Kinematic Modeling and Analysis of Skid-Steered Mobile Robots With Applications to Low-Cost Inertial-Measurement-Unit-Based Motion Estimation

Skid-steered mobile robots are widely used because of their simple mechanism and high reliability. Understanding the kinematics and dynamics of such a robotic platform is, however, challenging due to the complex wheel/ground interactions and kinematic constraints. In this paper, we develop a kinematic modeling scheme to analyze the skid-steered mobile robot. Based on the analysis of the kinematics of the skid-steered mobile robot, we reveal the underlying geometric and kinematic relationships between the wheel slips and locations of the instantaneous rotation centers. As an application example, we also present how to utilize the modeling and analysis for robot positioning and wheel slip estimation using only low-cost strapdown inertial measurement units. The robot positioning and wheel slip-estimation scheme is based on an extended Kalman filter (EKF) design that incorporates the kinematic constraints for accuracy enhancement. The performance of the EKF-based positioning and wheel slip-estimation scheme are also presented. The estimation methodology is tested and validated experimentally on a robotic test bed.     

Game-based pursuit evasion for nonholonomic wheeled mobile robots subject to wheel slips

Pursuit-evasion (P-E) problem has been studied as a noncooperative zero-sum game in homicidal chauffer problem in 1960s and in the game of two identical cars most recently. The capture conditions in the two games, which govern the capture behavior, can be determined by solving Hamilton–Jacobi–Isaacs equations. However, the existing game theoretic solution does not consider wheel slip, and consequently, cannot answer the escape and capture conditions in the presence of wheel slip. In this paper, we investigate how to predict capture and escape conditions when the pursuer has wheel slip. We study a dynamic P-E game problem with a nonholonomic wheeled mobile robot (WMR) pursuer subject to wheel slip and propose an equivalent kinematic model to develop escape and capture conditions in the presence of wheel slip. To our knowledge, this is the first time the P-E game problems with WMR have been analyzed with wheel slip. The presented framework will allow future development of realistic P-E strategies that do not ignore wheel slip and thus will be able to model high-speed P-E on different terrains.     

Gyro-based odometry associated with steering characteristics for wheeled mobile robot in rough terrain

Mobile robot used for planetary exploration performs several scientific missions over long distance travel and needs to have a high degree of autonomous mobility system because the communication delay from the Earth impedes its direct teleoperation. Localization of a mobile robot is of particular importance on the autonomous mobility. Classical localization methods such as wheel/visual odometry have been widely investigated and demonstrated, but they possess a well-known trade-off between computational cost and localization accuracy. This paper proposes an accurate gyro-based odometry method for a wheeled mobile robot in rough terrain. The robot in rough terrain is often subject to large wheel slip or vehicle sideslip related with its steering maneuver, and those slips degrade the localization accuracy. The basic approach of the proposed method is to exploit odometry data for the robot distance traveled as well as gyroscope data for the robot heading calculation; however each data-set is weighted in accordance with steering characteristics of a robot in rough terrain. The usefulness of the proposed method is examined through field experiments using a wheeled mobile robot testbed in Martian analog site. The experimental result confirms that the proposed method accurately estimates the robot trajectory.     

Switched Modeling and Task–Priority Motion Planning of Wheeled Mobile Robots Subject to Slipping

This study is devoted to the modelling and control of Wheeled Mobile Robots moving with longitudinal and lateral slips of all wheels. Due to wheel slippage we have to deal with systems with changing dynamics. Wheeled Mobile Robots can be thus modeled as switched systems with both autonomous switches (due to wheel slippage) and smooth controls (due to control algorithm). It is assumed that the slipping is counteracted by the slip reaction forces acting at contact points of the wheels with the ground. A model of these reaction forces, borrowed from the theory of automotive systems, has been adopted and included into the Lagrangian dynamic equations of the robot. A framework for designing motion planning schemes devoid of chattering effects for systems with changing dynamics is presented. A task–priority motion planning problem for wheeled mobile robots subject to slipping is addressed and solved by means of Jacobian motion planning algorithm based on the Endogenous Configuration Space Approach. Performance of the algorithm is presented in simulations of the Pioneer 2DX mobile platform. The robot dynamics equations are derived and 4 variants of motion are distinguished. The motion planning problem is composed of two sub-tasks: robot has to reach a desired point in the task space (proper motion planning) and the motion should minimize either the control energy expendinture or the wheel slippage. Performance of the motion planning algorithm is illustrated by a sort of the parking maneuver problem.     

Exploiting wheel slips of mobile robots to improve navigation performance

Improving navigation performance of autonomous wheeled mobile robot (WMR) in a dynamic unstructured environment requires improved maneuverability. In such cases, the dynamics of wheel slip may violate the ideal no-slip kinematic constraints generally used to model nonholonomic WMR. In this paper, a new method is proposed to tackle the modeling inadequacy that arises when slip is neglected by including both longitudinal and lateral slip dynamics into the overall dynamics of the WMR. This new model of the WMR provides a realistic simulation environment that can be utilized to develop model-based controllers to improve WMR navigation. In this paper, a dynamic planner with a path-following controller is designed to allow the WMR to navigate efficiently by autonomously regulating the generated traction force due to wheel slip. Extensive simulation results demonstrate the importance of the proposed modeling technique to capture slip phenomenon and the efficacy of the presented control technique to exploit such slip for better navigation performance.     

Kinematic modeling of wheeled mobile robots with slip

This work presents a kinematic modeling method for wheeled mobile robots with slip based on physical principles. First, we present the kinematic modeling of a mobile robot with no-slip considering four types of wheels: fixed, centered orientable, off-centered orientable (castor) and Swedish (also called Mecanum, Ilon or universal). Then, the dynamics of a wheeled mobile robot based on Lagrange formulation are derived and discussed. Next, a quasi-static motion is considered to obtain the kinematic conditions that provide the slip modeling equations. Several types of traction models for the slip between the wheel and the floor are indicated. In particular, for a frictional force linearly dependent on the sliding velocity, the no-slip kinematic equation of the wheeled mobile robot is related, through the weighted least-squares algorithm, with the slip modeling equations. To illustrate the applications of the proposed approach a tricycle vehicle is considered in a real situation. The experimental results obtained for the slip kinematic model are compared with the ones obtained for the well-known Kalman filter.     

A Dynamic-Model-Based Wheel Slip Detector for Mobile Robots on Outdoor Terrain

This paper introduces a model-based approach to estimating longitudinal wheel slip and detecting immobilized conditions of autonomous mobile robots operating on outdoor terrain. A novel tire traction/braking model is presented and used to calculate vehicle dynamic forces in an extended Kalman filter framework. Estimates of external forces and robot velocity are derived using measurements from wheel encoders, inertial measurement unit, and GPS. Weak constraints are used to constrain the evolution of the resistive force estimate based upon physical reasoning. Experimental results show the technique accurately and rapidly detects robot immobilization conditions while providing estimates of the robot's velocity during normal driving. Immobilization detection is shown to be robust to uncertainty in tire model parameters. Accurate immobilization detection is demonstrated in the absence of GPS, indicating the algorithm is applicable for both terrestrial applications and space robotics.      

Dynamic path tracking control of a vehicle on slippery terrain

This paper deals with accuracy and reliability for the path tracking control of a four wheel mobile robot with a double-steering system when moving at high dynamics on a slippery surface. An extended kinematic model of the robot is developed considering the effects of wheel–ground skidding. This bicycle type model is augmented to form a dynamic model that considers an actuation of the four wheels. Based on the extended kinematic model, an adaptive and predictive controller for the path tracking is developed to drive the wheels front and rear steering angles. The resulting control law is combined with a stabilization algorithm of the yaw motion which modulates the actuation torque of each four wheels, on the basis of the robot dynamic model. The global control architecture is experimentally evaluated on a wet grass slippery terrain, with speeds up to 7 m/s. Experimental results demonstrate enhancement of tracking performances in terms of stability and accuracy relative to the kinematic control.     

Adaptive motion control of wheeled mobile robot with unknown slippage

As a major representative nonholonomic system, wheeled mobile robot (WMR) is often used to travel across off-road environments that could be unstructured environments. Slippage often occurs when WMR moves in slopes or uneven terrain, and the slippage generates large accumulated position errors in the vehicle, compared with conventional wheeled mobile robots. An estimation of the wheel slip ratio is essential to improve the accuracy of locomotion control. In this paper, we propose an improved adaptive controller to allow WMR to track the desired trajectory under unknown longitudinal slip, where the stabilisation of the closed-loop tracking system is guaranteed by the Lyapunov theory. All system states use neural network online weight tuning algorithms, which ensure small tracking errors and no loss of stability in robot motion with bounded input signals. We demonstrate superior tracking results using the proposed control method in various Matlab simulations.     

Variable Structure Control of a Differentially Steered Wheeled Mobile Robot

This paper discusses dynamic modeling and robust control of a differentially steered mobile robot subject to wheel slip and external loads. Consideration of wheel slip and external loads is crucial for high load and/or high speed applications because they act as disturbances to the system. Furthermore, a tire model that adequately accounts for the tire/ground interaction is essential and Dugoff's pneumatic tire friction model is utilized herein in deriving the dynamic equations of motion of the mobile robot. It is shown that the dynamic equations satisfy the matching condition, and the variable structure control method is employed to design a tracking controller of the mobile robot. Numerical simulation shows the promise of the developed control algorithm.     

A novel method for non-linear control of wheel slip in anti-lock braking systems

Anti-lock braking system (ABS) provides active safety for vehicles during braking by regulation of the wheel slip at its optimum value. Due to the non-linear characteristics and model uncertainties in vehicle dynamics, a non-linear controller with increased robustness should be designed for ABS. In this paper, to achieve this aim, an optimization-based braking torque control law is developed for ABS using the prediction of the wheel slip response from a continuous non-linear vehicle dynamics model. To increase the robustness of the controller, the integral feedback technique is appended to the design method. The derived control law and its special cases are evaluated and discussed. At the end, the performance of the proposed controller is compared with that of a sliding mode controller, reported in the literature, through simulations of braking on dry and slippery roads. The simulation results indicate that, the wheel slip tracking error is remarkably decreased by the proposed controller. Moreover, the achieved control input is entirely smooth and suitable for implementation.     

Design and Testing of a 2-DOF Ball Drive

Omnidirectional mobile robots offer interesting features for industrial and service applications, in particular, when operating in tight spaces. Compared to car-like nonholonomic vehicles, they provide a higher degree of maneuverability, and often require less complex path planning and control schemes. Three different types of holonomic wheels that enable omnidirectional motion have been proposed in literature: universal, Mecanum, and ball wheel mechanisms. A problem commonly associated with the first two wheel types is that they induce vibrations in the system due to the discontinuous contact points. In this article, a ball wheel mechanism with superior features including slip measurement, free-wheel modus and attrition sensing is presented. The first prototype was built using additive manufacturing. The requirements for the design and possible improvements for future versions are discussed. Based on the presented ball wheel drive, a design for an omnidirectional mobile robot platform driven by three redundant ball wheel units is proposed. The velocity kinematic model of this mobile base is also addressed. Moreover, motion planning for an individual ball drive is demonstrated by means of an online trajectory generation scheme. The pseudocode of the trajectory planning algorithm implemented in LabVIEW is then presented. Finally, the motion characteristics of the ball drive mechanism are tested and its functionality is evaluated in detail. Measurements obtained from these tests show that the slip between the ball wheel and the ground can be estimated quite accurately. Hence, it is expected that these improved dead-reckoning estimates will result in a higher positioning accuracy of the final base.     

Intelligent adaptive model-based control of robotic dynamic systems with a hybrid fuzzy-neural approach

We describe in this paper a new method for adaptive model-based control of robotic dynamic systems using a new hybrid fuzzy-neural approach. Intelligent control of robotic systems is a difficult problem because the dynamics of these systems is highly nonlinear. We describe an intelligent system for controlling robot manipulators to illustrate our fuzzy-neural hybrid approach for adaptive control. We use a new fuzzy inference system for reasoning with multiple differential equations for model selection based on the relevant parameters for the problem. In this case, the fractal dimension of a time series of measured values of the variables is used as a selection parameter. We use neural networks for identification and control of robotic dynamic systems. We also compare our hybrid fuzzy-neural approach with conventional fuzzy control to show the advantages of the proposed method for control.     

Synthesis of the Resultant Force Position on a Radial Ply Tire of Off-Road Vehicle with a Comparative Trend Between Some Soft Computing Techniques

To obtain a qualitative understanding of tractive performance parameters, ride comfort, vibration control and the design of an off-road vehicle suspension system, it is essential to find the resultant force position on the wheel. To this aim, a soil bin facility assisted with a single-wheel tester was used for the synthesis of the objective parameter. Four levels of slip were induced to the wheel along with three levels of velocity and two wheel loads. The stochastic characteristic of soil–wheel interactions promoted the authors to apply two promising artificial intelligence approaches of artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) and compare the results with the statistical approach of multiple linear regression (MLR). Various structures of ANN and ANFIS tools were constructed to obtain the best representations. Two statistical performance criteria of mean squared error (MSE) and coefficient of determination \((R^{2})\) were employed to assess the potential of the constructed models. In view of the employed criteria, it was divulged that the supervised ANN outperformed the ANFIS model with MSE and \(R^{2}\) values of 0.02615 and 0.93628, respectfully, where ANFIS model yielded MSE and \(R^{2}\) values equal to 0.0439 and 0.8494, respectfully.     

Kinematic calibration for collaborative robots on a mobile platform using motion capture system

For modern robotic applications that go beyond the typical industrial environment, absolute accuracy is one of the key properties that make this possible. There are several approaches in the literature to improve robot accuracy for a typical industrial robot mounted on a fixed frame. In contrast, there is no method to improve robot accuracy when the robot is mounted on a mobile base, which is typical for collaborative robots. Therefore, in this work, we proposed and analyzed two approaches to improve the absolute accuracy of the robot mounted on a mobile platform using an optical measurement system. The first approach is based on geometric operations used to calculate the rotation axes of each joint. This approach identifies all rotational axes, which allows the calculation of the Denavit–Hartenberg (DH) parameters and thus the complete kinematic model, including the position and orientation errors of the robot end-effector and the robot base. The second approach to parameter estimation is based on optimization using a set of joint positions and end-effector poses to find the optimal DH parameters. Since the robot is mounted on a mobile base that is not fixed, an optical measurement system was used to dynamically and simultaneously measure the position of the robot base and the end-effector. The performance of the two proposed methods was analyzed and validated on a 7-DoF Franka Emika Panda robot mounted on a mobile platform PAL Tiago-base. The results show a significant improvement in absolute accuracy for both proposed approaches. By using the proposed approach with the optical measurement system, we can easily automate the estimation of robot kinematic parameters with the aim of improving absolute accuracy, especially in applications that require high positioning accuracy.     

Adaptive neuro-fuzzy wheel slip control

Due to complex and nonlinear dynamics of a braking process and complexity in the tire–road interaction, the control of automotive braking systems performance simultaneously with the wheel slip represents a challenging problem. The non-optimal wheel slip level during braking, causing inability to achieve the desired tire–road friction force strongly influences the braking distance. In addition, steerability and maneuverability of the vehicle could be disturbed. In this paper, an active neuro-fuzzy approach has been developed for improving the wheel slip control in the longitudinal direction of the commercial vehicle. The dynamic neural network has been used for prediction and an adaptive control of the brake actuation pressure, during each braking cycle, according to the identified maximum adhesion coefficient between the wheel and road surface. The brake actuation pressure was dynamically adjusted on the level that provides the optimal level of the longitudinal wheel slip vs. the brake pressure selected by driver, the current vehicle speed, the brake interface temperature, vehicle load conditions, and the current value of longitudinal wheel slip. Thus the dynamic neural network model operates (learn, generalize and predict) on-line during each braking cycle, fuzzy logic has been integrated with the neural model as a support to the neural controller control actions in the case when prediction error of the dynamic neural model reached the predefined value. The hybrid control approach presented here provided intelligent dynamic model – based control of the brake actuation pressure in order to keep the longitudinal wheel slip on the optimum level during a braking cycle.     

Evaluation of antilock braking system with an integrated model of full vehicle system dynamics

Antilock braking system (ABS), traction control system, etc. are used in modern automobiles for enhanced safety and reliability. Autonomous ABS system can take over the traction control of the vehicle either completely or partially. An antilock braking system using an on–off control strategy to maintain the wheel slip within a predefined range is studied here. The controller design needs integration with the vehicle dynamics model. A single wheel or a bicycle vehicle model considers only constant normal loading on the wheels. On the other hand, a four wheel vehicle model that accounts for dynamic normal loading on the wheels and generates correct lateral forces is suitable for reliable brake system design. This paper describes an integrated vehicle braking system dynamics and control modeling procedure for a four wheel vehicle. The vehicle system comprises several energy domains. The interdisciplinary modeling technique called bond graph is used to integrate models in different energy domains and control systems. The bond graph model of the integrated vehicle dynamic system is developed in a modular and hierarchical modeling environment and is simulated to evaluate the performance of the ABS system under various operating conditions.     

Neural network-based adaptive controller design of roboticmanipulators with an observer

A neural network (NN)-based adaptive controller with an observer is proposed for the trajectory tracking of robotic manipulators with unknown dynamics nonlinearities. It is assumed that the robotic manipulator has only joint angle position measurements. A linear observer is used to estimate the robot joint angle velocity, while NNs are employed to further improve the control performance of the controlled system through approximating the modified robot dynamics function. The adaptive controller for robots with an observer can guarantee the uniform ultimate bounds of the tracking errors and the observer errors as well as the bounds of the NN weights. For performance comparisons, the conventional adaptive algorithm with an observer using linearity in parameters of the robot dynamics is also developed in the same control framework as the NN approach for online approximating unknown nonlinearities of the robot dynamics. Main theoretical results for designing such an observer-based adaptive controller with the NN approach using multilayer NNs with sigmoidal activation functions, as well as with the conventional adaptive approach using linearity in parameters of the robot dynamics are given. The performance comparisons between the NN approach and the conventional adaptation approach with an observer is carried out to show the advantages of the proposed control approaches through simulation studies     

An approach to predict lower-order dynamic behaviors of a 5-DOF hybrid robot using a minimum set of generalized coordinates

This paper presents an effective semi-analytical approach for predicting lower-order dynamics of a five degrees-of-freedom (DOF) hybrid robot named TriMule, which is composed of a 3-DOF parallel mechanism plus a 2-DOF A/C wrist. In this method, the governing equations of motion of limbs within the parallel mechanism are first formulated by finite element analysis (FEA) and then reduced to super-element models. This is followed by exploiting a general stiffness model of multiple DOF joints connecting the super-elements. These two threads lead to the reduced dynamic model of the parallel mechanism while keeping the full set of lower-order modes retained. Finally, the dynamic model of entire system is established by merging the models of parallel mechanism and wrist. The computational results show that the lower-order natural frequencies, mode shapes of the entire system, and the frequency response functions (FRFs) of the robot tool center point (TCP) estimated by the proposed approach have very good agreement with those obtained by a full order FE model and experimental modal tests. The merits of this approach lie in that the established model allows the full set of lower-order dynamics of the entire system to be predicted effectively and accurately by only using fourteen generalized coordinates.     

轮子纵向打滑条件下的移动机器人自适应跟踪控制

针对纵向滑动参数未知的轮式移动机器人的轨迹跟踪问题,提出一种自适应跟踪控制策略.利用两个未知参数来描述移动机器人左右轮的纵向打滑程度,建立了产生纵向滑动的差分驱动轮式移动机器人的运动学模型;设计了补偿纵向滑动的自适应非线性反馈控制律;应用 Lyapunov 稳定性理论与 Barbalat 定理证明了闭环系统的稳定性;同时,提出了一种由极点配置方法在线调整控制器增益的方法.仿真结果验证了所提出控制方法的有效性.