Slip Ratio Estimation Research Articles

Sequential track fusion in multi-sensor networks of unscented Kalman filters: A case of slip estimation in planetary mobile robots

Accurate wheel slip estimation facilitates Wheeled Mobile Robots (WMRs) with improved localization and traversability monitoring which are crucial to their autonomy in challenging planetary environments. Although distributed track-level fusion offers better computational efficiency, often sensor-level fusion is adopted in slip estimators of planetary rovers. Extending upon our earlier work, we develop a novel explicit track-to-track fusion algorithm for multi-sensor networks of unscented Kalman filters that has immediate application to slip ratio estimation in WMRs. The algorithm demonstrates better consistency compared to the existing fusion techniques since it implements a sub-optimal fusion rule to sequentially combine local tracks. It also saves computational power due to the recursive propagation of cross-covariance matrices based on the statistical linearization technique, instead of performing online optimizations. We prove that this recursion only requires the information of the first and last tracks in a sequence if all local tracks are unbiased. We rigorously study various key properties of the developed fusion algorithm and show its superior level of confidence when compared to the two prominent fusion methods of sequential and batch covariance intersection. The slip ratio estimation in a six-wheel WMR is considered as a case study, where the steerable wheel sets act as a network of sensors. The proposed slip estimator works based on the rigid body kinematics and readings of purely proprioceptive sensors, i.e., an inertial measurement unit and encoders. The slip estimator’s performance is evaluated in a high-fidelity software-in-the-loop simulation environment connecting MATLAB and CM Lab’s Vortex Studio software. In a comparison study that considers four rival strategies, we show the superiority of the proposed fusion method offering a balance between consistency, accuracy, and speed in real-time slip estimations.

Slip ratio adaptive control for distributed drive electric vehicle based on wheel speed

Aiming at the problems of poor control effect and poor robustness for distributed drive electric vehicles driving on complex and changeable roads, this paper proposes a slip ratio adaptive control method based on wheel speed. Firstly, an optimal slip ratio estimator considering axle load transfer was developed by analyzing the single-wheel dynamics of the vehicle and based on the Burckhardt tire model. Secondly, a cubic polynomial function is used to fit and optimize the optimal slip ratio-peak adhesion coefficient curve, which effectively improves the accuracy of obtaining the optimal slip ratio. Then, a conditional integral sliding mode controller based on wheel speed is designed in order to enhance the transient characteristics of the sliding mode control, to avoid integral saturation, and to improve the control effect of the sliding ratio controller in the low speed start-up phase. Finally, three typical working conditions, namely single road, flat road, and slip road, were established for simulation and experimental validation. The results show that the method in this paper is able to estimate the optimal slip ratio of the road in real time, realize the wheel slip ratio adaptive control, and improve the dynamic performance and lateral stability of distributed drive electric vehicle.

Slip Ratio Adaptive Control Based on Wheel Angular Velocity for Distributed Drive Electric Vehicles

In order to solve the adaptability problem of acceleration slip regulation for distributed drive electric vehicles, a slip ratio adaptive control strategy based on wheel angular velocity is proposed. The principle of road estimation algorithm based on the Burckhardt tire model is analyzed, and an improved estimation principle for optimal slip ratio is designed to improve the speed and accuracy of optimal slip ratio estimation. A slip ratio control strategy based on a conditional integral sliding mode control is designed, and its stability is proven. To make the slip ratio control strategy have better practicability, the slip ratio control strategy is combined with the road estimation algorithm, and the control variable of the slip ratio adaptive control strategy based on a conditional integral sliding mode control is redesigned to obtain a faster vehicle dynamic response. Finally, the effectiveness of the designed road estimation algorithm and the slip ratio adaptive control strategy is verified by simulation of acceleration on joint road and split road. Results show that the designed road estimator can obtain the road adhesion coefficient and optimal slip ratio quickly and accurately; the slip ratio adaptive controller, based on a conditional integral sliding mode control, can maintain the wheel slip ratio near the optimal slip ratio and reduce the steady-state error of the wheel slip ratio.

Slip ratio estimation of electric wheels based on tire force and road conditions

The independently controlled electric wheels of distributed drive vehicles provide faster and more accurate actuators for vehicle slip ratio control. Meanwhile, the estimation of the slip ratio of electric wheels has been of vital importance for the dynamics control of distributed drive electric vehicles. However, the conventional slip ratio estimation method is hard to accurately estimate the slip ratio under steering conditions without multiple observations, increasing the cost and introducing errors. Considering that the output torque and motor rotation rate of electric wheels can be accurately collected, the novel slip ratio estimation method takes advantage of the signals of the electric wheels and requires fewer vehicle sensors. Based on the torsional vibration model of electric wheel, the slip ratio estimation method was proposed and validated by simulations and experiments. With the drum dynamometer, the slip ratio estimation method was applied to a single electric wheel for testing, proving the feasibility and accuracy of the proposed method. The slip ratio estimation was finally applied to a fuel cell heavy truck for road tests, of which the results show that the error index is reduced from 0.0152 to 0.0064 compared to the conventional slip ratio estimation method, confirming the good estimation performance achievable via the proposed method.

A Model Predictive Control Approach With Slip Ratio Estimation for Electric Motor Antilock Braking of Battery Electric Vehicle

In this article, based on the estimation of optimal slip ratio, a model predictive control approach is proposed for the antilock braking system with motor of a battery electric vehicle. A wheel dynamics model with a virtual control quantity is established. A method for estimating the optimal slip ratio of different roads is introduced, which consists of a sliding mode observer for longitudinal braking force and a recognizer of slip ratio. A ground slip map that describes the relationship between slip ratio and ground adhesion coefficient is proposed, which is utilized to identify the optimal slip ratio. Based on the model predictive control algorithm, a braking torque controller is designed to track the optimal slip ratio for good performance of braking stability and security. The vehicle control unit embedded with the estimator and model predictive control law is tested in a battery electric vehicle on the dry and wet roads. The experimental results indicate that the proposed approach has a good performance for the estimation and control of slip ratio during the antilock braking with electric motor, especially suitable for the low adhesion road conditions.

Direct tire slip ratio estimation using intelligent tire system and machine learning algorithms

Accurate estimation of the tire slip ratio is critical for vehicle safety, as it is necessary for vehicle control purposes. In this paper, an intelligent tire system is presented to develop a novel slip ratio estimation model using machine learning (ML) algorithms. The accelerations, generated by a triaxial accelerometer installed onto the inner liner of the tire, are varied when the tire rotates to update the contact patch. Meanwhile, the reference value of slip ratio can be measured by the MTS Flat-Trac tire test platform. Then, by analyzing the variation between the accelerations and slip ratio, highly useful features are discovered, which are especially promising for assessing vertical acceleration. For these features, ML algorithms are trained to build the slip ratio estimation model, in which the ML algorithms include artificial neural networks (ANNs), gradient boosting machines (GBMs), random forests (RFs), and support vector machines (SVMs). Finally, the estimated NRMS errors are evaluated using 10-fold cross-validation (CV). The proposed estimation model is able to estimate the slip ratio continuously and stably using only the acceleration from the intelligent tire system, and the estimated slip ratio range can reach 30%. The estimation results have high robustness to vehicle velocity and load, where the best NRMS errors can reach 4.88%. In summary, the present study with the fusion of an intelligent tire system and machine learning paves the way for the accurate estimation of the tire slip ratio under different driving conditions, which creates new opportunities for autonomous vehicles, intelligent tires, and tire slip ratio estimation.

Integrated control of braking and steering systems to improve vehicle stability based on optimal wheel slip ratio estimation

Integrated control of braking and steering systems to improve vehicle stability based on optimal wheel slip ratio estimation

A control strategy for efficient slip ratio regulation of a pneumatic brake system for commercial vehicles

This paper presents a control strategy for efficient slip ratio regulation of a pneumatic brake system for commercial vehicles. A model-based estimator for brake pressure estimation has been developed. The braking torque applied to the wheel has been computed using the estimated brake pressure for the control of the wheel slip both in braking and traction situations. The vehicle velocity and wheel slip ratio estimation algorithms have been designed using only wheel speed sensors. The proposed slip regulation algorithm has also been successfully implemented for the antilock braking system (ABS) and traction control system (TCS). In ABS, the slip ratio and wheel acceleration are stabilized by a limit cycle control of the braking pressure. The TCS has been implemented by combining engine torque control and pneumatic brake pressure control. The brake controller is based on the valve switched control that incorporates the wheel dynamics and valve on/off characteristics. The ABS and TCS algorithms are integrated into the slip regulation algorithm to reduce the computation load of an Electrical Control Unit (ECU). Four-wheel independent slip monitoring and slip ratio control algorithms have been implemented on the ECU, and their performance has been investigated via both computer simulations and vehicle tests. Both results show that the proposed algorithms enhance the acceleration and braking performance without vehicle acceleration information. Moreover, the proposed split-mu strategy has improved the lateral stability during braking, and the acceleration performance during accelerating on the split-mu road. It has been shown via vehicle tests that, compared to the reference commercial algorithm, the braking distance was reduced by more than 4% on the split-mu and low-mu roads, and the acceleration performance was improved by 7.9% on the split-mu road.

Adaptive slip ratio estimation for active braking control of high-speed trains

Active braking control systems in high-speed trains are vital to ensure safety and are intended to reduce brake distances and prevent the wheels from locking. The slip ratio, which represents the relative difference between the wheel speed and vehicle velocity, is crucial to the design and successful implementation of active braking control systems. Slip ratio estimation and active braking control are challenging owing to the uncertainties of wheel–rail adhesion and system nonlinearities. Therefore, this paper proposes a novel adaptive slip ratio estimation approach for the active braking control based on an improved extended state observer. The extended state observer is developed through the augmentation of the system state-space to estimate the unmeasured train states as well as the model uncertainty. The accurate slip ratio is estimated using the observed extended states. Furthermore, the adaptability of the observer is improved by introducing the beetle antennae search algorithm to determine the optimal observer parameters. Finally, a feedback linearization braking control law is established to stabilize the closed-loop system due to its potential in coping with nonlinearities, which benefits the proven theoretical bounded stability. Experimental results validate the effectiveness of the proposed method.

Behavior of slip ratio during subcooled flow boiling in a vertical tube: A CFD approach

Slip ratio can be readily measured in an adiabatic two-phase flow experiment. However, in the flow boiling experiments, as the phase velocities keep varying, the estimation of slip ratio becomes difficult. In the absence of reliable methodology, the slip ratio for boiling flows is either taken simply as unity or deduced from void fraction experiments. It is noticed in literature that the experimental results reveal the effects of pressure and mass flux on void fraction and hence slip ratio. In the present work, numerical simulations to estimate slip ratio are carried out based on a well established wall boiling model. The computationally obtained void fraction values for subcooled boiling conditions in the vertical tube are verified with the available experimental data. The effect of operating variables, such as the tube diameter, the inlet mass flux and the degree of subcooling, on the variation of slip ratio is presented. The results show that the values of slip ratio vary along the length of the tube. A new correlation is proposed relating slip ratio with the thermodynamic quality, implicitly taking into account the effect of length and the operating conditions.

이륜 역진자 주행 로봇의 자세제어 성능 향상을 위한 슬립방지 제어기 설계

When a two-wheeled inverted pendulum (TWIP)-type personal transporter is driven on slippery or low-friction surfaces or experiences abrupt friction changes of the ground, its postural stability is difficult to maintain using conventional control schemes. Hence, in order to improve the driving performance of TWIPs in an uneven friction environment, an extra compensation technique must be established to maintain the appropriate traction force of the two driving wheels and avoid excessive wheel slips. In this paper, we give a detailed analysis on the TWIP vehicle behavior under various low-traction conditions and suggest an easy-to-apply antislip control algorithm based on the slip-ratio estimation. The simulation results demonstrate the effectiveness of the proposed control method.

Monocular Vision-based Estimation of Wheel Slip Ratio for Planetary Rovers in Soft Terrain

Monocular Vision-based Estimation of Wheel Slip Ratio for Planetary Rovers in Soft Terrain

Simple discrete time traction control for a two-wheeled mobile robot

Traction controls usually need dynamic parameters as an approximated reference in the model, such as inertia and friction or heavily computational estimator, such as slip ratio estimator and friction estimator. This paper is shown that the dynamic parameters in the traction controller can be negligible in some cases, internal sensor state variables and gain parameters are enough to retain some traction controllability. The controller is derived from the model following control method (MFC) on a discrete domain. Experiments are performed, in order to evaluate the efficiency of the simplified controller using a two-wheeled mobile robot, by comparing slippage between the position and velocity control scheme with and without the traction control scheme. The experimental results show that the proposed traction control scheme is able to suppress the slip and very simple to implement.

Adaptive optimal slip ratio estimator for effective braking on a non-uniform condition road

ABSTRACTIn this paper, an adaptive algorithm is developed which senses the road condition change and estimates a (time-varying) optimal braking slip ratio. This is conducted by two on-line simultaneously operating tire-road friction-curve slope calculators: one based on the accelerometer output and the other based on the wheel speed. The required vehicle speed is estimated using a robust sliding-mode observer. Enforcement of the online optimal braking reference is left to an adaptive sliding mode controller to cope with the system strong nonlinearity, time dependency and the speed and friction-coefficient estimation errors. The algorithm is applied to a half model car and the braking performance is examined. The results indicate that the proposed algorithm substantially reduces the stopping time and distance. The performance of the algorithm is verified using different vehicle initial speeds and especially non-uniform road condition where 8% improvement versus the nonadaptive optimal slip ratio algorithm is recorded.

Enhanced Sliding Mode Control and Online Estimation of Optimal Slip Ratio for Railway Vehicle Braking Systems

This paper proposes an optimal anti-locking control scheme so as to improve the braking performance of railway vehicles. The controlling effect of sliding mode control is improved, and the optimal slip ratio is achieved by extreme seeking algorithm. Firstly, a substitute function for the conventional sign function is proposed. Secondly, a closed loop observer for braking systems is used to enhance the estimation value of adhesion force, which can also be used for calculating reference speed. Finally Sliding Mode Controlbased controller needs to be entered a reference slip ratio called optimal slip ratio, which is searched by extreme seeking algorithm from the functional relationship between slip ratio and friction coefficient. Thus, the maximum adhesion is achieved despite wheel/ rail surface changes. The simulation result demonstrates the effect of real-time adjustment for braking torque, which guarantees the braking performance.

Antilock braking control system for electric vehicles

In recent years, brushless DC motors (BLDCMs) have replaced brushed DC motors in the design of electric scooters (ESs). This study proposes a new antilock braking system (ABS) based on a slip ratio estimator for ES utilising the braking force generated by the BLDCM when electrical energy is released to the virtual load, yielding an effect analogous to the ABS control in gas-powered vehicles. Compared with mechanical ABS, the proposed design possesses the advantage of rapid torque responses because no mechanical parts needed. Current control design is used to adjust the braking torque, and the sliding-mode control strategy is adopted to regulate the slip ratio to attain the optimal road adhesion during emergency braking. A variety of experiments are conducted for functional and performance verification.

Tracking control of WMRs on loose soil based on mixed H2/H∞ control with longitudinal slip ratio estimation

Wheeled mobile robots (WMRs) often suffer from the longitudinal slipping when moving on the loose soil of the surface of the moon during exploration. Longitudinal slip is the main cause of WMRs' delay in trajectory tracking. In this paper, a nonlinear extended state observer (NESO) is introduced to estimate the longitudinal velocity in order to estimate the slip ratio and the derivative of the loss of velocity which are used in modelled disturbance compensation. Owing to the uncertainty and disturbance caused by estimation errors, a multi-objective controller using the mixed H2/H∞ method is employed to ensure the robust stability and performance of the WMR system. The final inputs of the trajectory tracking consist of the feedforward compensation, compensation for the modelled disturbances and designed multi-objective control inputs. Finally, the simulation results demonstrate the effectiveness of the controller, which exhibits a satisfactory tracking performance.

Interaction of In-wheel permanent magnet synchronous motor with tire dynamics

Drive wheel systems combined with the in-wheel permanent magnet synchronous motor (I-PMSM) and the tire are highly electromechanical-coupled. However, the deformation dynamics of this system, which may influence the system performance, is neglected in most existing literatures. For this reason, a deformable tire and a detailed I-PMSM are modeled using Matlab/Simulink. Furthermore, the influence of tire/road contact interface is accurately described by the non-linear relaxation length-based model and magic formula pragmatic model. The drive wheel model used in this paper is closer to that of a real tire in contrast to the rigid tire model which is widely used. Based on the near-precise model mentioned above, the sensitivity of the dynamic tire and I-PMSM parameters to the relative error of slip ratio estimation is analyzed. Additionally, the torsional and longitudinal vibrations of the drive wheel are presented both in time and frequency domains when a quarter vehicle is started under conditions of a specific torque curve, which includes an abrupt torque change from 30 N · m to 200 N · m. The parameters sensitivity on drive wheel vibrations is also studied, and the parameters include the mass distribution ratio of tire, the tire torsional stiffness, the tire damping coefficient, and the hysteresis band of the PMSM current control algorithm. Finally, different target torque curves are compared in the simulation, which shows that the estimation error of the slip ratio gets violent, and the longitudinal force includes more fluctuation components with the increasing change rate of the torque. This paper analyzes the influence of the drive wheel deformation on the vehicle dynamic control, and provides useful information regarding the electric vehicle traction control.

Influence of tire dynamics on slip ratio estimation of independent driving wheel system

The independent driving wheel system, which is composed of in-wheel permanent magnet synchronous motor(I-PMSM) and tire, is more convenient to estimate the slip ratio because the rotary speed of the rotor can be accurately measured. However, the ring speed of the tire ring doesn’t equal to the rotor speed considering the tire deformation. For this reason, a deformable tire and a detailed I-PMSM are modeled by using Matlab/Simulink. Moreover, the tire/road contact interface(a slippery road) is accurately described by the non-linear relaxation length-based model and the Magic Formula pragmatic model. Based on the relatively accurate model, the error of slip ratio estimated by the rotor rotary speed is analyzed in both time and frequency domains when a quarter car is started by the I-PMSM with a definite target torque input curve. In addition, the natural frequencies(NFs) of the driving wheel system with variable parameters are illustrated to present the relationship between the slip ratio estimation error and the NF. According to this relationship, a low-pass filter, whose cut-off frequency corresponds to the NF, is proposed to eliminate the error in the estimated slip ratio. The analysis, concerning the effect of the driving wheel parameters and road conditions on slip ratio estimation, shows that the peak estimation error can be reduced up to 75% when the LPF is adopted. The robustness and effectiveness of the LPF are therefore validated. This paper builds up the deformable tire model and the detailed I-PMSM models, and analyzes the effect of the driving wheel parameters and road conditions on slip ratio estimation.

A Research on Anti-Slip Regulation of In-Wheel Motor Driven Electric Vehicle

In order to develop the four in-wheel motors driven Electric Vehicle (EV), this paper designed a skidding detector depending on the motor torque, established a slip-ratio estimator. Then, the Model Following Control (MFC) and Optimal Slip-ratio Control algorithms were analysed, compared and optimized. All of the algorithms were simulated using the one-wheel vehicle model. The simultion results show that the algorithms can make full use of the road adhesion characteristics and do good work on the ASR and the vehicle dynamics.