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The article introduces a novel class of 4R1H mechanisms, where 4R indicates four revolute joints and 1H indicates one helical joint. The paper starts with the type synthesis of these mechanisms, which involves combining two kinematic chains with planar and cylindrical motion types into a single closed-loop kinematic chain. If we fix any link in such a chain, we get a workable mechanism. The synthesis procedure considers two options for the relative arrangement of these two kinematic chains. Adding an H joint to the kinematic chain allows us to design mechanisms whose output link performs spatial motion. Using the proposed synthesis procedure, we develop a family of 4R1H mechanisms. Next, we choose one mechanism as a representative example and consider its mobility, singularity, kinematic, and dynamic analysis. Using screw theory, we confirm the mechanism has one degree of freedom and determine its singular configurations. Kinematic analysis provides closed-form expressions to calculate displacements, velocities, and accelerations of all the mechanism links. Dynamic analysis uses these results to compute the motor torque required for one motion cycle. To verify the suggested analytical algorithms and obtained results, we use computer-aided design tools, which allow us to develop virtual and physical prototypes.
We present our library for universal algebra in the UniMath framework dealing with multi-sorted signatures, their algebras and the basics for equation systems. We show how to implement term algebras over a signature without resorting to general inductive constructions (currently not allowed in UniMath) still retaining the computational nature of the definition. We prove that our single sorted ground term algebras are instances of homotopy W-types. From this perspective, the library enriches UniMath with a computationally well-behaved implementation of a class of W-types. Moreover, we give neat constructions of the univalent categories of algebras and equational algebras by using the formalism of displayed categories and show that the term algebra over a signature is the initial object of the category of algebras. Finally, we showcase the computational relevance of our work by sketching some basic examples from algebra and propositional logic.
Several African countries are developing artificial intelligence (AI) strategies and ethics frameworks with the goal of accelerating responsible AI development and adoption. However, many of these governance actions are emerging without consideration for their suitability to local contexts, including whether the proposed policies are feasible to implement and what their impact may be on regulatory outcomes. In response, we suggest that there is a need for more explicit policy learning, by looking at existing governance capabilities and experiences related to algorithms, automation, data, and digital technology in other countries and in adjacent sectors. From such learning, it will be possible to identify where existing capabilities may be adapted or strengthened to address current AI-related opportunities and risks. This paper explores the potential for learning by analysing existing policy and legislation in twelve African countries across three main areas: strategy and multi-stakeholder engagement, human dignity and autonomy, and sector-specific governance. The findings point to a variety of existing capabilities that could be relevant to responsible AI; from existing model management procedures used in banking and air quality assessment to efforts aimed at enhancing public sector skills and transparency around public–private partnerships, and the way in which existing electronic transactions legislation addresses accountability and human oversight. All of these point to the benefit of wider engagement on how existing governance mechanisms are working, and on where AI-specific adjustments or new instruments may be needed.
This volume provides a unique perspective on an emerging area of scholarship and legislative concern: the law, policy, and regulation of human-robot interaction (HRI). The increasing intelligence and human-likeness of social robots points to a challenging future for determining appropriate laws, policies, and regulations related to the design and use of AI robots. Japan, China, South Korea, and the US, along with the European Union, Australia and other countries are beginning to determine how to regulate AI-enabled robots, which concerns not only the law, but also issues of public policy and dilemmas of applied ethics affected by our personal interactions with social robots. The volume's interdisciplinary approach dissects both the specificities of multiple jurisdictions and the moral and legal challenges posed by human-like robots. As robots become more like us, so too will HRI raise issues triggered by human interactions with other people.
In the continuous transportation process of coal in mining, exploring real-time detection technology for longitudinal tear of conveyor belts on mobile devices can effectively prevent transport failures. To address the challenges associated with single-dimensional detection, high network complexity, and difficulties in mobile deployment for longitudinal tearing detection in conveyor belts, we have proposed an efficient parallel acceleration method based on field-programmable gate arrays (FPGA) for the ECSMv3-YOLO network, which is an improved version of the you only look once (YOLO) network, enabling multidimensional real-time detection. The FPGA hardware acceleration architecture of the customized network incorporates quantization and pruning methods to further reduce network parameters. The convolutional acceleration engines were specifically designed to optimize the network’s inference speed, and the incorporation of dual buffers and multiple direct memory access channels can effectively mitigate data transfer latency. The establishment of a multidimensional longitudinal tear detection experimental device for conveyor belts facilitated FPGA acceleration experiments on ECSMv3-YOLO, resulting in model parameters of 6.257 M, mean average precision of 0.962, power consumption of 3.2 W, and a throughput of 15.56 giga operations per second (GOP/s). By assessing the effects of different networks and varying light intensity, and comparing with CPU, GPU, and different FPGA hardware acceleration platforms, this method demonstrates significant advantages in terms of detection speed, recognition accuracy, power consumption, and energy efficiency. Additionally, it exhibits strong adaptability and interference resilience.
This paper presents Hybrid Modified A* (HMA*) algorithm which is used to control an omnidirectional mecanum wheel automated guided vehicle (AGV). HMA* employs Modified A* and PSO to determine the best AGV path. The HMA* overcomes the A* technique’s drawbacks, including a large number of nodes, imprecise trajectories, long calculation times, and expensive path initialization. Repetitive point removal refines Modified A*’s path to locate more important nodes. Real-time hardware control experiments and extensive simulations using Matlab software prove the HMA* technique works well. To evaluate the practicability and efficiency of HMA* in route planning and control for AGVs, various algorithms are introduced like A*, Probabilistic Roadmap (PRM), Rapidly-exploring Random Tree (RRT), and bidirectional RRT (Bi-RRT). Simulations and real-time testing show that HMA* path planning algorithm reduces AGV running time and path length compared to the other algorithms. The HMA* algorithm shows promising results, providing an enhancement and outperforming A*, PRM, RRT, and Bi-RRT in the average length of the path by 12.08%, 10.26%, 7.82%, and 4.69%, and in average motion time by 21.88%, 14.84%, 12.62%, and 8.23%, respectively. With an average deviation of 4.34% in path length and 3% in motion time between simulation and experiments, HMA* closely approximates real-world conditions. Thus, the proposed HMA* algorithm is ideal for omnidirectional mecanum wheel AGV’s static as well as dynamic movements, making it a reliable and efficient alternative for sophisticated AGV control systems.
In this introductory chapter, we will formally introduce the main variants of the traveling salesman problem, symmetric and asymmetric, explain a very useful graph-theoretic view based on Euler’s theorem, and describe the classical simple approximation algorithms: Christofides’ algorithm and the cycle cover algorithm.
We also introduce basic notation, in particular from graph theory, and some fundamental combinatorial optimization problems.
A major step towards the first constant-factor approximation algorithm for the Asymmetric TSP was made by Svensson. He devised a constant-factor approximation algorithm for Asymmetric Graph TSP, which is the special case of the Asymmetric TSP with c(e)=1 for all e ∈ E.
In this chapter, we present Svensson’s algorithm for the Asymmetric Graph TSP. We also incorporate some improvements, from Traub and Vygen, who gave a variant of Svensson’s algorithm with improved approximation ratio. Moreover, we present an improved algorithm for finding a graph subtour cover, which is the main subroutine of Svensson’s algorithm. Overall, we will obtain an approximation ratio of 8+ε for Asymmetric Graph TSP, for every ε>0.
Almost all techniques presented in this chapter will be used again in Chapters 7 and 8 for the general Asymmetric TSP.
The random sampling approach described in Chapter 5 for the Asymmetric TSP has also been used successfully for the Symmetric TSP. First, Oveis Gharan, Saberi, and Singh obtained the first algorithm with approximation ratio less than 3/2 for Graph TSP. More recently, Karlin, Klein, and Oveis Gharan proved that essentially the same algorithm has approximation ratio less than 3/2 for the general Symmetric TSP.
The algorithm is simple, but its analysis is very complicated. While for Graph TSP we know simpler and better algorithms today (see Chapters 12 and 13), the random sampling algorithm is still the best-known approximation algorithm for Symmetric TSP.
The algorithm samples a spanning tree from an (approximately) marginal-preserving λ-uniform distribution and then proceeds with parity correction like Christofides’ algorithm. After briefly discussing the analysis for Graph TSP, we present the first part of the analysis by Karlin, Klein, and Oveis Gharan, with some simplifications suggested by Drees. The main point is to reduce the set of relevant cuts that need to be considered to bound the cost of parity correction and obtain a nice structure that will be exploited in Chapter 11.
Optical microrobots are activated by a laser in a liquid medium using optical tweezers. To create visual control loops for robotic automation, this work describes a deep learning-based method for orientation estimation of optical microrobots, focusing on detecting 3-D rotational movements and localizing microrobots and trapping points (TPs). We integrated and fine-tuned You Only Look Once (YOLOv7) and Deep Simple Online Real-time Tracking (DeepSORT) algorithms, improving microrobot and TP detection accuracy by $\sim 3$% and $\sim 11$%, respectively, at the 0.95 Intersection over Union (IoU) threshold in our test set. Additionally, it increased mean average precision (mAP) by 3% at the 0.5:0.95 IoU threshold during training. Our results showed a 99% success rate in trapping events with no false-positive detection. We introduced a model that employs EfficientNet as a feature extractor combined with custom convolutional neural networks (CNNs) and feature fusion layers. To demonstrate its generalization ability, we evaluated the model on an independent in-house dataset comprising 4,757 image frames, where microrobots executed simultaneous rotations across all three axes. Our method provided mean rotation angle errors of $1.871^\circ$, $2.308^\circ$, and $2.808^\circ$ for X (yaw), Y (roll), and Z (pitch) axes, respectively. Compared to pre-trained models, our model provided the lowest error in the Y and Z axes while offering competitive results for X-axis. Finally, we demonstrated the explainability and transparency of the model’s decision-making process. Our work contributes to the field of microrobotics by providing an efficient 3-axis orientation estimation pipeline, with a clear focus on automation.
Traub and Vygen used recursive dynamic programming to obtain a (3/2+ε)-approximation algorithm for Path TSP for any ε>0. This approach was then improved and simplified by Zenklusen, who obtained a 3/2-approximation for Path TSP. After discussing the dynamic programming approach in a simple context, we present Zenklusen’s algorithm.
Then we present a black-box reduction from Path TSP to Symmetric TSP, similar to the one proposed by Traub, Vygen, and Zenklusen. This shows that the former is not much harder to approximate than the latter. This implies the currently best-known approximation guarantees for Path TSP and the special case Graph Path TSP. Our new proof, again based on dynamic programming, actually yields the same result even for a more general problem, which we call Multi-Path TSP.
So far, all algorithms for Symmetric TSP began with a spanning tree and then added edges to make the graph Eulerian. In contrast, Mömke and Svensson suggested to begin with a 2-connected graph; then we may also delete some edges for making it Eulerian, and this may be cheaper overall. They introduced the notion of removable pairings, which allow to control that we maintain connectivity when deleting edges.
This idea led to a substantial improvement and is still used for the best algorithm for Graph TSP that we know today (cf. Chapter 12). It also yields the ratio 4/3 for the special case of subcubic graphs.
In this chapter, we mention further results on the approximability of variants or special cases of the traveling salesman problem. We will also briefly mention a few important related problems for which the best-known approximation algorithms use a TSP approximation algorithm as a subroutine.
In particular, we discuss inapproximability results, geometric special cases, the minimum 2-edge-connected spanning subgraph problem, the prize-collecting TSP, the a priori TSP, and capacitated vehicle routing.
A natural generalization of the (asymmetric) traveling salesman problem arises when we are given a start vertex s and an end vertex t and ask for a tour that begins in s and ends in t, rather than a round trip.
While this problem seems to be harder, we will see in this chapter that it can be tackled by similar techniques. In particular, we show black-box reductions (by Feige and Singh, and by Köhne, Traub, and Vygen) to Asymmetric TSP and prove, as new results, the best-known approximation ratios and bounds on the integrality ratio of the natural LP relaxation.