can reach 129.8° and the bending force can reach 24.96 N. After repairing, the bending angle can reach 108.2°, and the bending force can reach 21.85 N. The repaired soft actuator can complete normal locomotion.

Currently, most of the robot path planning methods for spray painting are based on slicing the Computer-Aided Design model of the target surface to generate a series of path points. They usually neglect the geometric boundary of the model and the smoothness of the generated path, leading to a non-uniform coating thickness. To ameliorate it, an improved “boundary fitting approach” is proposed. In this method, the upper and lower boundaries of the target surface are firstly detected based on the topology of the stereolithography model. For each pass, several sample points are extracted with a uniform length interval from the intersection points generated by the basic slicing method. The path pass is then described by a fourth-order polynomial curve. It fits the boundary points and sample points for the $z$-$t$ and $y$-$t$ relationships, respectively. Based on the spray gun’s motion direction and spray direction, the orientation of each path point is also defined. The parameters of the path pass are optimized by particle swarm optimization to get the optimal uniformity of the resulting coating thickness. Both of the global uniformity and the local uniformity between two adjacent passes are considered. The strength of the proposed approach is validated by comparing the simulation with the basic and other typical algorithms. The results denote that boundary fitting approach could improve the uniformity of coating thickness. It brings about a better performance for the painted workpiece.

In this paper, we present a broad learning control method for a two-link flexible manipulator with prescribed performance (PP) and actuator faults. The trajectory tracking errors are processed through two consecutive error transformations to achieve the constraints in terms of the overshoot, transient error, and steady-state error. And the barrier Lyapunov function is employed to implement constraints on the transition state variable. Then, the improved radial basis function neural networks combined with broad learning theory are constructed to approximate the unknown model dynamics of flexible robotic manipulator. The proposed fault-tolerant PP control cannot only ensure tracking errors converge into a small region near zero within the preset finite time but also address the problem caused by actuator faults. All the closed-loop error signals are uniformly ultimately bounded via the Lyapunov stability theory. Finally, the feasibility of the proposed control is verified by the simulation results.

For a random binary noncoalescing feedback shift register of width $n$, with all $2^{2^{n-1}}$ possible feedback functions $f$ equally likely, the process of long cycle lengths, scaled by dividing by $N=2^n$, converges in distribution to the same Poisson–Dirichlet limit as holds for random permutations in $\mathcal{S}_N$, with all $N!$ possible permutations equally likely. Such behaviour was conjectured by Golomb, Welch and Goldstein in 1959.

The equivalence of folding left and right over Peano numbers and lists makes it possible to minimalistically inter-derive (1) structurally recursive functions in direct style, (2) structurally tail-recursive functions that use an accumulator, and (3) structurally tail-recursive functions in delimited continuation-passing style, using Ohori and Sasano’s lightweight fusion by fixed-point promotion. When the fold-left and the fold-right functions account for primitive iteration for Peano numbers, this equivalence is unconditional. When they account for primitive recursion for Peano numbers, this equivalence is modulo left permutativity of their induction-step parameter – a property which is more general than associativity and commutativity. And when they account for primitive iteration or for primitive recursion over lists, this equivalence is modulo left permutativity of their induction-step parameter if these two fold functions have the same type. Since the 1980s, however, the two fold functions for lists do not have the same type: the arguments for their induction-step parameter are swapped, a re-ordering that complicated Bird and Wadler’s duality theorems and whose history is reviewed in an appendix. Without this re-ordering, Bird and Wadler’s second duality theorem more visibly accounts for “re-bracketing,” which is a key step to make recursive programs tail recursive in the general area of program development, from Cooper in the 1960s and onwards.

In this paper, we answer the multiple calls for systematic analysis of paradigms and subdisciplines in political science—the search for coherence within a fragmented field. We collected a large dataset of over seven hundred thousand writings in political science from Web of Science since 1946. We found at least two waves of political science development, from behaviorism to new institutionalism. Political science appeared to be more fragmented than literature suggests—instead of ten subdisciplines, we found 66 islands. However, despite fragmentation, there is also a tendency for integration in contemporary political science, as revealed by co-existence of several paradigms and coherent and interconnected topics of the “canon of political science,” as revealed by the core-periphery structure of topic networks. This was the first large-scale investigation of the entire political science field, possibly due to newly developed methods of bibliometric network analysis: temporal bibliometric analysis and island methods of clustering. Methodological contribution of this work to network science is evaluation of islands method of network clustering against a hierarchical cluster analysis for its ability to remove misleading information, allowing for a more meaningful clustering of large weighted networks.

We introduce a broad class of multi-hooking networks, wherein multiple copies of a seed are hooked at each step at random locations, and the number of copies follows a predetermined building sequence of numbers. We analyze the degree profile in random multi-hooking networks by tracking two kinds of node degrees—the local average degree of a specific node over time and the global overall average degree in the graph. The former experiences phases and the latter is invariant with respect to the type of building sequence and is somewhat similar to the average degree in the initial seed. We also discuss the expected number of nodes of the smallest degree. Additionally, we study distances in the network through the lens of the average total path length, the average depth of a node, the eccentricity of a node, and the diameter of the graph.

Contact force is one of the most significant feedback for robots to achieve accurate control and safe interaction with environment. For continuum robots, it is possible to estimate the contact force based on the feedback of robot shapes, which can address the difficulty of mounting dedicated force sensors on the continuum robot body with strict dimension constraints. In this paper, we use local curvatures to estimate the magnitude and location of single or multiple contact forces based on Cosserat rod theory. We validate the proposed method in a thin elastic tube and calculate the curvatures via Fiber Bragg Grating (FBG) sensors or image feedback. For the curvature feedback obtained from multicore FBG sensors, the overall force magnitude estimation error is $0.062 \pm 0.068$ N and the overall location estimation error is $3.51 \pm 2.60$ mm. For the curvature feedback obtained from image, the overall force magnitude estimation error is $0.049 \pm 0.048$ N and the overall location estimation error is $2.75 \pm 1.71$ mm. The results demonstrate that the curvature-based force estimation method is able to accurately estimate the contact force.

In an unstructured environment, the arm can perform complicated tasks with rapidity, flexibility, and robustness. It is difficult to configure multiple artificial muscles similar to an arm in the compact space of a robotic arm. When muscle tension is transferred, mechanisms like tendon-sheath/tendon-pulley may be installed in a compact space to develop musculoskeletal robots that are closer to the arm. However, handling variable frictional nonlinearity and elastic cable deformation is necessary for transmission stability. In this study, the modular artificial muscle system (MAMS), including motor cable artificial muscle and tendon sheath–pulley system (TSPS), that can be installed remotely and transmit muscle tension in narrow paths, is designed. The feed-forward multi-layer neural network (FF-MNN) approach is utilized to discuss the relationship between the measurable input tension of TSPS and the unmeasurable output tension and cable elongation. Subsequently, the lightweight musculoskeletal arm (LM-Arm) is built to verify the validity of MAMS. Through trials, the experiments of MAMS after friction compensating and the LM-Arm’s end-point 3D trajectory tracking are investigated. The results show that average errors of the active and passive muscles tension are 3.87 N and 3.51 N, respectively, under conditions of larger load and higher contraction velocity. The average muscle length error of trajectory tracking is 0.00078 m (0.72%). The suggested MAMS may successfully build a musculoskeletal robot that has similar flexibility and morphology to the arm. It can also be utilized to power various pieces of machinery, such as rescue robot, invasive surgical robots, dexterous hands, and wearable exoskeletons.