Industrial robots are widely used in the painting industry, such as automobile manufacturing and solid wood furniture industry. An important problem is how to improve the efficiency of robot programming, especially in the current furniture industry with multiple products, small batches and increasingly high demand for customization. In this work, we propose an outer loop adaptive control scheme, which allow users to realize the practical application of the zero-moment lead-through teaching method based on dynamic model without opening the inner torque control interface of robots. In order to accurately estimate the influence of joint friction, a friction model is established based on static, Coulomb and viscous friction characteristics, and the Sigmoid function is used to represent the transition between motion states. An identification method is used to quickly identify the dynamic parameters of the robot. The joint position/speed command of the robot’s inner joint servo loop is dynamically generated based on the user-designed adaptive control law. In addition, the zero-moment lead-through teaching scheme based on the dynamic model is applied to a spray-painting robot with closed control system. In order to verify our method, CMA GR630ST is used to conduct experiments. We identified the parameters of the dynamic model and carried out the zero-moment lead-through teaching experiment to track the target trajectory. The results show that the proposed method can realize the application of modern control methods in industrial robot with closed control systems, and achieve a preliminary exploration to improve the application scenarios of spray-painting robots.

In this paper, we propose an approach to tune optimal parameters of a robust PID controller by means of computed torque control (CTC) strategy for trajectory tracking of a Delta parallel robot, using a hybrid optimization algorithm of Particle Swarm Optimization (PSO) and differential evolution (DE). It differs from previous works that they propose robust PID controller parameters tuning based on conventional gradient-based optimization algorithms and apply them to process control. First, we reduce the tuning problem of a robust PID controller with CTC strategy satisfying requirements including robustness and disturbance attenuation to an optimization problem with nonlinear constraints by considering the nonlinear dynamic model of a Delta parallel robot. Second, we set up the design characteristics for the trajectory tracking of a Delta parallel robot. Then, we propose a robust PID controller in a way of obtaining the global optimization solution of the nonlinear optimization problem by running a PSO-DE hybrid optimization algorithm of finding the global optimal solution by maintaining the diversity of swarm during evolution based on the evolution of cognitive experience. Simulation and experimental results demonstrate that the proposed controller outperforms previous works with respect to robust performance and active disturbance attenuation when it is applied to tracking control of a Delta parallel robot.

An old conjecture of Erdős and McKay states that if all homogeneous sets in an $n$-vertex graph are of order $O(\!\log n)$ then the graph contains induced subgraphs of each size from $\{0,1,\ldots, \Omega \big(n^2\big)\}$. We prove a bipartite analogue of the conjecture: if all balanced homogeneous sets in an $n \times n$ bipartite graph are of order $O(\!\log n)$, then the graph contains induced subgraphs of each size from $\{0,1,\ldots, \Omega \big(n^2\big)\}$.

Gambling marketing is frequently visible in the United Kingdom, especially around the national sport, soccer. Previous research has documented the frequency with which gambling marketing logos can be seen in domestic club soccer, and also the frequency of television advertising around international tournaments. The present research investigates the frequency and content of television advertising during the men’s 2020 Euro soccer tournament, a high-profile tournament shown since the industry’s voluntary “whistle-to-whistle ban” on gambling advertising came into effect. Overall, 113 gambling adverts were recorded (4.5 adverts per relevant match). Financial inducements were the most frequently shown category (56.6%), followed by adverts raising awareness of a given operator’s brand (19.5%), adverts featuring the odds on specific complex bets (18.6%), and adverts promoting safer gambling (5.3%). Adverts featured a range of safer gambling messages, with the “when the fun stops, stop” message featuring in 56.6% of adverts. This research indicates that gambling advertising remains a frequent part of the experience of watching live televised soccer in the UK, and shows how the content of this advertising was comparable to what has been seen in the previous literature.

Given a graphon $W$ and a finite simple graph $H$, with vertex set $V(H)$, denote by $X_n(H, W)$ the number of copies of $H$ in a $W$-random graph on $n$ vertices. The asymptotic distribution of $X_n(H, W)$ was recently obtained by Hladký, Pelekis, and Šileikis [17] in the case where $H$ is a clique. In this paper, we extend this result to any fixed graph $H$. Towards this we introduce a notion of $H$-regularity of graphons and show that if the graphon $W$ is not $H$-regular, then $X_n(H, W)$ has Gaussian fluctuations with scaling $n^{|V(H)|-\frac{1}{2}}$. On the other hand, if $W$ is $H$-regular, then the fluctuations are of order $n^{|V(H)|-1}$ and the limiting distribution of $X_n(H, W)$ can have both Gaussian and non-Gaussian components, where the non-Gaussian component is a (possibly) infinite weighted sum of centred chi-squared random variables with the weights determined by the spectral properties of a graphon derived from $W$. Our proofs use the asymptotic theory of generalised $U$-statistics developed by Janson and Nowicki [22]. We also investigate the structure of $H$-regular graphons for which either the Gaussian or the non-Gaussian component of the limiting distribution (but not both) is degenerate. Interestingly, there are also $H$-regular graphons $W$ for which both the Gaussian or the non-Gaussian components are degenerate, that is, $X_n(H, W)$ has a degenerate limit even under the scaling $n^{|V(H)|-1}$. We give an example of this degeneracy with $H=K_{1, 3}$ (the 3-star) and also establish non-degeneracy in a few examples. This naturally leads to interesting open questions on higher order degeneracies.