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This paper presents the design and implementation of a SLAM-based online mapping and autonomous trajectory execution system for the Nimbulus-e, a concept vehicle designed for agile maneuvering in confined spaces. The Nimbulus-e uses individual steer-by-wire corner modules with in-wheel motors at all four corners. The associated eight joint variables serve as control inputs, allowing precise trajectory following. These control inputs can be derived from the vehicle’s trajectory using nonholonomic constraints. A LiDAR sensor is used to map the environment and detect obstacles. The system processes LiDAR data in real time, continuously updating the environment map and enabling localization within the environment. The inclusion of vehicle odometry data significantly reduces computation time and improves accuracy compared to a purely visual approach. The A* and Hybrid A* algorithms are used for trajectory planning and optimization, ensuring smooth vehicle movement. The implementation is validated through both full vehicle simulations using an ADAMS Car—MATLAB co-simulation and a scaled physical prototype, demonstrating the effectiveness of the system in navigating complex environments. This work contributes to the field of autonomous systems by demonstrating the potential of combining advanced sensor technologies with innovative control algorithms to achieve reliable and efficient navigation. Future developments will focus on improving the robustness of the system by implementing a robust closed-loop controller and exploring additional applications in dense urban traffic and agricultural operations.

As a universal principle in analytical mechanics, Gauss principle is characterized by its extremal property, which differs from other differential variational principles. Because of its universality and extreme properties, the Gauss principle is not only theoretically important, but also has great practical value, such as in robot dynamics, multi-body systems, approximate solutions to dynamics equations, etc. In this paper, the arbitrary-order Gauss principle is proposed and its application in nonholonomic mechanics is studied. Firstly, the concept of the space spanned by arbitrary-order derivative of acceleration is proposed, and Gauss principle of mechanical system with two-sided ideal constraints is established in this space. By defining the generalized compulsion function, it is proved that in the arbitrary-order derivative space of acceleration this function yields a stationary value along the path of real motion. Secondly, three kinds of arbitrary-order Gauss principles in generalized coordinates are derived. Thirdly, by constructing the generalized compulsion function of nonholonomic systems, the arbitrary-order Gauss principles are extended to nonholonomic systems, and Appell equations, Lagrange equations and Nielsen equations are derived.

In this paper, a visibility-based pursuit-evasion game in an environment with obstacles is addressed. A pursuer wants to maintain the visibility of an evader at all times. Both players are nonholonomic robots shaped like discs. To determine the players’ motion policies and their trajectories–subject to differential constraints–, an RRT* approach that minimizes the time traveled is utilized. The proposed formulation presents an alternative for computing a strategy of persistent surveillance of the evader, difficult to model from a classical differential games perspective given that there is no clear termination condition when the pursuer can maintain the evader’s visibility forever. A sufficient condition to keep evader surveillance is also provided. Additionally, the proposed approach is general because it can be adapted to address a variety of scenarios. To illustrate such flexibility, we address different aspects of the problem: (1) Knowledge of the environment (availability of a global map vs. a local representation). (2) Strategies of the players (execution of optimal strategies vs. deviations from the optimal ones to deceive the opponent). (3) Sensor capabilities (limited vs. unlimited sensor range).

In this paper, we survey our recent results on the variational formulation of nonequilibrium thermodynamics for the finite-dimensional case of discrete systems, as well as for the infinite-dimensional case of continuum systems. Starting with the fundamental variational principle of classical mechanics, namely, Hamilton’s principle, we show, with the help of thermodynamic systems with gradually increasing complexity, how to systematically extend it to include irreversible processes. In the finite dimensional cases, we treat systems experiencing the irreversible processes of mechanical friction, heat, and mass transfer in both the adiabatically closed cases and open cases. On the continuum side, we illustrate our theory using the example of multicomponent Navier–Stokes–Fourier systems.

The problem of flocking and formation of a group of nonholonomic wheeled mobile robot is addressed in this paper. Based on the cascade structure of the kinematic model, two kinematic controllers are proposed to achieve formation and flocking behaviors. The proposed control laws present a P and PI-like structure plus a feedforward term and do not require complex calculations. The interaction between the robots is modeled using graph theory. The performance of the proposed control laws is validated by experimental tests on a group of four differential-drive wheeled mobile robots.

Multistability is an area of interest in robotics and locomotion because the ability to achieve multiple configurations or generate multiple gaits allows a single robotic or mechanical system to perform versatile tasks. This multistability is often achieved by adding multistable elements to the system. However, this work finds that two bodies pinned together with a linear rotational spring can exhibit multistable behavior with the introduction of a nonholonomic constraint. Multistable fixed points of the unforced and undamped system are found to correspond to multistable limit cycles with the introduction of damping and periodic forcing, some of which result in fast net turning. This finding has potential implications in understanding the sharp turns executed by biological swimmers and could be exploited to perform efficient turns in low degree of actuation robots.

Modeling of dynamic systems with nonholonomic constraints usually involves constraint multipliers. Consequently, the dynamic equations in the laboratory coordinate system have a complex form, and as a result, the corresponding numerical algorithms need to be improved in terms of both efficiency and accuracy. This paper addresses establishing the mathematical model of the hydrodynamic sleigh in the Hamel framework. Firstly, the Lie symmetry and the Noether theorem conserved quantities of classic Chaplygin sleigh in which the inertial frame is reviewed. Based on the symmetries and the nonholonomic constraints, the frame of the sleigh can be directly realized in the algebraic space. Based on the mutual coupling mechanism between the fluid and the sleigh in a potential flow environment, the reduced equations in the moving frame are proposed in nonintegrable constraint distributions. The corresponding Hamel integrator is constructed based on the discrete variational principle. For the sleigh model in potential flow, the Hamel integrator is used to verify the feasibility of parameter control based on rotation angles and mass distribution, and to obtain the dynamic characteristics of the sleigh blade with both a rotational offset and translational offset. Numerical results indicate that the modeling method in the Hamel framework provides a more concise and efficient approach for exploring the dynamic behavior of the hydrodynamic sleigh.

This paper studies a model predictive hybrid tracking control scheme under a multiple harmonics time‐varying disturbance observer for a discrete‐time dynamics nonholonomic autonomous mobile robot (AMR) with disturbance. To solve the robust tracking control problem of the AMR and unmanned aerial vehicle (UAV) air–ground cooperative, a hybrid tracking control strategy combined with improved model predictive control (MPC) method is presented. First, a time‐varying air‐ground cooperative tracking control model based on the nonholonomic constraints AMR and UAV is established by polar coordinate transformation. Second, to estimate disturbances of the time‐varying model, a multiple harmonics disturbance observer with time‐varying gains is designed. A hybrid tracking control scheme for the AMR based on the estimated states and MPC method with relaxing factor and kinematics constraints is proposed. Finally, experimental results show the effectiveness of the proposed control strategy. A time‐varying air‐ground cooperative tracking control model had been presented. A multiple harmonics disturbance observer with time‐varying gains had been designed for cooperative tracking. A hybrid tracking control scheme had been solved by improved MPC method with relaxing factor.

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.

The control and motion planning of bioinspired swimming robots is complicated by the fluid–robot interaction, which is governed by a very high (infinite)-dimensional nonlinear system. Many high-dimensional nonlinear systems, often have low-dimensional attractors. From the perspective of swimming robots, such low-dimensional attractors simplify the analysis of the mechanics of swimming and prove to be useful to design controllers. This paper describes such a low-dimensional model for the swimming of a class of robots that are propelled by the motion of an internal reaction wheel. The model of swimming on a low-dimensional attractor is itself motivated by recent work on the dissipative Chaplygin sleigh, a well-known nonholonomic system, that exhibits limit cycle dynamics. We show that the governing equations of the Chaplygin sleigh are a very useful surrogate model for the swimming robot. The Chaplygin sleigh model is used to demonstrate certain maneuvers by the robot through computations. Experiments with such a robot provide evidence of limit cycle dynamics. Computational models based on discrete-point vortex–body interaction confirm this behavior. Our work also suggests that there is a close phenomenological and mathematical similarity between the dynamics of swimming robots and those of ground-based nonholonomic robots, which could motivate the development of very low-dimensional mathematical models for the motion of other fish-like swimming robots.