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Dieses Kapitel befasst sich mit der Entwicklung einer Steuerungsarchitektur zur Lösung des Trajektorverfolgungsproblems für Konvois vernetzter elektrischer Kleinbusse. Die Studie verwendet eine geometrische Regelungstechnik, die als Pure Pursuit-Regler für die seitliche Regelung bekannt ist, unterstützt durch einen PID-Regler für die Längsregelung. Ziel ist es, sicherzustellen, dass ein nachfolgendes Fahrzeug die Flugbahn eines führenden Fahrzeugs genau verfolgen kann und dabei einen stabilen Abstand einhält, wodurch Längslagefehler minimiert werden. Die Forschung umfasst die Simulation des Datentransfers mit zeitgesteuerten Informationsvektoren und realen GNSS-Daten von einem fahrenden Fahrzeug. Das kinematische Fahrradmodell wird verwendet, um die seitliche Bewegung des Fahrzeugs anzunähern, wobei von vernachlässigbaren Schlupfwinkeln und planaren Bewegungen ausgegangen wird. Der Pure Pursuit-Controller berechnet den Lenkeinschlag auf Basis des vorausschauenden Abstands und des vorausschauenden Winkels, wobei der vorausschauende Abstand proportional zur Längsgeschwindigkeit des Fahrzeugs ist. Die Steuerungssystemarchitektur wird in einem Blockdiagramm dargestellt, das den Fluss der Steuerungslogik und die Ein- und Ausgänge jedes Blocks hervorhebt. Simulationen wurden in der Umgebung von MATLAB / Simulink durchgeführt, wobei reale Flugbahnen durch ein GNSS-Gerät in der Nähe des Fahrzeugschwerpunkts erfasst wurden. Die Ergebnisse zeigen, dass das implementierte Kontrollsystem trotz Störungen eine genaue Verfolgung der Flugbahn gewährleistet, mit relativ niedrigen Fehlerwerten, insbesondere bei Querfehlern. Die Ergebnisse deuten darauf hin, dass eine konforme Verbindung, die eine Verschiebung von 0,2 Metern zulässt, ausreichen kann, um erhebliche Kräfte zwischen den Fahrzeugen zu verhindern. Der Vorschlag eines neuen Mobilitätsprogramms, bei dem Fahrzeuge unterschiedlicher Automatisierungsgrade miteinander verschmelzen können, bildet eine straßenbahnähnliche Transportalternative, die nur einen aktiven Fahrer erfordert und keinen vorgeschriebenen Weg einschlägt.
KI-Generiert
Diese Zusammenfassung des Fachinhalts wurde mit Hilfe von KI generiert.
Abstract
In this work, a control architecture is proposed for controlling a convoy of automated vehicles that are mechanically connected to each other. Connection allows them to circulate without specific permissions in any environment, even if a driver is present only in the leading vehicle. The connection in the real case is an elastic and compliant connection, a condition mediating the cases of rigid connection and absence of mechanical connection. To evaluate the capabilities of automation control algorithms in maintaining a prescribed path and estimate the required stiffness of the mechanical connection, simulations have been performed considering a geometric control algorithm (Pure Pursuit controller) for lateral control mixed with a PID controller for longitudinal control. Considering several trajectories of two convoyed vehicles, the control method has been analyzed based on the minimum value of errors (longitudinal and lateral) in vehicle trajectories. The ideal case is considered where all communication and environment scanning systems operate with maximum efficiency. While subsequent steps will be made to further decrease the trajectory error by modifying the vehicle control, the results enable an estimation of the required compliance of the mechanical connection expressed in terms of trajectory error.
Introduction
The aim of the work is to propose a control architecture for solving the Trajectory Tracking problem for a convoy of connected electric mini-buses by a geometric control technique (as the Stanley controller [1]); the technique is known in the literature as Pure Pursuit controller [2, 3] for lateral control, supported by a PID controller for longitudinal control. In particular, the objective is to ensure that a following vehicle is capable of traveling a trajectory communicated by a moving leading vehicle [4] and maintaining a certain distance, minimizing the longitudinal position error and ensuring that this is stable in a certain error range; this enables to design the stiffness of the mechanical connection so that forces exchanged between the vehicles are reduced (e.g., using a shock absorber). Data transfer to the following vehicle is first simulated through the generation of timed information vectors (to simulate the release of values over time) and subsequently by using GNSS data from a real vehicle as input to the proposed control system. Here, it is proposed to contextualize these solutions for application to mini-buses available to the research team, previously customized and whose main specifications can be found in previous work [5].
As known in literature [6], a common approach to modeling the lateral motion of a vehicle is the so-called “Bicycle Kinematic Model”. Taking Fig. 1 as a reference, the vehicle is approximated as a bicycle where the two left and right front wheels are represented by one single wheel and similarly for the rear wheels. In particular, we assume that only the front wheel can be steered; since the vehicle in question has a maximum speed of approximately 8 m/s, we can also assume that the wheel slip angles are negligible. Furthermore, let us consider that the vehicle has only planar motion, so that the coordinates required to describe the vehicle’s motion are only three: X, Y and \(\vartheta \). Therefore, \((x_{c}, y_{c})\) are the inertial coordinates of the Centre of Gravity (CG) while \(\vartheta \) describes the orientation of the vehicle; all these parameters are defined with respect to a fixed reference system (O; X, Y, Z). Finally, to account for the positioning of the GNSS, the CG was considered as a reference. Under these hypotheses, it is possible to write the following kinematic equations with respect to the fixed reference system (where the vehicle’s CG speed is denoted by \(V_{c}\) and defines an angle \(\beta \) with respect to the longitudinal axis of the vehicle known as “slip angle”):
Regarding the vehicle’s lateral control, a Pure Pursuit controller has been implemented. Taking Fig. 2 as a reference, the main idea of the Pure Pursuit controller is to compute the steering angle \(\delta \) of the front wheel based on the concepts of look-ahead distance \(l_{d}\) and look-ahead angle \(\alpha \), so that the vehicle can steer towards the reference coordinate \((x_{ref}, y_{ref})\) following a circular arc trajectory with its rear wheel. Based on the wide literature on the subject, there are different versions of the Pure Pursuit controller; specifically, the version is considered in which the look-ahead distance \(l_{d}\) is proportional to the longitudinal speed of the vehicle [7], i.e. (\(l_{d} = K_{p} \cdot V_{long}\)) (\(V_{long}\) can be obtained by projecting the speed of the CG of the vehicle \(V_{c}\) on its longitudinal axis via the slip angle \(\beta \)). As regards the look-ahead angle \(\alpha \), this can be easily obtained through the following equation:
Finally, under the hypotheses previously considered, it is possible to write the nonlinear feedback control law that controls the steering angle \(\delta (t)\) (For implementation purposes, the equation was subsequently modified as follows \(\delta (t) = atan2(2 \cdot L \cdot sin(\alpha (t)),K_{p} \cdot V_{long}(t) + c)\).):
To account for the physical limitations of the steering system of the real vehicle under consideration, \(\delta (t)\) was saturated between the values \([-22.5^{\circ } , 22.5^{\circ }]\). The architecture of the used control system is depicted in Fig. 3 through a block diagram. This diagram shows the flow of the control logic highlighting the inputs and outputs of each block. After some experiments, it was decided to modify the reference speed value using a feedforward term proportional to the longitudinal error \(E_{long}\) (i.e. \(V_{ref, ff} = V_{ref} + K_{ff} \cdot E_{long}\)), at the input to the Speed Error Computation block, to allow the system to accelerate if it was too far from the reference position. Lastly, as regards the tuning phase, all controller gains were tuned empirically.
All simulations were carried out in the MATLAB/Simulink® environment. The ideal reference trajectories were generated through scripts in MATLAB. Timed arrays were generated to simulate the sampling of the input data over time. As regards the real trajectories, however, these were acquired through a GNSS device placed near the CG of the moving vehicle. The device had a maximum frequency of 25 Hz, but to guarantee a certain stability in the data acquisition it was decided to limit it to 20 Hz. The data thus obtained were then filtered through a moving average filter and used as input to the control system. Acquisition and filtering were carried out through a MATLAB script. In all Simulink simulations we used a fixed step of 0.01 s and ode14x as solver. The value of 0.01 s was coherent with the one for the hardware onboard the vehicle.
2 Results and Discussion
For brevity, only the results will be shown and discussed regarding the simulation of a real trajectory, i.e., acquired through the use of the previously introduced GNSS device. Therefore, from Fig. 4 it can be seen how the implemented control system guarantees close tracking of the trajectory despite the disturbances (partially filtered) present in the measurements with a maximum speed of approximately 36 km/h. Furthermore, as can be seen from Fig. 4, the trajectory is reproduced smoothly, without cutting corners or rapid changes in orientation thanks to the mixed control architecture used (Pure Pursuit + PID). Cutting corners and rapid changes in orientation are typical problems in Pure Pursuit applications, partly because Pure Pursuit ignores trajectory/path curvature [7].
The trend over time of the error values, relating to the simulated trajectory, is shown in Fig. 5 where it is possible to observe how the implemented controller manages to obtain relatively low error values, especially in the case of lateral error (\(0.02 \pm 0.01\) m). As regards the longitudinal error (\(0.09 \pm 0.07\) m), however, this tends to have higher values than the lateral error, probably because the dynamics of the vehicle was not considered at this stage.
The proposed and implemented control architecture demonstrated good performance in terms of error minimization (particularly in the case of lateral error, with an average absolute value of \(0.02 \pm 0.01\) m) even when using real acquisitions as a reference. Conversely, an average absolute value of \(0.09 \pm 0.07\) m was achieved in longitudinal error, which requires special attention and might be reduced also considering vehicle dynamics. Further steps will be moved to improve the control algorithm already implemented (e.g., modelling the dynamics and the connection between the two vehicles at a kinematic and/or dynamic level) and implementing new algorithms to perform comparisons between different control architectures. The findings highlight that a compliant connection allowing a displacement of 0.2 m can be sufficient to prevent the discharge of significant forces between vehicles; this information will guide the proposal of a new mobility scheme where vehicles at a different level of automation will be able to merge, forming a tram-like transportation alternative that needs only one active driver at a time and does not follow a prescribed path (as railway lines).
Acknowledgments
Not applicable.
Funding
The project has received funding from the Sustainable Mobility center (MOST) in the framework of Italian PNRR (CUP B13C22001000001).
Availability of Data
Data may be provided on request by the authors.
Competing Interests
Not applicable.
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