Search Results (37)

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

This paper extends the fractional calculus of variations to include generalized fractional derivatives with dependence on a given kernel, encompassing a wide range of fractional operators. We focus on variational problems involving the composition of functionals, deriving the Euler–Lagrange equation for this generalized case and providing optimality conditions for extremal curves. We explore problems with integral and holonomic constraints and consider higher-order derivatives, where the fractional orders are free. Full article

Velocity saturation constraints are a significant issue for wheeled mobile robots (WMRs) when designing kinematics-based control laws. To handle the problem of velocity saturation constraints, a novel monocular visual servoing controller is developed for WMRs to solve tracking problems and enable unknown depth estimation. By analyzing the kinematic model of the robot system and employing the homography decomposition technique, measurable signals are obtained to develop a visual tracking error model for non-holonomic mobile robots. To ensure that the velocity commands are consistently constrained within the allowed limits, a saturation function is employed in the designed visual servoing control law. Furthermore, an adaptive updating law is designed to estimate the unknown depth information. The boundedness of the velocity commands is analyzed to evaluate the saturation performance of the developed visual servoing controller. With the aid of Lyapunov techniques and Barbalat’s lemma, the stability of this scheme is demonstrated. The simulation and experiment verify the performance of the proposed method. Full article

The main objective of this work is to address problems related to the speed control of mobile robots with non-holonomic constraints and differential traction—specifically, robots for football games in the VSS (Very Small Size) category. To achieve this objective, an implementation and comparison is carried out between two control strategies: an adaptive control strategy by gain scheduling and a fuzzy multimodel intelligent control strategy. The mathematical models of the wheel motors for each operating range are approximated by a first-order system since data acquisition is performed using the step response. Tuning of the proportional and integral gains of the local controllers is carried out using the root locus technique in discrete time. For each mathematical model obtained for an operating range, a local controller is tuned. Finally, with the local controllers in hand, the implementation of and comparison between the gain scheduling adaptive control strategy and the fuzzy multimodel intelligent control strategy are carried out, in which the control strategies are programmed into the low-level code of a non-holonomic robot with a differential drive to verify the performance of the speed tracking dynamics imposed on the wheel motors to improve robot navigation during a robot football match. 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

Autonomous exploration in unknown environments is a fundamental problem for the practical application of unmanned ground vehicles (UGVs). However, existing exploration methods face difficulties when directly applied to UGVs due to limited sensory coverage, conservative exploration strategies, inappropriate decision frequencies, and the non-holonomic constraints of wheeled vehicles. In this paper, we present IB-PRM, a hierarchical planning method that combines Incremental B-splines with a probabilistic roadmap, which can support rapid exploration by a UGV in complex unknown environments. We define a new frontier structure that includes both information-gain guidance and a B-spline curve segment with different arrival orientations to satisfy the non-holonomic constraint characteristics of UGVs. We construct and maintain local and global graphs to generate and store filtered frontiers. By jointly solving the Traveling Salesman Problem (TSP) using these frontiers, we obtain the optimal global path traversing feasible frontiers. Finally, we optimize the global path based on the Time Elastic Band (TEB) algorithm to obtain a smooth, continuous, and feasible local trajectory. We conducted comparative experiments with existing advanced exploration methods in simulation environments of different scenarios, and the experimental results demonstrate that our method can effectively improve the efficiency of UGV exploration. 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

We have proposed an open-source holonomic mobile manipulator composed of the KUKA youBot holonomic mobile platform with four Swedish wheels and a stationary aboard six-degrees-of-freedom Kinova Jaco Gen 2H manipulator, and we have developed corresponding kinematic problems. We have defined forward and inverse analytic Jacobians and designed Jacobian algorithms of forward and inverse mobile manipulator kinematics. An experimental test conducted with the designed laboratory prototype of the investigated mobile manipulator with the described kinematics was used to verify the obtained theoretical results. The goal of the test was to keep constant the position of the gripper in 3D space while the mobile platform is moving to some extend in the 2D workspace. Full article

The trajectory or moving-target tracking feature is desirable, because it can be used in various applications where the usefulness of UAVs is already proven. Tracking moving targets can also be applied in scenarios of cooperation between mobile ground-based and flying robots, where mobile ground-based robots could play the role of mobile landing pads. This article presents a novel proposition of an approach to position-tracking problems utilizing artificial potential fields (APF) for quadcopter UAVs, which, in contrast to well-known APF-based path planning methods, is a dynamic problem and must be carried out online while keeping the tracking error as low as possible. Also, a new flight control is proposed, which uses roll, pitch, and yaw angle control based on the velocity vector. This method not only allows the UAV to track a point where the potential function reaches its minimum but also enables the alignment of the course and velocity to the direction and speed given by the velocity vector from the APF. Simulation results present the possibilities of applying the APF method to holonomic UAVs such as quadcopters and show that such UAVs controlled on the basis of an APF behave as non-holonomic UAVs during 90° turns. This allows them and the onboard camera to be oriented toward the tracked target. In simulations, the AR Drone 2.0 model of the Parrot quadcopter is used, which will make it possible to easily verify the method in real flights in future research. 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

By replacing the internal energy with the free energy, as coordinates in a “space of observables”, we slightly modify (the known three) non-holonomic geometrizations from Udriste’s et al. work. The coefficients of the curvature tensor field, of the Ricci tensor field, and of the scalar curvature function still remain rational functions. In addition, we define and study a new holonomic Riemannian geometric model associated, in a canonical way, to the Gibbs–Helmholtz equation from Classical Thermodynamics. Using a specific coordinate system, we define a parameterized hypersurface in ${\mathbb{R}}^4$ as the “graph” of the entropy function. The main geometric invariants of this hypersurface are determined and some of their properties are derived. Using this geometrization, we characterize the equivalence between the Gibbs–Helmholtz entropy and the Boltzmann–Gibbs–Shannon, Tsallis, and Kaniadakis entropies, respectively, by means of three stochastic integral equations. We prove that some specific (infinite) families of normal probability distributions are solutions for these equations. This particular case offers a glimpse of the more general “equivalence problem” between classical entropy and statistical entropy. Full article

The goal of this paper is to present the necessary and sufficient conditions that every extremizer of a given class of functionals, defined on the set $C^1[a,b]$, must satisfy. The Lagrange function depends on a generalized fractional derivative, on a generalized fractional integral, and on an antiderivative involving the previous fractional operators. We begin by obtaining the fractional Euler–Lagrange equation, which is a necessary condition to optimize a given functional. By imposing convexity conditions over the Lagrange function, we prove that it is also a sufficient condition for optimization. After this, we consider variational problems with additional constraints on the set of admissible functions, such as the isoperimetric and the holonomic problems. We end by considering a generalization of the fundamental problem, where the fractional order is not restricted to real values between 0 and 1, but may take any positive real value. We also present some examples to illustrate our results. Full article

The increasing demand for safe and efficient maritime transportation has underscored the necessity of developing effective path-planning algorithms for Unmanned Surface Vehicles (USVs). However, the inherent complexities of the ocean environment and the non-holonomic properties of the physical system have posed significant challenges to designing feasible paths for USVs. To address these issues, a novel path planning framework is elaborately designed, which consists of an optimization model, a meta-heuristic solver, and a Clothoid-based path connector. First, by encapsulating the intricate nature of the ocean environment and ship dynamics, a multi-objective path planning problem is designed, providing a comprehensive and in-depth portrayal of the underlying mechanism. By integrating the principles of the candidate set random testing initialization and adaptive probability set, an enhanced genetic algorithm is devised to fully exploit the underlying optimization problem in constrained space, contributing to the global searching ability. Accounting for the non-holonomic constraints, the fast-discrete Clothoid curve is capable of maintaining and improving the continuity of the path curve, thereby promoting strong coordination between the planning and control modules. A thorough series of simulations and comparisons conducted in diverse ocean scenarios has conclusively demonstrated the effectiveness and superiority of the proposed path planning framework. 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