The motion of wheeled robots

The equations of motion of three-wheeled robots with two drive wheels and one passive caster wheel are derived and investigated. The control of longitudinal motion and turns of such a robot is implemented by appropriate control of the independent motors of the drive wheels. The research is carried out under the assumption that the robot is moving on a horizontal plane surface and that the wheels do not slip. A system of two non-linear equations with two controls is obtained for the non-holonomic system considered. The dependence of the phase portrait on the values of the constant controls and parameters of the system, taking into account the asymmetry of the robot, is investigated. The results obtained are not only of theoretical but also of practical interest.     

Rapid fault-tolerant control prototyping for mobile robots

The main purpose of the paper is to present a fault-tolerant control system of an autonomous mobile robot. The authors present a framework for rapid prototyping of a behavior-based control system relying on tools and technologies of the Microsoft R Robotics Developer Studio. Fault detection and isolation is carried out with the help of the model-based and knowledge-based diagnostics. The first approach is developed by applying recurrent neural networks for residual generation and fuzzy logic for their evaluation. The second approach depends on scalar feature estimation and fuzzy reasoning. Basing on this information rules represented in the form of a decision table are applied for robot's behavior reconfiguration. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Discrete neural dynamic programming in wheeled mobile robot control

In this paper we propose a discrete algorithm for a tracking control of a two-wheeled mobile robot (WMR), using an advanced Adaptive Critic Design (ACD). We used Dual-Heuristic Programming (DHP) algorithm, that consists of two parametric structures implemented as Neural Networks (NNs): an actor and a critic, both realized in a form of Random Vector Functional Link (RVFL) NNs. In the proposed algorithm the control system consists of the DHP adaptive critic, a PD controller and a supervisory term, derived from the Lyapunov stability theorem. The supervisory term guaranties a stable realization of a tracking movement in a learning phase of the adaptive critic structure and robustness in face of disturbances. The discrete tracking control algorithm works online, uses the WMR model for a state prediction and does not require a preliminary learning. Verification has been conducted to illustrate the performance of the proposed control algorithm, by a series of experiments on the WMR Pioneer 2-DX.     

Sequentially switched fuzzy-model-based control for wheeled mobile robot with visual odometry

This study focused on the Takagi–Sugeno (T–S) fuzzy-model-based control design for the differentially-driven wheeled mobile robot with visual odometry. The position and posture of the mobile robot are estimated by visual odometry. The polar kinematic model of the mobile robot is exactly converted to the T–S fuzzy model and then the fuzzy control design is synthesized to the fuzzy model. The sequentially switched fuzzy control design includes turning, forward motion as well as position and posture control modes. The stabilization is guaranteed based on the Lyapunov stability criterion. The practical constraints on the visual odometry are also satisfied in the control design. Finally, the experiment results demonstrate the effectiveness of the fuzzy-model-based control design for the mobile robot with visual odometry.     

On quadratic stage costs for mobile robots in model predictive control

We consider nonholonomic mobile robots. Since the system is finite time controllable, it is stabilizable by a receding horizon control scheme with purely quadratic stage costs if an infinite optimization horizon is employed. However, due to the so called short-sightedness of model predictive control, these stability properties are not preserved if the control problem is only optimized on a truncated and, thus, finite prediction horizon — even if an arbitrarily large terminal weight is added. Hence, it is necessary to either incorporate structurally different terminal costs or use non-quadratic stage costs to appropriately penalize the deviation from the desired set point. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The control of a wheeled mechanical system

Non-holonomic systems with rolling or wheeled systems are investigated. The investigation is restricted to kinematic models and the dynamics of the drive mechanism of the system are taken into account. A control law is constructed which stabilizes the motion of a wheeled system along a specified trajectory (a plane smooth curve). For the basic variables of the system, the property of stabilizability is substantiated in the large.     

Neuro-fuzzy technique for navigation of multiple mobile robots

In this paper, navigation techniques for several mobile robots are investigated in a totally unknown environment. In the beginning, Fuzzy logic controllers (FLC) using different membership functions are developed and used to navigate mobile robots. First a fuzzy controller has been used with four types of input members, two types of output members and three parameters each. Next two types of fuzzy controllers have been developed having same input members and output members with five parameters each. Each robot has an array of sensors for measuring the distances of obstacles around it and an image sensor for detecting the bearing of the target. It is found that the FLC having Gaussian membership function is best suitable for navigation of multiple mobile robots. Then a hybrid neuro-fuzzy technique has been designed for the same problem. The neuro-fuzzy technique being used here comprises a neural network, which is acting as a pre processor for a fuzzy controller. The neural network considered for neuro-fuzzy technique is a multi-layer perceptron, with two hidden layers. These techniques have been demonstrated in simulation mode, which depicts that the robots are able to avoid obstacles and reach the targets efficiently. Amongst the techniques developed neuro-fuzzy technique is found to be most efficient for mobile robots navigation. Experimental verifications have been done with the simulation results to prove the authenticity of the developed neuro-fuzzy technique.     

Quantized-states-based adaptive control against unknown slippage effects of uncertain mobile robots with input and state quantization

An adaptive tracking design strategy based on quantized state feedback is developed for uncertain nonholonomic mobile robots with unknown wheel slippage effects. All state variables and control torques are assumed to be quantized by the state and input quantizers, respectively, in a network control environment. Thus, the quantized state feedback information is only available for the tracking control design. An approximation-based adaptive controller using quantized states is recursively designed to ensure the robust adaptive tracking against unknown wheel slippage effects where the quantized-states-based adaptive mechanism is derived to compensate for unknown wheel slippage effects, system nonlinearities, and quantization errors. The boundedness of the quantization errors and estimated parameters in the closed-loop system is analyzed by presenting some theoretical lemmas. Based on these lemmas, we prove the uniform ultimate boundedness of closed-loop signals and the convergence of the trajectory tracking error in the presence of wheel slippage effects. Simulations verify the effectiveness of the resulting tracking scheme.     

Fuzzy uncertainty modeling for grid based localization of mobile robots

This paper presents a localization method using fuzzy logic to represent the different facets of uncertainty present in sensor data. Our method follows the typical predict-update cycle of recursive state estimators to estimate the robot’s location. The method is implemented on a fuzzy position grid, and several simplifications are introduced to reduce computational complexity. The main advantages of this fuzzy logic method compared to most current ones are: (i) only an approximate sensor model is required, (ii) several facets of location uncertainty can be represented, and (iii) ambiguities in the sensor information are directly represented, thus avoiding having to solve the data association problem separately. Our method has been validated experimentally on two different platforms, a legged robot equipped with vision and a wheeled robot equipped with range sensors. The experiments show that our method can solve both the tracking and the global localization problem. They also show that this method can successfully cope with ambiguous observations, when several features may be associated to the same observation, and with robot kidnapping situations. Additional experiments are presented that compare our approach with a state-of-the-art probabilistic method.     

Bacterial memetic algorithm for offline path planning of mobile robots

The goal of the path planning problem is to determine an optimal collision-free path between a start and a target point for a mobile robot in an environment surrounded by obstacles. This problem belongs to the group of combinatorial optimization problems which are approached by modern optimization techniques such as evolutionary algorithms. In this paper the bacterial memetic algorithm is proposed for path planning of a mobile robot. The objective is to minimize the path length and the number of turns without colliding with an obstacle. The representation used in the paper fits well to the algorithm. Memetic algorithms combine evolutionary algorithms with local search heuristics in order to speed up the evolutionary process. The bacterial memetic algorithm applies the bacterial operators instead of the genetic algorithm??s crossover and mutation operator. One advantage of these operators is that they easily can handle individuals with different length. The method is able to generate a collision-free path for the robot even in complicated search spaces. The proposed algorithm is tested in real environment.     

Adaptive control of kinematically redundant robots

A redundant robot has more degrees of freedom than those neededto position the Robert end-effector uniquely. In a usual robotictask, only end-effector position trajectory is specified. Thejoint position trajectory is unknown, and it must be selectedfrom a self-motion manifold for a specified end-effector. Inmany situations, the robot dynamic parameters such as the linkmass, inertia, and joint viscous friction are unknown. The lackof knowledge of the joint trajectory and the dynamic parametersmake it difficult to control redundant robots. In this paper we show, through careful formulation of the problem,that the adaptative control of redundant robots can be addressedas a reference-velocity traking problem in the joint space.A control law ensures bounded estimation of the unknown dynamicparameters of the robot, and the convergence to zero of thevelocity traking error is derived. To ensure the joint motionon the self-motion manifold remains bounded, a homeomorphictransformation is found. This transformation decomposes thedynamics of the velocity tracking error into a cascade systemconsisting of the dynamics in the end-effector error coordinatesand the dynamics on the self-motion manifold. The dynamics onthe self-motion manifold is shown to be related to the conceptof zero dynamics. In the shown that, if the reference jointtrajectory is selected to optimize a certain type of objectivefunction, then stable dynamics on the self-motion manifold result.This ensures the overall stability of the adaptive system. Detailedsimulations are given to test the theoretical developments.The proposed adaptive scheme does not require measurements ofthe joint acceleration or the inversion of the inertia matrixof the robot.     

Optimal control of robots under stochastic uncertainty: robust feedback control

The most important aspect in the optimal control and design of manipulators is the determination of the basic movement, i.e. the calculation of the optimal trajectory on which the robot has to move. Having an optimal reference trajectory and an optimal open-loop control, there is the need of control corrections by applying a certain feedback control. Different attempts exist for this. In this article a method will be shown which is based on classical control theory, that works with cost functions being minimized. The aim is to take into account stochastic parameter variations in order to obtain robust optimal feedback controls. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A velocity observer design for tracking task-based motions of unicycle type mobile robots

The paper presents a design of a nonlinear velocity observer and its application within a model-based tracking control strategy for tracking task-based motions of unicycle type mobile robots. The strategy is the model reference tracking control strategy for programmed motion and it enables switching between controllers employed in it to improve a tracking precision as well as switching between coordinates used for modeling based on a type of a nonholonomic system. The strategy benefits by adding the velocity observer to its architecture due to the reduction of a number of measurements needed for feedback tracking.     

Robust control of multiple robots handling a constrained load

Multiple-robot systems are usually confronted with uncertainties,such as uncertainties in the manipulators and load parameters,and unmodelled dynamics. In this paper, the problem of controllingmultiple manipulators handling a constrained load is addressed.A reduced-order dynamic model of the system is first derived,and several properties of this model are established. Usingthe reduced-order model, a robust control law is proposed. Thiscontroller guarantees the uniform ultimate boundedness of theposition error, the internal-force error, and the constraint-forceerror. The proposed control law requires only the bounds onthe uncertainties of the parameters. Simulation results of twoplanar robots moving a load along a horizontal plane are givento illustrate the theoretical developments.     

Flexible-link robots with combined trajectory tracking and vibration control

This work deals with asymptotic trajectory tracking and active damping injection on a flexible-link robot by application of Multiple Positive Position Feedback. The flexible-link robot is modeled and validated by using finite element methods and experimental modal analysis, and then a reduced order model of the flexible-link robot dynamics, up to the first dominant vibration modes, is employed for experimental evaluation on a test rig. Then, a combined control scheme is synthesized in two parts: first, a Sliding-Mode Control based on a cascaded Proportional-Integral-Derivative for regulation and trajectory tracking tasks, via a direct current motor torque as the control input for the overall system dynamics, and, second, a Multiple Positive Position Feedback for active vibration control and attenuation of residual vibrations on the tip position, via the input voltage applied to a piezoelectric patch actuator attached directly on the flexible beam. The results are evaluated on an experimental platform, where the dynamic performance of the overall active vibration control scheme leads to fast and effective tracking results, with damping ratios increased up to 300%.     

The problem of coordination and consensus achievement in groups of autonomous mobile robots with limited communication

The paper considers a consensus seeking problem for a multirobot system with limited communication. Multirobot systems with limited communication are modelled as hybrid dynamical systems. The proposed model is a modification of some mathematical models introduced in physics and biology. We derive a necessary and sufficient condition for the system to converge to a single value of the coordination variable with probability 1.     

Switched control of a nonholonomic mobile robot

We present a switched control algorithm to stabilize a car-like mobile robot which possesses velocity level nonholonomic constraint. The control approach rests on splitting the system into several second-order subsystems and then stabilizing the system sequentially using finite-time controllers, finally resulting in the mobile robot being moved from one point to another point. State dependent switching control is employed in which the controllers switches on a thin surface in the state-space. Robustness analysis is presented by redefining the switching signal using relaxed switching surface. Both, non-robust and robust controllers are validated through numerical simulation.     

Tracking control of high-performance robots via stabilizing controllers for uncertain systems

The development of flexible manufacturing systems calls for industrial robots characterized by robustness of performance with regard to the variations of the loads and real time specification of the trajectory in the work space. In this paper, the design of a feedback controller guaranteeing such performance is considered. At first, the manipulator dynamics are embedded into a larger class of uncertain dynamical systems and a class of feedback controls is proposed that guarantees uniform ultimate boundedness of the tracking error. Successively, the methodology is specialized for the case of robotic manipulators to track trajectories described in task-oriented coordinates; the proposed control algorithm operates without requiring any explicit coordinate transformation.