This paper presented an optimal torque distribution scheme for the stability improvement of a distributed-driven electric vehicle (DEV). The nonlinear dynamics and tire model of the DEV are constructed. Moreover, the single-point preview optimal curvature model with the proportional-integral-derivative (PID) process is developed to simulate the driver's behavior. By using coordinated control and sliding mode control, a three-layer hierarchical control system was developed. In the upper level, the integral two degree-of-freedom (DOF) linear model is used to compute the equivalent yaw moment for vehicle stability. With the actuators' restrictions, the middle level solved the linear quadratic regulator (LQR) problem via a weighted least square (WLS) method to optimally distribute the wheel torque. In the lower level, a slip rate controller (SRC) was presented to reallocate the actual torques based on the sliding mode method. The simulation results show that the proposed scheme has high path-tracking accuracy and that vehicle stability under limited conditions is improved efficiently. Moreover, the safety under actuator failure is enhanced.

This paper presents a new approach to estimate the orientation of a quadrotor using single low-cost inertial measurement unit (IMU) sensor. The proposed hybrid solution uses two extended Kalman filters (EKF) along with a direction cosine matrix (DCM) algorithm. An EKF utilizes the dynamics of the quadrotor to filter the noise on the body-frame (B-frame) angular rates measured by the three-axis gyroscope sensor. Then, a DCM algorithm uses the filtered gyro signal along with the reading from a three-axis accelerometer and a three-axis magnetometer sensor to estimate the Euler angles. Finally, an additional EKF is presented to enhance the final estimates of the Euler angles. The performance of the proposed hybrid approach is tested and compared with other commonly used methods. Results are presented at the end of the paper to verify the performance of the proposed method. The results show an improvement in the estimated quadrotor's state. Monte Carlo tests are performed to ensure sustained high accuracy estimation.

The optimization-based dynamic prediction of 3D human running motion is studied in this paper. A predictive dynamics method is used to formulate the running problem, and normal running is formulated as a symmetric and cyclic motion. Recursive Lagrangian dynamics with analytical gradients for all the constraints and objective function are incorporated in the optimization process. The dynamic effort is used as the performance measure, and the impulse at the foot strike is also included in the performance measure. The joint angle profiles and joint torque profiles are calculated for the full-body human model, and the ground reaction force (GRF) is determined. Several cause-and-effect cases are studied, and the formulation for upper-body yawing motion is proposed and simulated. Simulation results from this methodology show good correlation with experimental data obtained from human subjects and the existing literature.

Improving the running safety and reducing the risk of derailments are the key objectives in the assessment of the running characteristics of railway vehicles. The present study of the safety against derailment is focused on the effect of wheelset hunting on the derailment coefficient Y/Q and, especially, how it is reflected in the power spectral density (PSD) of Y/Q. The lateral Y and vertical Q forces at the wheel/rail contact are obtained in numerical simulations for a four-axle railway vehicle moving at a constant velocity along a tangent track with random geometrical irregularities. The PSD of Y/Q, calculated as a function of spatial frequency, is found to have a characteristic structure with three peaks for the leading wheelsets and one peak for the trailing wheelsets of the front and rear bogies. The positions of the PSD maxima remain unchanged with increasing ride velocity, while their magnitudes and shapes evolve. One of the PSD peaks occurs for all wheelsets at the same spatial frequency corresponding to the wheelset hunting, while an additional peak at the double hunting frequency is found for the leading wheelsets. Such a peak structure is also found in the PSD of Y/Q determined in simulations with modified parameters of the vehicle primary suspension and for different track sections. The peak at the double hunting frequency is shown, by a detailed analysis of the contact forces, the flange angles and their PSDs, to result from the nonlinear geometry of the wheel/rail contact leading to the second-harmonic term in Y/Q. The emergence of this peak is also closely related to the phase difference between the hunting oscillations of the wheelset lateral displacement and the oscillations of its yaw angle, for which the difference is significantly smaller for the leading wheelset than for the trailing one. Finally, the effect of wheelset hunting is also shown to manifest itself in the strong dependence of the running average of Y/Q, which is used in the railway technical safety standards for the assessment of the safety against derailment (with the Nadal criterion), on the applied window width.

In vehicle system dynamics, the effect of the gyroscopic moments can be significant during curve negotiations. The absolute angular velocity of the body can be expressed as the sum of two vectors; one vector is due to the curvature of the curve, while the second vector is due to the rate of change of the angles that define the orientation of the body with respect to a coordinate system that follows the body motion. In this paper, the configuration of the body in the global coordinate system is defined using the trajectory coordinates in order to examine the effect of the gyroscopic moments in the case of curve negotiations. These coordinates consist of arc length, two relative translations, and three relative angles. The relative translations and relative angles are defined with respect to a trajectory coordinate system that follows the motion of the body on the curve. It is shown that when the yaw and roll angles relative to the trajectory coordinate system are constrained and the motion is predominantly rolling, the effect of the gyroscopic moment on the motion becomes negligible and, in the case of pure rolling and zero yaw and roll angles, the generalized gyroscopic moment associated with the system degrees of freedom becomes identically zero. The analysis presented in this investigation sheds light on the danger of using derailment criteria that are not obtained using laws of motion and, therefore, such criteria should not be used in judging the stability of railroad vehicle systems. Furthermore, the analysis presented in this paper shows that the roll moment, which can have a significant effect on the wheel/rail contact forces, depends on the forward velocity in the case of curve negotiations. For this reason, roller rigs that do not allow for the wheelset forward velocity cannot capture these moment components and, therefore, should not be used in the analysis of curve negotiations. A model of a suspended railroad wheelset is used in this investigation to study the gyroscopic effect during curve negotiations.

The stability assessment is an important task in the mechanical design of railway vehicles. For a detailed model of a railway passenger coach, the hunting behavior depending on the running speed, on wheel-rail contact conditions, and on different model configurations is analyzed using two different methods: The path-following method based on a direct computation of limit cycles enables an automatic computation. However, due to the direct computation, which exploits the periodicity of the solution, this method is restricted to strictly periodic behavior. In the brute-force method, an initial disturbance limited to a certain time interval is applied to the model. This method allows the analysis of the behavior independently from the type of the solution, but requires manual intervention. The comparison of the results obtained with both methods shows a good agreement and thereby the reliability of the results and the methods.

In this investigation, dynamic characteristics of independently rotating wheel systems are discussed. To this end, a multibody independently rotating wheelset (IRW) model is developed using the method of velocity transformation. The linear stability analysis of a two-axle IRW truck is performed, the hunting stability and vibration characteristics of IRW truck are investigated, and the results are compared with those obtained using the multibody dynamics model. Good agreement is obtained in hunting frequencies and critical speeds. It is shown using the linear IRW equations that since a constant forward speed is assumed for IRW, the longitudinal slip can occur due to the change in the wheel rolling radius. This leads to longitudinal creep forces even in the case of IRW and it contributes to a coupling of the lateral, yaw, and pitch motions of IRW. Furthermore, it is observed in several numerical examples that, due to small self-centering forces of IRW, continuous flange contact occurs on tangent track, while in curve negotiation, flange contacts on outer wheel of the front axle, as well as that on inner wheel of the rear axle, occur. Such an effect can be more significant when sharp curve negotiation is considered as encountered in light rail vehicle applications.

In this investigation, a numerical procedure that can be used for the analysis of a wheel and rail contact geometry is developed using the constraint contact formulation. The locations of contact points are determined for given lateral and yaw displacements of a wheelset when one-point contact is considered for each wheel, while these two displacements are no longer independent when the two-point contact occurs. A systematic procedure for predicting the flange, as well as the back-of-flange contact points, is developed and used for the two-point contact geometry analysis of a wheel and rail. Numerical results that involve tread, flange, and back-of-flange contacts are presented in order to demonstrate the use of the contact algorithm developed in this investigation. In particular, the back-of-flange contact is discussed for assessing contact configurations of a wheel and a grooved rail in light rail vehicle applications.