Maciej Trojnacki

Dynamics Model of a Four-Wheeled Mobile Robot for Control Applications – A Three-Case Study

The problem of dynamics modeling of a four-wheeled mobile robot is analyzed in this paper. All wheels of the robot are non-steered and the servomotors are used for driving the robot. Three cases of the robot drive system are considered. In the first case, two out of four wheels of the robot are independently driven, i.e., a pair of front or rear wheels. In the second case, the same wheels of the robot are driven but drive is also transmitted to the remaining wheels via toothed belts at each side of the robot. Finally, in the third case all four wheels are independently driven. Kinematic structure of the robot and its kinematics are described. The dynamics model of the robot dedicated for control applications is derived. It takes into account tire-ground contact conditions and wheel slips. The tire-ground contact conditions are characterized by coefficients of friction and rolling resistance. A simple form of the tire model, which considers only the most important effects of tire-ground interaction, is applied. The robot dynamics model also includes the presence of friction in kinematic pairs and the electromechanical model of servomotor drive unit. The presented robot dynamics model can be used for simulation-based investigations of control systems under development. Because the model was also formulated in a form linear with respect to parameters, it is possible to use it as a part of the robust or adaptive type control system.

Requirements for Tire Models of the Lightweight Wheeled Mobile Robots

Tire models for vehicle dynamics studies have been developed for many years to suit the needs of automobiles and the automotive industry. Recently, the growing use of advanced simulation techniques in design of wheeled mobile robots calls for analysis of the possibility to use the existing automotive tire models in the wheeled mobile robots dynamics studies. This analysis is especially important in the case of the skid-steered lightweight mobile robots, which are very common type of design, but exhibit many differences in the tire–ground system as compared to a typical car. In the present work the differences between lightweight wheeled robots and automobiles are examined in the following areas: tires, environment, maneuvers, ways of control, and vehicle systems. The influence of the found differences on the tire–ground system is examined in detail. Finally, the requirements for the tire models of the lightweight wheeled mobile robots are formulated with emphasis on the requirements different than those for tire models of the automobiles.

Determination of Motion Parameters with Inertial Measurement Units – Part 1: Mathematical Formulation of the Algorithm

The paper tackles the problem of determination of motion parameters of a wheeled mobile robot using the inertial measurement method. By the motion parameters one means: positions, linear velocities and accelerations of characteristic points of the robot, as well as Euler angles and angular velocity and acceleration of a robot body. Existing methods of determination of robot motion parameters, including the inertial method, the satellite navigation method and hybrid methods, are briefly discussed. The method of determination of motion parameters of a wheeled mobile robot with Inertial Measurement Units is described in details. It involves measurement of three components of acceleration of a selected point on the robot using a three-axial accelerometer and three components of angular velocity of the robot body using a three-axial gyroscope. Desired motion parameters are obtained as a result of differentiation, integration and other mathematical transformations. It was assumed that most of the analyzed motion parameters are calculated both in the coordinate system associated with the robot (moving) and in the reference coordinate system (stationary). The presented method is simple, but enables measurement of wide range of 3D motions, and as such it can be used as a benchmark for advanced algorithms of determination of motion parameters. In the Part 2 of this article, the proposed measurement method is verified in empirical experiments with a wheeled mobile robot using the Inertial Measurement Unit based on low-cost MEMS sensors.

Localization of the Wheeled Mobile Robot Based on Multi-Sensor Data Fusion

The paper presents a method of localization of a mobile robot which relies on aggregation of data from several sensors. A review of the state of the art regarding methods of localization of ground mobile robots is presented. An overview of design of the four-wheeled mobile robot used for the research is given. The way of representation of robot environment in the form of maps is described. The localization algorithm which uses the Monte Carlo localization method is described. The simulation environment and results of simulation investigations are discussed. The measurement and control equipment of the robot is described and the obtained results of experimental investigations are presented. The obtained results of simulation and experimental investigations confirm the validity of the developed robot localization method. They are the foundation of further research, where additional sensors supporting the localization process could be used.

Neural Network Identifier of a Four-wheeled Mobile Robot Subject to Wheel Slip

The paper presents a sequential neural network (NN) identification scheme for the four-wheeled mobile robot subject to wheel slip. The sequential identification scheme, different from conventional methods of optimization of a cost function, attempts to ensure stability of the overall system while the neural network learns the nonlinearities of the mobile robot. An on-line weight learning algorithm is developed to adjust the weights so that the identified model can adapt to variations of the characteristics and operating points in the four-wheeled mobile robot. The proposed identification system that can guarantee stability is derived from the Lyapunov stability theory. Computer simulations have been conducted to illustrate the performance of the proposed solution by a series of experiments on the emulator of the wheeled mobile robot.

Neural Network Control of a Four-Wheeled Mobile Robot Subject to Wheel Slip

The paper presents design of a control structure that enables integration of a kinematic and a neural network controller for a four-wheeled mobile robot subject to wheels slip. The controller is proposed to make the actual velocity of the wheeled mobile robot reach the desired velocity, although the wheeled mobile robot is even with system uncertainties and disturbances. The proposed tracking control system consists of: the kinematic and proportional controller, the neural approximated term and robust term derived from the stability analysis carried out using Lyapunov stability theorem. The proposed control system works on-line, weights adaptation is realized in every discrete step of the control process, and a preliminary learning phase of neural networks weights is not required. Computer simulation was conducted to illustrate performance of the control system.

Determination of Motion Parameters with Inertial Measurement Units – Part 2: Algorithm Verification with a Four-Wheeled Mobile Robot and Low-Cost MEMS Sensors

The paper is concerned with the problem of determination of motion parameters of a wheeled mobile robot using the inertial measurement method. The algorithm proposed in Part 1 of the article is verified in empirical experiments with a four-wheeled mobile robot PIAP SCOUT. Main design features of the robot are presented. The measurement and control system is described in details. The measurement system is based on a low-cost MEMS Inertial Measurement Unit. Selected results of empirical experiments are shown and thoroughly discussed. Performance of the algorithm with the low-cost sensors is evaluated. It is concluded that the presented simple method enables determination of unknown motion parameters, especially in applications where only short duration of experiments is required. Quality of the obtained results, however, shows scope for improvement. The weakest point of the measurement system are unreliable changes of the Euler angles obtained from the low-cost MEMS gyroscopes.

Trajectory Tracking Control of a Four-Wheeled Mobile Robot with Yaw Rate Linear Controller

The paper concerns the problem of trajectory tracking control of a four-wheeled PIAP SCOUT mobile robot with non-steered wheels. For this kind of wheeled robots, it is impossible to find kinematic relationship between robot’s body motion and motion of driven wheels, because of inherent sliding of wheels on the ground during turning. This is an important problem from the point of view of control of the robot. The approach followed in the present work relies on introducing a simple linear controller with feedback of actual yaw rate of robot’s body. The yaw velocity is measured by inexpensive MEMS gyroscope. Experiments were conducted on two kinds of floor typical for office buildings: PVC flooring and carpet flooring. Measurements of motion parameters were possible with INS technique. It was found that the proposed yaw rate controller significantly reduces the angular error of path tracking for 90 degrees turn maneuver.

Comparison of Configurations of Inertial Measurement Units for Determination of Motion Parameters of Mobile Robots – Part 1: Theoretical Considerations

The paper is concerned with the problem of determination of motion parameters of a mobile robot using Inertial Measurement Units (IMUs) in three different configurations. The practical goal of this research is investigation of possibilities of improvement of quality of data obtained from a 3D scanning head thanks to the application of information about motion parameters of the robot in a cost effective way. PIAP GRANITE four-wheeled skid-steered mobile robot was used as a mobile platform for the investigations. The following configurations of IMUs are considered: 1st – comprising one 3-axis accelerometer and one 3-axis gyroscope located in central part of the robot, 2nd – consisting of four identical 3-axis gyroscopes located on the robot to reduce the effect of drift of measurement of the angular velocities, 3rd – containing four 3-axis accelerometers deployed in different locations on the robot to realize so-called Gyroscope-Free Inertial Measurement Unit. The three configurations of IMUs are discussed and formulas for obtaining the motion parameters are given. In Part 2 of this article, the results of experimental research involving the three above mentioned configurations of IMUs are presented and discussed.

Comparison of Configurations of Inertial Measurement Units for Determination of Motion Parameters of Mobile Robots – Part 2: Experimental Investigations

The paper is concerned with the problem of determination of motion parameters of a mobile robot using Inertial Measurement Units (IMUs) in three different configurations. The practical goal of this research is investigation of possibilities of improvement of quality of data obtained from a 3D scanning head thanks to the application of information about motion parameters of the robot in a cost effective way. PIAP GRANITE four-wheeled skid-steered mobile robot was used as a mobile platform for the investigations. In Part 1 of the paper, the three configurations of IMUs are discussed and formulas for obtaining the motion parameters are given. In Part 2, methods discussed in Part 1 are compared experimentally. Main metrological properties of the IMUs used during experiments are provided. The precisions of measurements for particular configurations of IMUs were estimated using the introduced quality indexes. Main findings are stated in the conclusion.