Search Results (29)

Efficient autonomous exploration in unknown obstacle cluttered environments with interior obstacles remains a challenging task for mobile robots. In this work, we present a novel exploration process for a non-holonomic agent exploring 2D spaces using onboard LiDAR sensing. The proposed method generates velocity commands based on the calculation of the solution of an elliptic Partial Differential Equation with Dirichlet boundary conditions. While solving Laplace’s equation yields collision-free motion towards the free space boundary, the agent may become trapped in regions distant from free frontiers, where the potential field becomes almost flat, and consequently the agent’s velocity nullifies as the gradient vanishes. To address this, we solve a Poisson equation, introducing a source point on the free explored boundary which is located at the closest point from the agent and attracts it towards unexplored regions. The source values are determined by an exponential function based on the shortest path of a Hybrid Visibility Graph, a graph that models the explored space and connects obstacle regions via minimum-length edges. The computational process we apply is based on the Walking on Sphere algorithm, a method that employs Brownian motion and Monte Carlo Integration and ensures efficient calculation. We validate the approach using a real-world platform; an AmigoBot equipped with a LiDAR sensor, controlled via a ROS-MATLAB interface. Experimental results demonstrate that the proposed method provides smooth and deadlock-free navigation in complex, cluttered environments, highlighting its potential for robust autonomous exploration in unknown indoor spaces. Full article

Aiming at the problem that the pseudo-velocity measurement noise of non-holonomic constraints (NHCs) in the integrated navigation of vehicle-mounted a global navigation satellite system/inertial navigation system (GNSS/INS) is time-varying and thick-tailed in complex road conditions (turning, sideslip, etc.) and cannot be accurately predicted, an adaptive estimation method for the initial value of NHC lateral velocity noise based on multiple linear regression is proposed. On the basis of this method, a Gaussian Student’s T distribution variational Bayesian filtering algorithm (Ga-St VBAKF) based on NHC pseudo-velocity measurement noise modeling is proposed through modeling and analysis of pseudo-velocity measurement noise. Firstly, in order to adaptively adjust the initial value of NHC lateral velocity noise, a vehicle turning detection algorithm is used to detect whether the vehicle is turning. Secondly, based on the vehicle motion state, the variational Bayesian method is used to adaptively estimate the statistical characteristics of the measurement noise in real time based on modeling of the lateral velocity noise as Gaussian white noise or Student’s T distribution thick-tail noise. The test results show that compared to the traditional Kalman filtering algorithm with fixed noise, the Ga-St VBAKF algorithm with noise adaptation reduces the maximum horizontal position error by 65.9% in the GNSS/NHC/OD/INS (where OD stands for odometer and INS stands for inertial measurement unit) system when the vehicle is in a turning state, and by 42.3% in the NHC/OD/INS system. This indicates that the algorithm can effectively suppress the divergence of positioning errors during turning and improve the performance of integrated navigation. Full article

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

Equations of a heavy rotating body with one fixed point can be deduced starting from a variational problem with holonomic constraints. When applying this formalism to the particular case of a Lagrange top, in the formulation with a diagonal inertia tensor the potential energy has a more complicated form as compared with that assumed in the literature on dynamics of a rigid body. This implies the corresponding improvements in equations of motion. Therefore, we revised this case, presenting several examples of analytical solutions to the improved equations. The case of precession without nutation has a surprisingly rich relationship between the rotation and precession rates, which is discussed in detail. Full article

Euler–Poisson equations of a charged symmetrical body in external constant and homogeneous electric and magnetic fields are deduced starting from the variational problem, where the body is considered as a system of charged point particles subject to holonomic constraints. The final equations are written for the center-of-mass coordinate, rotation matrix and angular velocity. A general solution to the equations of motion is obtained for the case of a charged ball. For the case of a symmetrical charged body (solenoid), the task of obtaining the general solution is reduced to the problem of a one-dimensional cubic pseudo-oscillator. In addition, we present a one-parametric family of solutions to the problem in elementary functions. Full article

This paper studies a cooperative modeling framework to reduce the complexity in deriving the governing dynamical equations of complex systems composed of multiple bodies such as biped robots and unmanned aerial and ground vehicles. The approach also allows for an optimization-based trajectory generation for the complex system. This work also studies a fast–slow model predictive control strategy with task prioritization to perform docking maneuvers on cooperative systems. The method allows agents and a single agent to perform a docking maneuver. In addition, agents give different priorities to a specific subset of shared states. In this way, overall degrees of freedom to achieve the docking task are distributed among various subsets of the task space. The fast–slow model predictive control strategy uses non-linear and linear model predictive control formulations such that docking is handled as a non-linear problem until agents are close enough, where direct transcription is calculated using the Euler discretization method. During this phase, the trajectory generated is tracked with a linear model predictive controller and addresses the close proximity motion to complete docking. The trajectory generation and modeling is demonstrated on a biped robot, and the proposed MPC framework is illustrated in a case study, where a quadcopter docks on a non-holonomic rover using a leader–follower topology. Full article

The essence of biomimetics in human–computer interaction (HCI) is the inspiration derived from natural systems to drive innovations in modern-day technologies. With this in mind, this paper introduces a biomimetic adaptive pure pursuit (A-PP) algorithm tailored for the four-wheel differential drive robot (FWDDR). Drawing inspiration from the intricate natural motions subjected to constraints, the FWDDR’s kinematic model mirrors non-holonomic constraints found in biological entities. Recognizing the limitations of traditional pure pursuit (PP) algorithms, which often mimic a static behavioral approach, our proposed A-PP algorithm infuses adaptive techniques observed in nature. Integrated with a quadratic polynomial, this algorithm introduces adaptability in both lateral and longitudinal dimensions. Experimental validations demonstrate that our biomimetically inspired A-PP approach achieves superior path-following accuracy, mirroring the efficiency and fluidity seen in natural organisms. Full article

Complex and high-computational-cost algorithms are usually the state-of-the-art solution for autonomous driving cases in which non-holonomic robots must be controlled in scenarios with spatial restrictions and interaction with dynamic obstacles while fulfilling at all times safety, comfort, and legal requirements. These highly complex software solutions must cover the high variability of use cases that might appear in traffic conditions, especially when involving scenarios with dynamic obstacles. Reinforcement learning algorithms are seen as a powerful tool in autonomous driving scenarios since the complexity of the algorithm is automatically learned by trial and error with the help of simple reward functions. This paper proposes a methodology to properly define simple reward functions and come up automatically with a complex and successful autonomous driving policy. The proposed methodology has no motion planning module so that the computational power can be limited like in the reactive robotic paradigm. Reactions are learned based on the maximization of the cumulative reward obtained during the learning process. Since the motion is based on the cumulative reward, the proposed algorithm is not bound to any embedded model of the robot and is not being affected by uncertainties of these models or estimators, making it possible to generate trajectories with the consideration of non-holonomic constrains. This paper explains the proposed methodology and discusses the setup of experiments and the results for the validation of the methodology in scenarios with dynamic obstacles. A comparison between the reinforcement learning algorithm and state-of-the-art approaches is also carried out to highlight how the methodology proposed outperforms state-of-the-art algorithms. Full article

Using general fractional calculus (GFC) of the Luchko form and non-holonomic variational equations of Sedov type, generalizations of the standard action principle and first Noether theorem are proposed and proved for non-local (general fractional) non-Lagrangian field theory. The use of the GFC allows us to take into account a wide class of nonlocalities in space and time compared to the usual fractional calculus. The use of non-holonomic variation equations allows us to consider field equations and equations of motion for a wide class of irreversible processes, dissipative and open systems, non-Lagrangian and non-Hamiltonian field theories and systems. In addition, the proposed GF action principle and the GF Noether theorem are generalized to equations containing general fractional integrals (GFI) in addition to general fractional derivatives (GFD). Examples of field equations with GFDs and GFIs are suggested. The energy–momentum tensor, orbital angular-momentum tensor and spin angular-momentum tensor are given for general fractional non-Lagrangian field theories. Examples of application of generalized first Noether’s theorem are suggested for scalar end vector fields of non-Lagrangian field theory. Full article

In cooperative tasks, the ability to keep a kinematic relationship between the robots involved is essential. The main goal in this work is to design a synchronization control law for mobile manipulator robots (MMRs) considering a (2,0) differential mobile platform, which possesses a non-holonomic motion constraint. To fulfill this purpose, a generalized trajectory tracking control law based on the computed torque technique, for an MMR with n degrees of freedom, is presented. Using Lyapunov stability theory, it is shown that the closed loop system is semiglobal and uniformly ultimately boundedness (UUB) stable. To add position-level static coupling terms to achieve synchronization on a group of MMRs, the control law designed for the trajectory tracking problem is extended. Both experimental and numerical simulation results are presented to show the designed controllers performance. A successful experimental validation for the trajectory tracking problem using an 8 degrees of freedom (DoF) robot model (KUKA youBot) is depicted. Finally, numerical simulations in the CoppeliaSim environment are shown, which are used to test the synchronization control law made on the hypothetical scenario, where a two robot system has to manipulate an object over a parametric trajectory. Full article

In this work, we address the single robot navigation problem within a planar and arbitrarily connected workspace. In particular, we present an algorithm that transforms any static, compact, planar workspace of arbitrary connectedness and shape to a disk, where the navigation problem can be easily solved. Our solution benefits from the fact that it only requires a fine representation of the workspace boundary (i.e., a set of points), which is easily obtained in practice via SLAM. The proposed transformation, combined with a workspace decomposition strategy that reduces the computational complexity, has been exhaustively tested and has shown excellent performance in complex workspaces. A motion control scheme is also provided for the class of non-holonomic robots with unicycle kinematics, which are commonly used in most industrial applications. Moreover, the tuning of the underlying control parameters is rather straightforward as it affects only the shape of the resulted trajectories and not the critical specifications of collision avoidance and convergence to the goal position. Finally, we validate the efficacy of the proposed navigation strategy via extensive simulations and experimental studies. Full article

There are numerous prospects for automated unmanned forklifts in the fields of intelligent logistics and intelligent factories. However, existing unmanned forklifts often operate according to offline path planning first followed by path tracking to move materials. This process does not meet the needs of flexible production in intelligent logistics. To solve this problem, we proposed an optimized online motion planner based on the output of the state grid as the original path. Constraints such as vehicle kinematics; dynamics; turning restriction at the end of the path; spatial safety envelope; and the position and orientation at the starting point and the ending point were considered during path optimization, generating a precise and smooth trajectory for industrial forklifts that satisfied non-holonomic vehicle constraints. In addition, a new rapid algorithm for calculating the spatial safety envelope was proposed in this article, which can be used for collision avoidance and as a turning-angle constraint term for path smoothing. Finally, a simulation experiment and real-world tray-insertion task experiment were carried out. The experiments showed that the proposal was effective and accurate via online motion planning and the tracking of automated unmanned forklifts in a complicated environment and that the proposal fully satisfied the needs of industrial navigation accuracy. Full article

In this study, an XYθ position sensor is designed/proposed to realize the precise control of the XYθ position of a holonomic inchworm robot in the centimeter to submicrometer range using four optical encoders. The sensor was designed to be sufficiently compact for mounting on a centimeter-sized robot for closed-loop control. To simultaneously measure the XYθ displacements, we designed an integrated two-degrees-of-freedom scale for the four encoders. We also derived a calibration equation to decrease the crosstalk errors among the XYθ axes. To investigate the feasibility of this approach, we placed the scale as a measurement target for a holonomic robot. We demonstrated closed-loop sequence control of a star-shaped trajectory for multiple-step motion in the centimeter to micrometer range. We also demonstrated simultaneous three-axis proportional–integral–derivative control for one-step motion in the micrometer to sub-micrometer range. The close-up trajectories were examined to determine the detailed behavior with sub-micrometer and sub-millidegree resolutions in the MHz measurement cycle. This study is an important step toward wide-range flexible control of precise holonomic robots for various applications in which multiple tools work precisely within the limited space of instruments and microscopes. Full article

Thanks to their strong maneuverability and high load capacity, car-like robots with non-holonomic constraints are often used in logistics to improve efficiency. However, it is difficult to plan a safe and smooth optimal path in real time on the restricted narrow roads of the logistics park. To solve this problem, an optimization-based motion planning method inspired by the Timed-Elastic-Band algorithm is proposed, called Narrow-Roads-Timed-Elastic-Band (NRTEB). Three optimization modules are added to the inner and outer workflow of the Timed-Elastic-Band framework. The simulation results show that the proposed method achieves safe reversing planning on narrow roads while the jerk of the trajectory is reduced by 72.11% compared to the original method. Real-world experiments reveal that the proposed method safely and smoothly avoids dynamic obstacles in real time when navigating forward and backward. The motion planner provides a safer and smoother trajectory for car-like robots on narrow roads in real time, which greatly enhances the safety, robustness and reliability of the Timed-Elastic-Band planner in logistics parks. Full article

The feedback integrators method is improved, via the celebrated Dirac formula, to integrate the equations of motion for mechanical systems with holonomic constraints so as to produce numerical trajectories that remain in the constraint set and preserve the values of quantities, such as energy, that are theoretically known to be conserved. A feedback integrator is concretely implemented in conjunction with the first-order Euler scheme on the spherical pendulum system and its excellent performance is demonstrated in comparison with the RATTLE method, the Lie–Trotter splitting method, and the Strang splitting method. Full article