Nonholonomic Unicycle Research Articles

Universal Control for Both Rendezvous and Tracking of Multiple Nonholonomic Unicycles

This paper studies the universal control for multiple nonholonomic unicycles, i.e., finding a control law that allows for both rendezvous and tracking uses. The reduced-order approach and optimal technique are applied to design an exponential observer that estimates the leader's states. Using the observer signal, we convert the pose errors into the form of nonholonomic integrators and derive a local tracking control law. The obtained control law guarantees exponential convergence of tracking errors and maintains the solution trajectory of converted states in an invariant set. More importantly, the original pose error between each unicycle and the leader is proven exponentially convergent to zero, whether or not the leader satisfies persistency of excitation (PE) conditions. The extension of the proposed control algorithm to leader-following formation control is also illustrated. Numerical simulations validate the control design.

Comparative Study between Fuzzy Logic and Interval Type-2 Fuzzy Logic Controllers for the Trajectory Planning of a Mobile Robot

In this study, Fuzzy Logic (FL) and Interval Type-2 FL (IT-2FL) controllers were applied to a mobile robot in order to determine which method facilitates navigation and enables the robot to overcome real-world uncertainties and track an optimal trajectory in a very short time. The robot under consideration is a non-holonomic unicycle mobile robot, represented by a kinematic model, evolving in two different environments. The first environment is barrier-free, and moving the robot from an initial to a target position requires the introduction of a single action module. Subsequently, the same problem was approached in an environment closer to reality, with objects hindering the robot's movement. This case requires another controller, called obstacle avoidance. This system allows the robot to reach autonomously a well-defined target by avoiding collision with obstacles. The robustness of the structures of the defined controllers is tested in Matlab simulations of the studied controllers. The results show that the IT-2FL controller performs better than the FL controller.

Global formation control of nonholonomic unicycle vehicles with guaranteed rate of convergence

AbstractThis paper studies the full‐state formation control problem of multiple nonholonomic unicycle vehicles. Firstly, the formation error model is transformed into standard nonholonomic chained form, including orientation and position error subsystems. For orientation subsystem, an angular velocity control law is designed to be a cooperative term plus an exponential decay function of time, ensuring orientations reach an agreement on a common value. For position error subsystem, a time‐varying output‐like variable is carefully constructed to ensure a stable zero dynamics, that is, the consensus of these output variables guarantees position formation, overcoming the intrinsic underactuated control difficulty. Then, a linear velocity control law is derived to realize consensus of outputs. It is proved that the proposed distributed time‐varying controller is capable of steering the vehicles to globally exponentially make into desired geometric position shape with the same orientations and vanishing velocities, provided that the communication topology is directed and having a spanning tree. The calculated convergence rates are shown dependent on controller coefficients; thus, the controller is modified to additionally reach a prescribed rate of convergence by redesigning conditions of controller parameters. Finally, two numerical simulations are implemented for five unicycle vehicles, demonstrating the effectiveness of the proposed control scheme.

Normalized Extremum Seeking and Its Application to Nonholonomic Source Localization

A suitable normalization technique is introduced to improve the robustness properties of the conventional perturbation-based extremum seeking (ES). Following practical stability analysis, an appropriate expression is found for the normalization signal in the proposed normalized ES. Application of the proposed scheme in the source localization with nonholonomic unicycle has an additional advantage of ensuring that forward and angular velocities of the unicycle have a priori known bounds.

Fast convergence to Nash equilibria without steady-state oscillation

The problem of fast convergence to Nash equilibrium without steady state oscillation in static non-cooperative games with N players is considered in this paper. In this regard, players can generate their actions to achieve Nash equilibrium only by measuring their own payoff values, which means that the players do not need any information about the details of payoff function or other players’ actions. Additionally, in contrast to the most classical extremum seeking algorithms, this algorithm can converge to Nash equilibria without steady state oscillation and faster, because the amplitude of excitation sinusoidal signal in the conventional extremum seeking is adjusted to converge to zero, so the deleterious effects of steady state oscillation will be eliminated. Moreover, since each player can possess a dynamic, the actions are filtered before applying to the payoff function, which can make this algorithm appealing to many applications such as mobile sensor networks. In addition, the details of convergence to Nash equilibria are provided. Finally, we illustrate the application of this algorithm to solve the formation control problem of non-holonomic unicycles, and evasion of jammer attacks on unmanned autonomous vehicles (UAVs), which clearly shows the effectiveness and superiority of this algorithm through simulation results.

Formation-Tracking Control of Autonomous Vehicles Under Relaxed Persistency of Excitation Conditions

We present a smooth nonlinear time-varying formation-tracking controller for autonomous vehicles modeled as a nonholonomic unicycle. Our first result consists of a leader–follower tracking controller that guarantees uniform global asymptotic stability under the standing assumption that either the rotational or the translational reference velocity is persistently exciting. Then, we extend this result to the case of formation control of a swarm of vehicles. We show that this problem may be solved via decentralized tracking control, under the assumption that each robot communicates with one leader and one follower.

Multi‐vehicle formation in a controllable force field with non‐identical controller gains

In this brief, a non-identical gain based control design scheme is proposed to stabilise balanced collective formation in multi-vehicle systems, modelled with non-holonomic unicycle dynamics. Balanced collective formation refers to a situation in which the vehicles' motion causes their positional centroid to become stationary. This study mainly focuses on achieving stable balanced collective formation about the prescribed location of the collective centroid along with desired orientations of the vehicles. It is assumed that the vehicles are moving in a force field which is controlled externally. The proposed control algorithm consists of two controls - one of the controls, pertaining to the external force field, is directly applied to the system, and assumes the same value for all the vehicles. While the other control, which operates with heterogeneous gains, provides the steering force to the vehicles and is derived using Lyapunov analysis. Theoretical findings are validated through numerical simulations.

Rendezvous of multiple nonholonomic unicycles-based on backstepping

ABSTRACTRendezvous problem of nonholonomic unicycles has been considered in this paper and nonlinear distributed controllers based on backstepping are constructed to guarantee the consensus of both position and direction simultaneously. Cascaded theory of nonlinear system is utilised to reduce the rendezvous problem of nonholonomic unicycles to consensus problem of moving direction and consensus problem of position, respectively. The uncontrollable challenge of position system after consensus of moving direction has been successfully removed through dilated coordinate transformation. Then, a modified backstepping methodology based on the coupling structure of position system is derived to guarantee the consensus of each unicycle's position. In the end, not only consensus of position but also consensus of direction has been realised for multiple nonholonomic unicycles using the controllers proposed in this paper. Simulation results using Matlab illustrate the effectiveness of the results of this paper.

New Schemes for GPS-Denied Source Localization Using a Nonholonomic Unicycle

Inspired by the extremum seeking (ES) algorithm, new approaches for source localization in global positioning system denied environments are presented using a nonholonomic unicycle. Existing ES-based schemes apply an excitation signal that causes difficulties in the analysis and performance of the unicycle. The aim of this brief is to develop schemes without employing any excitation signal. To this end, two control schemes are developed for tuning the forward and angular velocities of the unicycle. The first scheme only tunes the forward velocity and is based on the conventional form of ES. In this form, a high-frequency excitation signal (dither) is employed to find the gradient of an unknown function that is optimized. The proposed scheme benefits from the fact that the dither part already exists in the unicycle model. The second scheme only tunes the angular velocity and is based on the recently developed form of ES. In this form, the function that is optimized appears as the argument of a sine/cosine function. The presented scheme takes the advantage from the fact that the sine/cosine function of this form of ES already exists in the vehicle model. Both schemes are structurally simple and significantly improve the unicycle motion. A stability analysis of the schemes is carried out using the averaging theory and their performances are illustrated through carefully studied simulation examples.

Bounded extremum seeking for angular velocity actuated control of nonholonomic unicycle

Summary We study control of the angular-velocity actuated nonholonomic unicycle, via a simple, bounded extremum seeking controller which is robust to external disturbances and measurement noise. The vehicle performs source seeking despite not having any position information about itself or the source, able only to sense a noise corrupted scalar value whose extremum coincides with the unknown source location. In order to control the angular velocity, rather than the angular heading directly, a controller is developed such that the closed loop system exhibits multiple time scales and requires an analysis approach expanding the previous work of Kurzweil, Jarnik, Sussmann, and Liu, utilizing weak limits. We provide analytic proof of stability and demonstrate how this simple scheme can be extended to include position-independent source seeking, tracking, and collision avoidance of groups on autonomous vehicles in GPS-denied environments, based only on a measure of distance to an obstacle, which is an especially important feature for an autonomous agent. Copyright © 2016 John Wiley & Sons, Ltd.

Control system of nonholonomic uniaxial wheeled module for monitoring geometry parameters of airfield pavements

We develop a control system of a nonholonomic measuring uniaxial wheeled module designed for monitoring the geometrical parameters of airfield pavements. Using a nonlinear approach, we synthesize a trajectory control subsystem based on a kinematic model of a nonholonomic unicycle locomotion control subsystem using the partial feedback linearization approach. We present the results of the numerical simulation of the synthesized control system with disturbances.

Discrete-time Stochastic Source Seeking via Tuning of Forward Velocity

We apply the method of discrete-time stochastic extremum seeking to navigate an autonomous vehicle towards the maximum of an unknown, spatially distributed signal field. We assume that the information of the vehicle's position is unavailable. Only using the measurement of the signal at the vehicle's location, we design a control law with controlling the forward velocity and keeping the angular velocity constant. We firstly build a discrete-time vehicle model by discretizing the model of a continuous nonholonomic unicycle with the help of the definition of integration. Then, we design a discrete-time control law in which a discrete-time ergodic stochastic process is taken as the probing signal.We prove local exponential convergence, both almost surely and in probability, to a small neighborhood near the source. A numerical simulation is given to illustrate the effectiveness of the control law.

A Single Forward-Velocity Control Signal for Stochastic Source Seeking With Multiple Nonholonomic Vehicles

With a single stochastic extremum seeking control signal, we steer multiple autonomous vehicles, modeled as nonholonomic unicycles, toward the maximum of an unknown, spatially distributed signal field. The vehicles, whose angular velocities are constant and distinct, travel at the same forward velocity, which is controlled by the stochastic extremum seeking controller. To determine the vehicles’ velocity, the controller uses measurements of the signal field at the respective vehicle positions and excitation based on filtered white noise. The positions of the vehicles are not measured. We prove local exponential convergence, both almost surely and in probability, to a small neighborhood near the source and provide a numerical example to illustrate the effectiveness of the algorithm.

CONTROL STRATEGIES FOR PLAYERS IN PURSUIT-EVASION GAMES BASED ON THEIR PREFERENCES

In this paper, a design of strategies for players in pursuit-evasion games, is provided. The design incorporates players' preferences captured in their goal functions which are constructed using particular functional forms that include multiattribute copulas. The approach provides closed-form strategies for the players governed by nonlinear models affine in control. A number of sufficient conditions based on differential inequalities for either evasion or capture is formulated. Finally, to demonstrate effectiveness of the proposed design, some illustrative simulations with players modeled as nonlinear and nonholonomic unicycles, are provided.

Approximate Steering of a Unicycle Under Bounded Model Perturbation Using Ensemble Control

This paper considers the problem of steering a nonholonomic unicycle despite model perturbation that scales both the forward speed and the turning rate by an unknown but bounded constant. We model the unicycle as an ensemble control system, show that this system is ensemble controllable, and derive an approximate steering algorithm that brings the unicycle to within an arbitrarily small neighborhood of any given Cartesian position. We apply our work to a differential-drive robot with unknown but bounded wheel radius and validate our approach with hardware experiments.

Nonlinear Stabilization Under Sampled and Delayed Measurements, and With Inputs Subject to Delay and Zero-Order Hold

Sampling arises simultaneously with input and output delays in networked control systems. When the delay is left uncompensated, the sampling period is generally required to be sufficiently small, the delay sufficiently short, and, for nonlinear systems, only semiglobal practical stability is generally achieved. For example, global stabilization of strict-feedforward systems under sampled measurements, sampled-data stabilization of the nonholonomic unicycle with arbitrarily sparse sampling, and sampled-data stabilization of LTI systems over networks with long delays, are open problems. In this paper, we present two general results that address these example problems as special cases. First, we present global asymptotic stabilizers for forward complete systems under arbitrarily long input and output delays, with arbitrarily long sampling periods, and with continuous application of the control input. Second, we consider systems with sampled measurements and with control applied through a zero-order hold, under the assumption that the system is stabilizable under sampled-data feedback for some sampling period, and then construct sampled-data feedback laws that achieve global asymptotic stabilization under arbitrarily long input and measurement delays. All the results employ “nominal” feedback laws designed for the continuous-time systems in the absence of delays, combined with “predictor-based” compensation of delays and the effect of sampling.

A Lie Bracket Approximation for Extremum Seeking Vehicles

AbstractIn this paper we propose a novel methodology for the analysis of autonomous vehicles seeking the extremum of an arbitrary smooth nonlinear map in the plane. By interpreting the extremum seeking schemes as input-affine systems with periodic excitations and by using the methodology of Lie brackets, we calculate a simplified system which approximates the qualitative behavior of the original one better than existing methods. By examining this approximate Lie bracket system, we are able to directly derive properties of the original one. Thus, by showing that the Lie bracket direction is directly related to the unknown gradient of the objective function we prove global uniform practical asymptotic stability of the extremum point for vehicles modeled as single integrators and non-holonomic unicycles. We illustrate the proposed method through simulations.

Collision-free control of mobile manipulators in a task space

This work offers the solution at the control feed-back level of the end-effector trajectory tracking problem for mobile manipulators subject to state equality and/or inequality constraints, suitably transformed into control dependent ones. Based on the Lyapunov stability theory, a class of controllers fulfilling the above constraints and generating a collision-free mobile manipulator trajectory with (instantaneous) minimal energy, is proposed. The problem of collision avoidance is solved here based on an exterior penalty function approach which results in continuous and bounded mobile manipulator controls even near boundaries of obstacles. The numerical simulation results carried out for a mobile manipulator consisting of a non-holonomic unicycle and a holonomic manipulator of two revolute kinematic pairs, operating both in a two-dimensional unconstrained task space and task space including the obstacles, illustrate the performance of the proposed controllers.

Trajectory Planning of Unicycle Mobile Robots With a Trapezoidal-Velocity Constraint

We propose an efficient stochastic scheme for minimum-time trajectory planning of a nonholonomic unicycle mobile robot under constraints on path curvature, velocities, and torques. This problem, which is known to be complex, often requires important runtimes, particularly if obstacles are present and if full dynamics is considered. The proposed technique is a fast variant of the random-profile approach recently applied to wheeled-mobile robots. It incorporates a trapezoidal-velocity-profile constraint that helps reduce the number of unknown parameters and that speeds up the calculation steps. Results are presented for two- and three-wheel mobile robots in free/constrained workspaces. A comparison with reference solutions, which were obtained independently, shows that the proposed variant is able to achieve almost the same quality of calculated trajectories while reducing the runtime considerably.

Stochastic source seeking for nonholonomic unicycle

We apply the recently introduced method of stochastic extremum seeking to navigate a nonholonomic unicycle towards the maximum of an unknown, spatially distributed signal field, using only the measurement of the signal at the vehicle’s location but without the measurement of the vehicle’s position. Keeping the forward velocity constant and controlling only the angular velocity, we design a stochastic source seeking control law which employs excitation based on filtered white noise, rather than sinusoidal perturbations used in the existing work. We study stability with the help of stochastic averaging theorems that we recently developed for general nonlinear continuous-time systems with stochastic perturbations. We prove local exponential convergence, both almost surely and in probability, to a small neighborhood near the source. We characterize the convergence speed explicitly and provide design guidelines for maximizing it, as well as for minimizing the residual set near the source. We present a detailed simulation study, including a study of the effect of saturation on the steering input.