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This article is concerned with developing an intelligent system for the control of a wheeled robot. An algorithm for training an artificial neural network for path planning is proposed. The trajectory ensures steering optimal motion from the current position of the mobile robot to a prescribed position taking its orientation into account. The proposed control system consists of two artificial neural networks. One of them serves to specify the position and the size of the obstacle, and the other forms a continuous trajectory to reach it, taking into account the information received, the coordinates, and the orientation at the point of destination. The neural network is trained on the basis of samples obtained by modeling the equations of motion of the wheeled robot which ensure its motion along trajectories in the form of Euler’s elastica.

The paper is devoted to multiple solutions of the classical problem on stationary configurations of an elastic rod on a plane; we describe boundary values for which there are more than two optimal configurations of a rod (optimal elasticae). We define sets of points where three or four optimal elasticae come together with the same value of elastic energy. We study all configurations that can be translated into each other by symmetries, i.e., reflections at the center of the elastica chord and reflections at the middle perpendicular to the elastica chord. For the first symmetry, the ends of the rod are directed in opposite directions, and the corresponding boundary values lie on a disk. For the second symmetry, the boundary values lie on a Möbius strip. As a result, we study both sets numerically and in some cases analytically; in each case, we find sets of points with several optimal configurations of the rod. These points form the currently known part of the reachability set where elasticae lose global optimality. [ABSTRACT FROM AUTHOR]

The left-invariant sub-Riemannian problem on the Engel group is considered. The problem gives the nilpotent approximation to generic rank two sub-Riemannian problems on four-dimensional manifolds. The global optimality of extremal trajectories is studied via geometric control theory. The global diffeomorphic structure of the exponential mapping is described. As a consequence, the cut time is proved to be equal to the first Maxwell time corresponding to discrete symmetries of the exponential mapping. [ABSTRACT FROM AUTHOR]

Control technology for wheeled mobile robots is one of the core focuses in the current field of robotics research. Within this domain, model-free adaptive control (MFAC) methods, with their advanced data-driven strategies, have garnered widespread attention. The unique characteristic of these methods is their ability to operate without relying on prior model information of the control system, which showcases their exceptional capability in ensuring closed-loop system stability. This paper extensively details three dynamic linearization techniques of MFAC: compact form dynamic linearization, partial form dynamic linearization and full form dynamic linearization. These techniques lay a solid theoretical foundation for MFAC. Subsequently, the article delves into some advanced MFAC schemes, such as dynamic event-triggered MFAC and iterative learning MFAC. These schemes further enhance the efficiency and intelligence level of control systems. In the concluding section, the paper briefly discusses the future development potential and possible research directions of MFAC, aiming to offer references and insights for future innovations in control technology for wheeled mobile robots. [ABSTRACT FROM AUTHOR]

In this work we study extremals on Lie groups G endowed with a left invariant polyhedral Finsler structure. We use the Pontryagin’s Maximal Principle (PMP) to find curves on the cotangent bundle of the group, such that its projections on G are extremals. Let g and g ∗ be the Lie algebra of G and its dual space respectively. We represent this problem as a control system a ′ (t) = - ad ∗ (u (t)) (a (t)) of Euler-Arnold type equation, where u (t) is a measurable control in the unit sphere of g and a (t) is an absolutely continuous curve in g ∗ . A solution (u (t) , a (t)) of this control system is a Pontryagin extremal and a (t) is its vertical part. In this work we show that for a fixed vertical part of the Pontryagin extremal a (t) , the uniqueness of u (t) such that (u (t) , a (t)) is a Pontryagin extremal can be studied through an asymptotic curvature of a (t) . [ABSTRACT FROM AUTHOR]

An extended four-dimensional version of the traditional Petitot–Citti–Sarti model on contour completion in the visual cortex is examined. The neural configuration space is considered as the group of similarity transformations, denoted as M = SIM(2) . The left-invariant subbundle of the tangent bundle models possible directions for establishing neural communication. The sub-Riemannian distance is proportional to the energy expended in interneuron activation between two excited border neurons. According to the model, the damaged image contours are restored via sub-Riemannian geodesics in the space M of positions, orientations and thicknesses (scales). We study the geodesic problem in M using geometric control theory techniques. We prove the existence of a minimal geodesic between arbitrary specified boundary conditions. We apply the Pontryagin maximum principle and derive the geodesic equations. In the special cases, we find explicit solutions. In the general case, we provide a qualitative analysis. Finally, we support our model with a simulation of the association field. [ABSTRACT FROM AUTHOR]

In this paper, we prove the existence theorem for longest paths in sub-Lorentzian problems, which generalizes the classical theorem for globally hyperbolic Lorentzian manifolds. We specifically address the case of invariant structures on homogeneous spaces, as the conditions for the existence theorem in this case can be significantly simplified. In particular, it turns out that longest paths exist for any left-invariant sub-Lorentzian structures on Carnot groups. [ABSTRACT FROM AUTHOR]

Precision control of multiple robotic fish visual navigation in complex underwater environments has long been a challenging issue in the field of underwater robotics. To address this problem, this paper proposes a multi-robot fish obstacle traversal technique based on the combination of cross-modal variational autoencoder (CM-VAE) and imitation learning. Firstly, the overall framework of the robotic fish control system is introduced, where the first-person view of the robotic fish is encoded into a low-dimensional latent space using CM-VAE, and then different latent features in the space are mapped to the velocity commands of the robotic fish through imitation learning. Finally, to validate the effectiveness of the proposed method, experiments are conducted on linear, S-shaped, and circular gate frame trajectories with both single and multiple robotic fish. Analysis reveals that the visual navigation method proposed in this paper can stably traverse various types of gate frame trajectories. Compared to end-to-end learning and purely unsupervised image reconstruction, the proposed control strategy demonstrates superior performance, offering a new solution for the intelligent navigation of robotic fish in complex environments. [ABSTRACT FROM AUTHOR]

Automated guided vehicles (AGVs) have become prevalent over the last decade. However, numerous challenges remain, including path planning, security, and the capacity to operate safely in unstructured environments. This study proposes an obstacle avoidance system that leverages deep action learning (DAL) to address these challenges and meet the requirements of Industry 4.0 for AGVs, such as speed, accuracy, and robustness. In the proposed approach, the DAL is integrated into an AGV platform to enhance its visual navigation, object recognition, localization, and decision-making capabilities. Then DAL itself was introduced to combine the work of You Only Look Once (YOLOv4), speeded-up robust features (SURF), and k-nearest neighbor (kNN) and AGV control in indoor visual navigation. The DAL system triggers SURF to differentiate two navigation images, and kNN is used to verify visual distance in real time to avoid obstacles on the floor while searching for the home position. The testing findings show that the suggested system is reliable and fits the needs of advanced AGV operations. [ABSTRACT FROM AUTHOR]

Tractors with multiple trailers are widely applied means of transport in manufacturing systems. There exist numerous designs of trailers and tractors, making the estimation of the system trajectory and the required transportation corridor a complex task. It is also difficult to achieve the same trajectory for a manually operated tractor for multiple runs. The problem is complicated if there are multiple towed trailers or a dynamic drive on slippery ground. One approach is to replace the driver with an automated steering system. This paper presents a dynamic model of a tractor with multiple trailer system, based on the Lagrange formalism, which is controlled by artificial neural networks. To account for the slip phenomenon, a sigmoidal tire model was used. The algorithm of the artificial neural network provides the most appropriate input parameters for tractor steering for a given transportation area. The input parameters are the torques applied to the tractor wheels and are determined by the algorithm based on the data collected by the LiDAR scanner during the train run. These data include distances for each unit from the obstacle (e.g., wall), information about the occurrence of a collision, and the distance traveled by the tractor. The simulation results of the integration of the dynamic model and the neural network modeled are presented in a graphic form. The proposed algorithm ensures a collision-free ride of the system. [ABSTRACT FROM AUTHOR]

A map construction method based on a collision probability model and an improved A* algorithm is proposed to address the issues of insufficient security in mobile robot map construction and path planning in complex environments. The method is based on modeling the asymmetry of paths, which complicates problem solving. Firstly, this article constructs a collision probability function model, and based on this model it is fused with the obstacle grid map, which is based on the grid method, to draw a collision probability grid map (CPGM) containing collision probability information. Secondly, incorporating the collision probability values from the CPGM into the actual cost function of the traditional A* algorithm improves the security of path planning in complex environments. The experimental results show that the improved A* algorithm decreases the percentage of dangerous nodes in complex environments by 69.23%, shortens the path planning length by 19.52%, reduces the search time by 16.8%, and reduces the number of turns by 46.67%. Therefore, the method in this paper solves the problem of traditional grid maps lacking security information and can plan a path with higher security and which is smoother, improving the security and robustness of mobile robot autonomous navigation in complex environments. [ABSTRACT FROM AUTHOR]

We study the geometric structures associated with curvature radii of curves with values on a Riemannian manifold (M, g). We show the existence of sub-Riemannian manifolds naturally associated with the curvature radii and we investigate their properties. In the particular case of surfaces these sub-Riemannian structures are of Engel type. The main character of our construction is a pair of global vector fields f 1 , f 2 , which encodes intrinsic information on the geometry of (M, g). [ABSTRACT FROM AUTHOR]

We study the local geometry of the sub-Finsler structure induced by a sub-Riemannian metric on a 3-dimensional manifold. We provide a description of the upper part of the cut locus of short geodesics, in some non generic cases. [ABSTRACT FROM AUTHOR]

We study a time-optimal problem in the roto-translation group with admissible control in a circular sector. The problem reveals the trajectories of a car model that can move forward on a plane and turn with a given minimum turning radius. Our work generalizes the sub-Riemannian problem by adding a restriction on the velocity vector to lie in a circular sector. The sub-Riemannian problem is given by a special case when the sector is the full disc. The trajectories of the system are applicable in image processing to detect salient lines. We study the local and global controllability of the system and the existence of a solution for given arbitrary boundary conditions. In a general case of the sector opening angle, the system is globally but not small-time locally controllable. We show that when the angle is obtuse, a solution exists for any boundary conditions, and when the angle is reflex, a solution does not exist for some boundary conditions. We apply the Pontryagin maximum principle and derive a Hamiltonian system for extremals. Analyzing a phase portrait of the Hamiltonian system, we introduce the rectified coordinates and obtain an explicit expression for the extremals in Jacobi elliptic functions. We show that abnormal extremals are of circular type, and they correspond to motions of a car along circular arcs of minimal possible radius. The normal extremals in a general case are given by concatenation of segments of sub-Riemannian geodesics in SE 2 and arcs of circular extremals. We show that, in a general case, the vertical (momentum) part of the extremals is periodic. We partially study the optimality of the extremals and provide estimates for the cut time in terms of the period of the vertical part. [ABSTRACT FROM AUTHOR]

Dispatching and cooperative trajectory planning for multiple autonomous forklifts in a warehouse is a widely applied research topic. The conventional methods in this domain regard dispatching and planning as isolated procedures, which render the overall motion quality of the forklift team imperfect. The dispatching and planning problems should be considered simultaneously to achieve optimal cooperative trajectories. However, this approach renders a large-scale nonconvex problem, which is extremely difficult to solve in real time. A joint dispatching and planning method is proposed to balance solution quality and speed. The proposed method is characterized by its fast runtime, light computational burden, and high solution quality. In particular, the candidate goals of each forklift are enumerated. Each candidate dispatch solution is measured after concrete trajectories are generated via an improved hybrid A* search algorithm, which is incorporated with an artificial neural network to improve the cost evaluation process. The proposed joint dispatching and planning method is computationally cheap, kinematically feasible, avoids collisions with obstacles/forklifts, and finds the global optimum quickly. The presented motion planning strategy demonstrates that the integration of a neural network with the dispatching approach leads to a warehouse filling/emptying mission completion time that is 2% shorter than the most efficient strategy lacking machine-learning integration. Notably, the mission completion times across these strategies vary by approximately 15%. [ABSTRACT FROM AUTHOR]