Search Results (21)

In the context of holonomic systems, the identification of virtual displacements is clear and consolidated. This provides the possibility, once the class of displacements have been coupled with Newton’s equations, for us to write the correct equations of motion. This method combines the d’Alembert principle with Lagrange formalism. As far as nonholonomic systems are concerned, the conjecture that dates back to $\check{\mathrm{C}}$etaev actually defines a class of virtual displacements through which the d’Alembert–Lagrange method can be applied again. A great deal of literature is dedicated to the $\check{\mathrm{C}}$etaev rule from both the theoretical and experimental points of view. The absence of a rigorous (mathematical) validation of the rule inferable from the constraint equations has been declared to have expired in a recent publication; one of our objectives is to produce a critical comment on this stated result. Finally, we explore the role of the $\check{\mathrm{C}}$etaev condition within the significant class of nonholonomic homogeneous constraints. Full article

This article delves into the problem of fuzzy adaptive event-triggered (ET) formation control for nonholonomic mobile robots (NMRs) subject to full-state constraints. Fuzzy logic systems (FLSs) are employed to identify the unknown nonlinear functions within the system. To guarantee that all system states remain within their constraint boundaries, barrier Lyapunov functions (BLFs) are meticulously constructed. Subsequently, within the framework of the backstepping control design algorithm, we propose a novel fuzzy adaptive ET formation controller. Our ET mechanism can achieve an overall resource-saving rate of 88.17% for the four robots. Rigorous theoretical analysis demonstrates that the designed strategy not only ensures the stability of the controlled NMRs but also enables the formation tracking errors to converge to a small neighborhood around zero. Notably, the BLFs-based control approach presented herein endows the system with the capacity to avoid collisions to a certain degree, enhancing the overall safety and reliability of the robot formation. Finally, a simulation example is provided. The results vividly illustrate the effectiveness and practicality of the proposed theory, validating its potential for real-world applications in the field of nonholonomic mobile robot formation control. Full article

The design and industrial innovation of intelligent agricultural machinery and equipment for saline alkali land are important means for comprehensive management and capacity improvement of saline alkali land. The autonomous and unmanned agricultural tractor is the inevitable trend of the development of intelligent machinery and equipment in saline alkali land. As an underactuated system with non-holonomic constraints, the independent trajectory planning and lateral stability control of the tractor-trailer system (TTS) face challenges in saline alkali land. In this study, based on the nonlinear underactuation characteristics of the TTS and the law of passive trailer steering, a dual-trajectory collaborative control model was designed. By solving the TTS kinematic/dynamic state space, a nonlinear leading system that can generate the reference pose of a tractor-trailer was constructed. Based on the intrinsic property of the lateral deviation of the TTS, a collaborative trajectory prediction algorithm that satisfies the time domain and system constraints is proposed. Combining the dual-trajectory independent offset and lateral stability parameter of the TTS, an energy function optimization control parameter was constructed to balance the system trajectory tracking performance and lateral control stability. The experimental results showed good agreement between the predicted trailer trajectory and the collaborative control trajectory, with an average lateral error not exceeding 0.1 m and an average course angle error not exceeding 0.054 rad. This ensures that the dynamic controller designed around the tractor-trailer underactuation system can guarantee the smoothness of the trailer trajectory and the controlling stability of the tractor in saline alkali land. Full article

Robots are becoming an integral part of space facilities construction and maintenance, and may need to move to and from different work locations. Robotic arms that are widely employed, which are mounted on fixed bases, have difficulty coping with increasingly complex missions. The challenge discussed in this paper is the problem of the efficient locomotion of robotic systems. Inspired by the gliding motion of a flying snake launched from a tree and combined with the weightlessness of the space environment, we design similar motions for the robot, including the following three steps. First, the robot folds its body like a snake and initiates flight by accelerating the global center of mass (CM), focusing on the movement direction and generating suitable momentum. Then, during the flight (free-floating) phase, the joint motions are planned using a nonlinear optimization technique, considering the nonholonomic constraints introduced by the momentum conservation and the system states at the initial and final states of the floating. Meanwhile, the difficulties caused by long-distance flights are addressed to reduce the motion computational cost and energy consumption by introducing the phase plane analysis method. Finally, the landing motion is designed to avoid rigid collisions and rollover on the radial plane. The numerical simulations illustrate that the three phases of maneuvers are smooth and continuous, which can help the space robots efficiently traverse the environment. Full article

In this paper, a novel adaptive control scheme is proposed for the path-following problem of a nonholonomic mobile robot with uncertain dynamics based on barrier functions. To optimize communication resources, we integrate an event-triggered mechanism that avoids Zeno behavior and ensures that the tracking error of the closed-loop system converges to a small neighborhood around zero within a fixed time, while consistently satisfying predefined transient performance requirements. Extensive simulation studies demonstrate the effectiveness of the proposed approach and validate the theoretical results. Full article

This paper presents a trajectory-tracking controller of an inverted pendulum system on a self-balancing differential drive platform. First, the system modeling is described by considering approximations of the swing angles. Subsequently, a discrete convex representation of the system via the nonlinear sector technique is obtained, which considers the nonlinearities associated with the nonholonomic constraint. The design of a discrete parallel distributed compensation controller is achieved through an alternative method due to the presence of uncontrollable points that avoid finding a solution for the entire polytope. Finally, simulations and experimental results using a prototype illustrate the effectiveness of the proposal. Full article

Most visual simultaneous localization and mapping (SLAM) systems are based on the assumption of a static environment in autonomous vehicles. However, when dynamic objects, particularly vehicles, occupy a large portion of the image, the localization accuracy of the system decreases significantly. To mitigate this challenge, this paper unveils DOT-SLAM, a novel stereo visual SLAM system that integrates dynamic object tracking through graph optimization. By integrating dynamic object pose estimation into the SLAM system, the system can effectively utilize both foreground and background points for ego vehicle localization and obtain a static feature points map. To rectify the inaccuracies in depth estimation from stereo disparity directly on the foreground points of dynamic objects due to their self-similarity characteristics, a coarse-to-fine depth estimation method based on camera–road plane geometry is presented. This method uses rough depth to guide fine stereo matching, thereby obtaining the 3 dimensions (3D)spatial positions of feature points on dynamic objects. Subsequently, by establishing constraints on the dynamic object’s pose using the road plane and non-holonomic constraints (NHCs) of the vehicle, reducing the initial pose uncertainty of dynamic objects leads to more accurate dynamic object initialization. Finally, by considering foreground points, background points, the local road plane, the ego vehicle pose, and dynamic object poses as optimization nodes, through the establishment and joint optimization of a nonlinear model based on graph optimization, accurate six degrees of freedom (DoFs) pose estimations are obtained for both the ego vehicle and dynamic objects. Experimental validation on the KITTI-360 dataset demonstrates that DOT-SLAM effectively utilizes features from the background and dynamic objects in the environment, resulting in more accurate vehicle trajectory estimation and a static environment map. Results obtained from a real-world dataset test reinforce the effectiveness. Full article

Due to the limitation of space rover onboard computing resources and energy, there is an urgent need for high-quality drive trajectories in complex environments, which can be provided by delicately designed motion optimization methods. The nonconvexity of the collision avoidance constraints poses a significant challenge to the optimization-based motion planning of nonholonomic vehicles, especially in unstructured cluttered environments. In this paper, a novel obstacle decomposition approach, which swiftly decomposes nonconvex obstacles into their constituent convex substructures while concurrently minimizing the proliferation of resultant subobstacles, is proposed. A safe convex corridor construction method is introduced to formulate the collision avoidance constraints. The numerical approximation methods are applied to transfer the resulting continuous motion optimization problem to a nonlinear programming problem (NLP). Simulation experiments are conducted to illustrate the feasibility and superiority of the proposed methods over the rectangle safe corridor method and the area method. Full article

Non-holonomic wheeled robots (NWR) comprise a type of robotic system; they use wheels for movement and offer several advantages over other types. They are efficient, highly, and maneuverable, making them ideal for factory automation, logistics, transportation, and healthcare. The control of this type of robot is complicated, due to the complexity of modeling, asymmetrical non-holonomic constraints, and unknown perturbations in various applications. Therefore, in this study, a novel type-3 (T3) fuzzy logic system (FLS)-based controller is developed for NWRs. T3-FLSs are employed for modeling, and the modeling errors are considered in stability analysis based on the symmetric Lyapunov function. An observer is designed to detect the error, and its effect is eliminated by a developed terminal sliding mode controller (SMC). The designed technique is used to control a case-study NWR, and the results demonstrate the good accuracy of the developed scheme under non-holonomic constraints, unknown dynamics, and nonlinear disturbances. Full article

This paper elaborates on the modeling and control of an Unmanned Aerial Vehicle (UAV) for delivery purposes, thereby integrating computer-aided design, multibody dynamic modeling, and motion control analysis in a unified framework. The UAV system designed in this study and utilized for item delivery has a quadcopter structure composed of four arms connected to a central trunk. In this investigation, the proposed design of the delivery drone is systematically modeled employing the multibody approach, while SIMSCAPE MULTIBODY is the software used for performing the dynamic analysis and for devising the final design of the control system. To this end, starting from the CAD model designed using SOLIDWORKS, the control system of the quadcopter is developed by performing dynamic simulations in the MATLAB/SIMULINK environment. Additionally, another fundamental contribution of this paper is the analytical derivation of the nonlinear set of algebraic constraint equations peculiar to the present multibody system, which characterizes the kinematics of the delivery drone and describes the relative angular velocity imposed between two rigid bodies as nonholonomic constraints. Furthermore, as discussed in detail in this paper, the choice of the propulsion system and the design of the individual components heavily depends on the structural and functional needs of the UAV under study. On the other hand, the control system devised in this work is based on cascaded Proportional-Integral-Derivative (PID) controllers, which are suitable for achieving different maneuvers that are fundamental for the motion control of the delivery drone. Therefore, the final performance of the UAV system is a consequence of the regulation of the feedback parameters that characterize the PID controllers. In this respect, the paper presents the refining of the parameters characterizing the PID controllers by using both an internal MATLAB tool, which automatically tunes the controller gains of single-input single-output systems, and by observing the resulting transient behavior of the UAV system, which is obtained through extensive dynamical simulations. The set of numerical results found in this investigation demonstrates the high performance of the dynamical behavior of the UAV system designed in this work. Full article

This paper investigates the cooperative control problem for a group of autonomous nonholonomic mobile robots, in which the robots are required to collaboratively enclose and track a stationary or moving target in a circular formation. In order to solve the challenging problem that the robots with speed constraints move uniformly to the exact position on the circles centered on the target while avoiding obstacles encountered, a distributed coupling controller scheme consisting of target encircling, phase positioning and spacing assignment, and the avoidance of obstacles is proposed. First, a novel circular motion control law based on the feedback control idea of trajectory tracking is proposed, which guides all robots move to the target-centered circles and maintains the expected distances between the robots and the target. Second, a phase positioning and spacing assignment control law by introducing a nonlinear function is proposed, which can be coupled into the circular motion controller to implement the robots converge to the specified position on the circles. Finally, the obstacles avoidance control law based on artificial potential field only with repulsive force is adopted to ensure each robot effectively avoids obstacles. The rigorous theoretical analysis of the convergence of the proposed controller is given, and then the simulations and experiments are provided to validate the effectiveness and applicability of the proposed control scheme. Full article

This paper presents a nonlinear, universal, path-following controller for Wheeled Mobile Robots (WMRs). This approach, unlike previous algorithms, solves the path-following problem for all common categories of holonomic and nonholonomic WMRs, such as omnidirectional, unicycle, car-like, and all steerable wheels. This generality is the consequence of a two-stage solution that tackles separately the platform path-following and wheels’ kinematic constraints. In the first stage, for a mobile platform divested of the wheels’ constraints, we develop a general paradigm of a path-following controller that plans asymptotic paths from the WMR to the desired path and, accordingly, we derive a realization of the presented paradigm. The second stage accounts for the kinematic constraints imposed by the wheels. In this stage, we demonstrate that the designed controller simplifies the otherwise impenetrable wheels’ kinematic and nonholonomic constraints into explicit proportional functions between the velocity of the platform and that of the wheels. This result enables us to derive a closed-form trajectory generation scheme for the asymptotic path that constantly keeps the wheels’ steering and driving velocities within their corresponding, pre-specified bounds. Extensive experimental results on several types of WMRs, along with simulation results for the other types, are provided to demonstrate the performance and the efficacy of the method. Full article

The aim of this paper is to construct Noether invariants for Lagrangian non-holonomic dynamics with affine or nonlinear constraints, considered to be adapted to a foliation on the base manifold. A set of illustrative examples is given, including linear and nonlinear Appell mechanical systems. Full article

We study new classes of generic off-diagonal and diagonal cosmological solutions for effective Einstein equations in modified gravity theories (MGTs), with modified dispersion relations (MDRs), and encoding possible violations of (local) Lorentz invariance (LIVs). Such MGTs are constructed for actions and Lagrange densities with two non-Riemannian volume forms (similar to two measure theories (TMTs)) and associated bimetric and/or biconnection geometric structures. For conventional nonholonomic 2 + 2 splitting, we can always describe such models in Finsler-like variables, which is important for elaborating geometric methods of constructing exact and parametric solutions. Examples of such Finsler two-measure formulations of general relativity (GR) and MGTs are considered for Lorentz manifolds and their (co) tangent bundles and abbreviated as FTMT. Generic off-diagonal metrics solving gravitational field equations in FTMTs are determined by generating functions, effective sources and integration constants, and characterized by nonholonomic frame torsion effects. By restricting the class of integration functions, we can extract torsionless and/or diagonal configurations and model emergent cosmological theories with square scalar curvature, $R^2$, when the global Weyl-scale symmetry is broken via nonlinear dynamical interactions with nonholonomic constraints. In the physical Einstein–Finsler frame, the constructions involve: (i) nonlinear re-parametrization symmetries of the generating functions and effective sources; (ii) effective potentials for the scalar field with possible two flat regions, which allows for a unified description of locally anisotropic and/or isotropic early universe inflation related to acceleration cosmology and dark energy; (iii) there are “emergent universes” described by off-diagonal and diagonal solutions for certain nonholonomic phases and parametric cosmological evolution resulting in various inflationary phases; (iv) we can reproduce massive gravity effects in two-measure theories. Finally, we study a reconstructing procedure for reproducing off-diagonal FTMT and massive gravity cosmological models as effective Einstein gravity or Einstein–Finsler theories. Full article

Vision-based sensors such as LiDAR (Light Detection and Ranging) are adopted in the SLAM (Simultaneous Localization and Mapping) system. In the 16-beam LiDAR aided SLAM system, due to the difficulty of object detection by sparse laser data, neither the grid-based nor feature point-based solution can avoid the interference of moving objects. In an urban environment, the pole-like objects are common, invariant and have distinguishing characteristics. Therefore, it is suitable to bring more robust and reliable positioning results as auxiliary information in the process of vehicle positioning and navigation. In this work, we proposed a scheme of a SLAM system using a GNSS (Global Navigation Satellite System), IMU (Inertial Measurement Unit) and LiDAR sensor using the position of pole-like objects as the features for SLAM. The scheme combines a traditional preprocessing method and a small scale artificial neural network to extract the pole-like objects in environment. Firstly, the threshold-based method is used to extract the pole-like object candidates from the point cloud, and then, the neural network is applied for training and inference to obtain pole-like objects. The result shows that the accuracy and recall rate are sufficient to provide stable observation for the following SLAM process. After extracting the poles from the LiDAR point cloud, their coordinates are added to the feature map, and the nonlinear optimization of the front end is carried out by utilizing the distance constraints corresponding to the pole coordinates; then, the heading angle and horizontal plane translation are estimated. The ground feature points are used to enhance the elevation, pitch and roll angle accuracy. The performance of the proposed navigation system is evaluated through field experiments by checking the position drift and attitude errors during multiple two-min mimic GNSS outages without additional IMU motion constrain such as NHC (Nonholonomic Constrain). The experimental results show that the performance of the proposed scheme is superior to that of the conventional feature point grid-based SLAM with the same back end, especially in congested crossroads where slow-moving vehicles are surrounded and pole-like objects are rich in the environment. The mean plane position error during two-min GNSS outages was reduced by 38.5%, and the root mean square error was reduced by 35.3%. Therefore, the proposed pole-like feature-based GNSS/IMU/LiDAR SLAM system can fuse condensed information from those sensors effectively to mitigate positioning and orientation errors, even in a short-time GNSS denied environment. Full article