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The effect of wheel slip in differential drive robots is investigated in this paper. We consider differential drive robots with two driven wheels and ball-type caster wheels that are used to provide balance and support to the mobile robot. The limiting values of traction forces for slip and no slip conditions are dependent on wheel-ground kinetic a...
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... the sketch of a differential drive robot shown in Fig. 1. Let the position and orientation of the robot center of mass (c) be given by the vector ½x c ; y c ; / T . The center of rotation of the two drive wheels are joined together with a rigid link perpendicu- lar to the wheel's plane of rotation. The length of this link is called the wheel base of the robot (2b) and its midpoint is the ...
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Citations
... Differential drive mobile robots (see [1][2][3][4][5][6][7][8][9]), being generally equipped with two separately driven wheels that are mounted on a common axis and a castor wheel for balance, provide advantages in various robotic vehicular applications. Their simplistic yet effective design enables precise turning and maneuvering capabilities, which prove crucial in confined or cluttered spaces. ...
... Here, the dynamics of the differential drive mobile robot depicted in Figure 1 are studied, under pure rolling and no lateral slip conditions. The active wheels of the mobile robot are driven by appropriate DC motors, indicatively see [1][2][3][4][5]. As already mentioned, the dynamics of the vehicle will be extended to include unknown external disturbances and unknown actuator faults. ...
... Regarding the first problem, the controller parameters 0,1 and 1,1 will be chosen such that (a) the transfer function mapping the external command 1 w to the performance output 1 y is equal to a desired model transfer function, as an exact model matching problem (see [42][43][44]), and (b) the influence of the modelling error to the first performance variable is in an acceptable range. Regarding the second problem, the controller parameters 0 and will be chosen such that (a) the forced response of the second performance variable resembles the response of an ideal model, being equivalent to a model following problem or an approximate model matching problem (see [11]), (b) the influence of the modelling error to the second performance variable is in an acceptable range, and (c) the influence of the measurement noise to the second performance variable is also in an acceptable range. ...
Differential drive mobile robots, being widely used in several industrial and domestic applications, are increasingly demanding when concerning precision and satisfactory maneuverability. In the present paper, the problem of independently controlling the velocity and orientation angle of a differential drive mobile robot is investigated by developing an appropriate two stage nonlinear controller embedded on board and also by using the measurements of the speed and accelerator of the two wheels, as well as taking remote measurements of the orientation angle and its rate. The model of the system is presented in a nonlinear state space form that includes unknown additive terms arising from external disturbances and actuator faults. Based on the nonlinear model of the system, the respective I/O relation is derived, and a two-stage nonlinear measurable output feedback controller, analyzed into an internal and an external controller, is designed. The internal controller aims to produce a decoupled inner closed-loop system of linear form, regulating the linear velocity and angular velocity of the mobile robot independently. The internal controller is of the nonlinear PD type and uses real time measurements of the angular velocities of the active wheels of the vehicle, as well as the respective accelerations. The external controller aims toward the regulation of the orientation angle of the vehicle. It is of a linear, delayed PD feedback form, offering feedback from the remote measurements of the orientation angle and angular velocity of the vehicle, which are transmitted to the controller through a wireless network. Analytic formulae are derived for the parameters of the external controller to ensure the stability of the closed-loop system, even in the presence of the wireless transmission delays, as well as asymptotic command following for the orientation angle. To compensate for measurement noise, external disturbances, and actuator faults, a metaheuristic algorithm is proposed to evaluate the remaining free controller parameters. The performance of the proposed control scheme is evaluated through a series of computational experiments, demonstrating satisfactory behavior.
... Note that a more complicated version also takes the center of mass into account [34], [35]. For simplicity, the pure rolling condition (i.e., no influence due to friction) is assumed. ...
... While producing this data, the odometric data of the vehicle is obtained by utilizing the transition equations given in Eqs. (4), (5), and (6) (Torres et al., 2014). ...
In this study, an autonomous vehicle that can avoid obstacles has been developed by using stereo imaging systems and artificial intelligence applications together. An integrated stereo camera module and NVIDIA Jetson Nano developer kit were used as computer vision system. Checkerboard calibration was performed to prevent camera distortions. The images of the cameras were rectified and the difference costs between the left and right image pairs on the same epipolar plane were calculated. These difference costs were passed through the weighted least squares (WLS) filter, thus a depth map of the left camera image was created. The rectified left camera view was also processed by artificial intelligence-based semantic segmentation. Segmentation was carried out using a previously trained artificial intelligence network (SegNet). These semantic segmentation outputs were passed through the HSV color mask and a mask image was hereby obtained. Using the mask image; movable ground, obstacle, and background information was extracted. Useful data analysis was performed on the depth map and semantic segmentation outputs of the same frame. This information is transmitted to the 2-wheeled vehicle which is designed based on ROS that provides the movement, and decisions are made within the scope of the avoidance algorithm. This study’s novel contribution involves the integration of a passive depth sensing system and artificial intelligence based semantic segmentation, in tandem with a real-time obstacle avoidance algorithm that utilizes these combined technologies. Consequently, the autonomous vehicle is capable of making semantic inferences about its environment while effectively avoiding obstacles.
... Early studies on differential drive robots ignored the behavior of caster wheels entirely (Xu and Collins, 2009;Torres et al., 2014;Beniak and Pyka, 2017), or tried to evade the issue by using other types of wheel for balancing (Papadopoulos and Misailidis, 2007). ...
... They can be found on both lightweight platforms (e.g., robotic vacuum cleaners) and on heavyweight platforms, such as Self-Driving Vehicles (SDVs) in intralogistics. However, they pose a particular challenge for precise motion planning and control, since depending on their alignment, high bore torques may arise, potentially causing deviations from the planned path or stalling the driven wheels [2]. ...
... Previous work has decoupled this problem from motion planning, treating it as a disturbance rejection problem [2,3] or applying velocity command filtering [4]. While both methods effectively mitigate the influence of the bore torque ...
... The mitigation of the caster wheel bore torques for differential drive robots has been studied previously in [2,3,4]. Firstly, in [2] Torres et al. model the caster wheel dynamics and limit the motor torques according to the identified threshold at which the driven wheels start spinning. ...
Differential drive mobile robots often use one or more caster wheels for balance. Caster wheels are appreciated for their ability to turn in any direction almost on the spot, allowing the robot to do the same and thereby greatly simplifying the motion planning and control. However, in aligning the caster wheels to the intended direction of motion they produce a so-called bore torque. As a result, additional motor torque is required to move the robot, which may in some cases exceed the motor capacity or compromise the motion planner's accuracy. Instead of taking a decoupled approach, where the navigation and disturbance rejection algorithms are separated, we propose to embed the caster wheel awareness into the motion planner. To do so, we present a caster-wheel-aware term that is compatible with MPC-based control methods, leveraging the existence of caster wheels in the motion planning stage. As a proof of concept, this term is combined with a a model-predictive trajectory tracking controller. Since this method requires knowledge of the caster wheel angle and rolling speed, an observer that estimates these states is also presented. The efficacy of the approach is shown in experiments on an intralogistics robot and compared against a decoupled bore-torque reduction approach and a caster-wheel agnostic controller. Moreover, the experiments show that the presented caster wheel estimator performs sufficiently well and therefore avoids the need for additional sensors.
... Maximum allowable drive torque on two driving wheels is limited by the available static friction between wheel surface and the floor, normal forces at driving wheels, and wheel radius. Whenever the drive torque exceeds this value, the vehicle tends to slip as stated in [22], which can lead to position estimation errors and even collisions. Selection of drive wheel type is important as wheel surface properties affect static friction coefficient. ...
... When the torque exceeds this limit, the wheel tends to slip, and the traction force reduces to (FTr)slip, which is less than (FTr)max. This is due to the change between static and kinetic friction coefficients, where the static friction coefficient is slightly higher than the kinetic friction coefficient [22]. So during slipping, traction forces are reduced, and generated higher torque would not result in useful output. ...
In this paper, the design process of an Automated
Guided Vehicle (AGV) is presented, which is intended to be used
inside a hospital environment as a multitasking robotic
platform. Other than logistics, the system can be used for remote
patient monitoring. The AGV will be used as a mobile platform
for a mobile manipulator system. A differential drive wheel
configuration is used for the vehicle, considering the simplicity
of control. The kinematic model of differential drive
configuration was used along with the dynamic model, AGV
design parameters, and maximum allowable traction forces to
simulate AGV motion in the MATLAB Simulink environment.
The suggested navigation method—magnetic line following—is
robust and accurate compared to other line tracking methods
... where v x and ω are longitudinal and angular velocities of the robot, respectively, F vx and τ ω are the longitudinal force and the angular torque on the robot respectively. The dynamics of the robot when the pure rolling conditions are relaxed and wheels slip in both longitudinal and lateral direction are derived in [12]. For a wheel that is moving in the longitudinal direction under pure rolling, assuming that each wheel of the robot bears half the total weight of the robot, the traction force on the Pagilla DS-15-1628 3 wheel (F wheel ) for applied shaft torque τ are related by the following equation, ...
In differential drive robots, wheel slip severely affects the ability to track a desired motion trajectory and the problem is exacerbated when differential drive robots are used in applications involving coordination of multiple robots. This problem is investigated and, based on the wheel-ground traction forces, a simple slip avoidance control strategy is discussed. Differential drive robots with two driven wheels and one or more ball-type caster wheels are considered. The traction forces between the wheels and the ground surface are determined by assuming rigid wheel, rigid ground interaction. These traction forces are used to determine the maximum value of the input wheel torque that can be applied on the wheel before it slips. To avoid wheel slip, this limiting torque value is used to set a saturation limit for the input torque computed by a trajectory tracking controller. Stability of the closed-loop system with the slip avoidance strategy is shown. Experiments are conducted with this strategy using a single robot as well as multiple robots in a platoon. A representative sample of the experimental results is presented and discussed.
... where v x and x are the longitudinal and angular velocities of the robot, respectively, F vx and s x are the longitudinal force and the angular torque on the robot, respectively. The dynamics of the robot when the pure rolling conditions are relaxed and wheels slip in both longitudinal and lateral directions are derived in Ref. [12]. For a wheel that is moving in the longitudinal direction under pure rolling, assuming that each wheel of the robot bears half the total weight of the robot, the traction force on the wheel (F wheel ) for the applied shaft torque s are related by the following equation: ...
... The robot parameter values are 2b ¼ 0.21 m, e ¼ 0.095 m, d ¼ 0.055 m, g ¼ 9.81 m/s, h ¼ 0.0216 m, m r ¼ 1.5 kg, I r ¼ 0.009753 kg/m 2 , I wz ¼ 0.000584 kg/m 2 , I wy ¼ 0.001168 kg/m 2 , r ¼ 0.0365 m, and m w ¼ 0.064 kg. Using these numerical values, the maximum allowable torque on each wheel is found to be 0.095 mN which is equivalent to an acceleration of approximately 45 rad/s 2 ; this is applied as a saturation between the computed input torque and the drive motors, see Fig. 2. Model simulations and experiments are conducted to verify the dynamics and the traction force relations and are shown in Ref. [12]. ...
Motion coordination of differential drive robots with wheel slip is considered in this work. In applications involving motion coordination of multiple wheeled vehicles, much of the existing work has assumed a pure rolling condition between the wheel and ground while deriving the vehicle dynamics and subsequently in the development of model-based controllers that can achieve and maintain the desired formation of vehicles. Wheel slip is common when using differential drive mobile robots as the orientation of the robot is achieved by commanding a velocity differential between the two driven wheels of the mobile robot. In formations of wheeled mobile robots, to maintain the desired spacing between vehicles, rapid accelerations and decelerations may be needed to maintain the desired spacing between vehicles. In this paper, we assume wheel slip and model the dynamics of each mobile robot with a simple Coulomb friction-based traction force model to distinguish between slip and no-slip conditions. Based on this dynamic model of the mobile robot with wheel slip, a formation controller is developed by limiting the torque to the wheel motors of each robot to avoid slip and achieve and maintain the desired formation. Experiments are conducted with a formation that is a platoon of three wheeled mobile robots. Experimental results are shown and discussed to investigate occurrence of wheel slip and its effect on coordination.
Here, a dual stage PI-PID controller is designed toward independent control of the velocity and orientation angle of a differential drive mobile robot. The control scheme uses real-time measurements of the kinematic variables of the mobile robot and measurements of its orientation angle, considered to be received through a wireless network introducing communication delays between the respective sensor and the controller. Based upon the linear approximant of the non-linear model of the robot, two independent PI controllers are designed toward regulation of the angular velocities of the wheels. Based upon the inner closed-loop system, a multivariable PID controller is designed for stability, independent regulation of the velocity and the orientation angle of the vehicle, and asymptotic command following. Determination of the controller parameters is performed in two stages, using a mixed analytic/metaheuristic approach. The performance of the proposed control scheme is illustrated through simulations.
