Method and device for calculating braking curves for autonomous rail vehicles

Abstract

A computer-implemented method for calculating braking curves for an autonomous rail vehicle (1) performing a pre-calculation phase by pre-calculating a common braking curve (14) for the autonomous rail vehicle (1) for a target position (5) based on spatial and temporal restrictions. A real-time calculation phase is performed by receiving a current position (10) and state of the autonomous rail vehicle (1) and calculating in real-time a phase-in curve (11) from the current position (10) to the common braking curve (14). The final braking curve (16) for the autonomous rail vehicle (1) uses both the at least one pre-calculated common braking curve (14) and the real-time calculated phase-in curve (11). The common braking curve (14) is re-used for the calculation of a next braking curve as long as the target position (5) and the spatial and temporal restrictions are unchanged.

Description

Technical Field

[0001] The present invention relates to a computer-implemented method for calculating braking curves for an autonomous rail vehicle according to claim 1, an Automatic Train Operation (ATO) device for calculating braking curves for an autonomous rail vehicle according to claim 10, and a computer program product according to claim 15.Background Art

[0002] Train control systems are essential components in modern railway operations, responsible for ensuring safe and efficient movement of trains along tracks. These systems typically encompass a range of functions, including speed regulation, route management, and collision avoidance. As railway networks have become increasingly complex and demands for higher capacity have grown, there has been a shift towards more sophisticated automated train operation (ATO) systems.

[0003] ATO systems rely on advanced algorithms to calculate and execute optimal train movements. A critical aspect of these algorithms is the computation of braking curves, which determine how a train should decelerate to safely reach a target position or speed. Braking curves must account for various factors such as train characteristics, track geometry, and environmental conditions to ensure precise and safe operations.

[0004] One of the challenges in implementing ATO systems is the need for real-time calculations of braking curves. As trains move along the track, their current state (position, speed, acceleration) is constantly changing, requiring continuous updates to the braking curve. This computational load can be significant, especially in high-density railway networks where multiple trains must be managed simultaneously.

[0005] Furthermore, the integration of ATO systems with existing railway signaling infrastructure, such as the European Train Control System (ETCS), introduces additional complexities. Ensuring compatibility and seamless operation between these systems while optimizing performance is an ongoing area of development in the field of train control.

[0006] It has been acknowledged that an improved method for calculating braking curves is needed that overcomes one or more of these problems.

[0007] CN 115743245 A discloses a method for train coupling at a platform, which involves sending instructions to a train to be coupled and a coupling train, calculating a braking curve for the coupling train based on the position relationship between the two trains, and controlling the coupling process based on the calculated braking curve. While this document addresses train coupling operations, it does not specifically address the challenges of real-time braking curve calculations for general train operations or the optimization of computational resources in ATO systems.

[0008] The paper "Evaluation of the capacity limitations and suitability of the European Traffic Management System to support Automatic Train Operation on Main Line Applications" of P. Thomas, D. Fisher, F. Sheikh, Computers in Railways XI, 2008 discusses various aspects of ETCS implementation, including the impact of braking curves on railway capacity. The paper highlights the importance of accurate braking curve calculations in determining train headways and overall system performance. However, it does not propose specific methods for optimizing the calculation of braking curves or reducing the computational load associated with real-time updates.

[0009] EP 4 173 924 A1 discloses a method and system for calculating braking curves for rail vehicles with automatic train protection. The method determines a target point and speed, calculates an initial braking curve, and refines it using more precise track data as the train approaches the target. The process involves first calculating a rough curve with coarse track data for the entire route. As the train nears the target, a second calculation refines the curve using detailed local data. The system handles different target types, adapts calculations based on target requirements, and integrates with existing train control systems. It considers train characteristics and environmental conditions but does not specifically address autonomous rail vehicles or optimizing real-time calculations for multiple trains in a network.

[0010] Based on the known computer-implemented methods for calculating braking curves, the present invention addresses the challenge of providing a computer-implemented method that enables efficient and accurate calculation of braking curves for autonomous rail vehicles while reducing computational load.

[0011] The invention solves this problem through a method according to claim 1.

[0012] The following paragraphs elaborate on definitions for the technical terms used in the claim set. The definitions should not be understood and limiting to the disclosure, but rather as hinting on some ways of understanding implementations of the invention while not excluding interpretations not mentioned in the definitions. Accordingly, other implementations are within the scope of the following paragraphs.

[0013] The term "autonomous rail vehicle" refers to a train or other rail-based vehicle capable of operating without direct human control or with less human control. This may include locomotives, passenger cars, freight cars, or specialized rail vehicles equipped with automated systems for propulsion, braking, navigation, and other operational functions. Autonomous rail vehicles typically utilize sensors, control algorithms, and communication systems to navigate tracks, respond to signals, and maintain safe operations.

[0014] A "braking curve" in the context of rail vehicles represents the deceleration profile of a train as it approaches a target position or speed. It describes how the vehicle's speed should decrease over distance to safely reach the intended stopping point or reduced speed. Braking curves consider factors such as vehicle mass, track gradient, adhesion conditions, and braking system capabilities to ensure smooth and controlled deceleration.

[0015] The "pre-calculation phase" refers to a computational process performed in advance of real-time operations. In the context of this invention, it involves calculating common braking curves based on known spatial and temporal restrictions. This phase can be implemented as a software module installed on a local computer like an onboard unit, a server or cloud infrastructure. A server may comprise one or more physical computers with processors, memory, and storage devices networked together to provide computational resources. Cloud architecture refers to distributed computing resources accessible over a network, often involving virtualized servers and scalable infrastructure.

[0016] The "real-time calculation phase" involves computations performed during the actual operation of the rail vehicle. This phase processes current position and state information to calculate immediate adjustments to the braking profile. Like the pre-calculation phase, it can be implemented as a software module on a local computer like an onboard unit, a server or cloud system. Alternatively, both phases could be implemented as dedicated hardware components utilizing application-specific integrated circuits (ASICs) or field-programmable gate arrays (FPGAs) for optimized performance.

[0017] A "common braking curve" represents a standardized deceleration profile pre-calculated for a specific target position and set of restrictions. It serves as a baseline that can be reused for multiple braking operations under consistent conditions. The output of the module calculating the common braking curve may become the input for the real-time calculation module, transmitted as a digital data telegram via a communication module.

[0018] The "phase-in curve" refers to the portion of the braking profile that connects the vehicle's current state to the pre-calculated common braking curve. It is calculated in real-time to account for the vehicle's immediate position and dynamics. The output of the real-time calculation module producing the phase-in curve may be transmitted to a vehicle control module for execution.

[0019] "Spatial and temporal restrictions" encompass various constraints affecting train operations. Spatial restrictions may include track geometry, tunnels, bridges, or station locations. Temporal restrictions could involve scheduled arrival times, track occupancy windows, or temporary speed restrictions. These restrictions form inputs to the braking curve calculations, ensuring that the vehicle's deceleration profile adheres to operational and safety requirements.

[0020] A "grid point" in the context of braking curves represents a specific point along the curve where kinematic properties change. This could include locations where track gradient changes, speed limits adjust, or other factors affecting the braking profile come into play. Storing braking curve states at grid points allows for efficient representation of the curve while enabling analytical calculation of intermediate points.

[0021] An "envelope curve" represents the minimum of all possible common braking curves for a given set of conditions and targets. It provides a conservative boundary for safe deceleration across various scenarios. The envelope curve may be calculated by a dedicated software or hardware module, with its output serving as input for subsequent real-time calculations and vehicle control decisions.

[0022] ATO (Automatic Train Operation) refers to a system that automates the operation of trains, reducing or eliminating the need for human intervention. In the context of rail vehicles, ATO may control functions such as acceleration, braking, and adherence to speed limits. ATO systems and ATO devices can be implemented as software modules installed on onboard computers or servers, or as part of a larger cloud-based infrastructure. These devices typically interface with other train control and signaling systems to ensure safe and efficient operations. ATO may have different levels of automation, ranging from basic assistance to fully autonomous operation. These levels of automation are commonly referred to as GoA1 to GoA4. The implementation of ATO can involve various hardware components, including sensors, communication devices, and control units, which work together to interpret track conditions, calculate optimal speed profiles, and execute train movements. ATO devices may be installed on locomotives or other parts of the train to facilitate automated control and decision-making during rail operations.Summary of Invention

[0023] The invention as described in claim 1 provides several significant advantages over previous solutions for calculating braking curves for autonomous rail vehicles: 1. Reduced computational load: By splitting the braking curve calculation into a pre-calculation phase and a real-time calculation phase, the invention significantly reduces the computational burden on the autonomous train control system. The pre-calculated common braking curve can be reused for multiple brake curve calculations, eliminating the need to recalculate the entire curve in real-time for each braking event. This is particularly advantageous in high-density railway networks where multiple trains must be managed simultaneously, as it frees up computational resources for other critical tasks. 2. Improved responsiveness: The real-time calculation of only the phase-in curve allows the system to quickly adapt to the current position and state of the rail vehicle. This enables more precise and timely adjustments to the braking profile, enhancing the overall safety and efficiency of train operations. The ability to respond rapidly to changes in the vehicle's state is crucial for maintaining safe distances between trains and adhering to complex timetables in modern railway systems. 3. Enhanced flexibility: The method's approach of pre-calculating common braking curves based on spatial and temporal restrictions, while allowing for real-time adjustments through the phase-in curve, provides a flexible framework that can accommodate various operating conditions. This flexibility is particularly valuable when dealing with changes in track adhesion, power limitations, weather conditions, or temporary speed restrictions, which can significantly impact braking performance. 4. Improved integration with existing systems: The method's compatibility with Automatic Train Operation (ATO) devices facilitates seamless integration with existing railway signaling infrastructure, such as the European Train Control System (ETCS). This compatibility ensures that the benefits of the invention can be realized without requiring extensive modifications to existing railway systems, reducing implementation costs and complexity. 5. Enhanced safety: The ability to quickly calculate and adjust braking curves in real-time, while still leveraging pre-calculated data, allows for more precise control of train movements. This enhanced precision can lead to improved safety margins, reducing the risk of collisions or overshooting stopping points. 6. Increased energy efficiency: By providing more accurate and adaptable braking curves, the invention enables smoother deceleration profiles. This can result in reduced energy consumption and wear on braking systems, leading to lower operational costs and environmental impact. 7. Improved capacity utilization: The more efficient calculation and application of braking curves can potentially allow for reduced headways between trains, as the system can more accurately predict and control train movements. This could lead to increased capacity on existing rail infrastructure without compromising safety. 8. Future-proofing: The modular approach of separating pre-calculation and real-time calculation phases provides a framework that can be easily updated or expanded as new technologies or operational requirements emerge. This ensures that the system can evolve alongside advancements in autonomous rail vehicle technology and changing regulatory landscapes.

[0024] In comparison to previous solutions, such as those described in CN 115743245 A and EP 4 173 924 A1, the invention offers a more comprehensive and efficient approach to braking curve calculation. While CN 115743245 A focuses specifically on train coupling operations, the present invention provides a general solution for calculating braking curves that can be applied to a wide range of operational scenarios. Similarly, although EP 4 173 924 A1 describes a method for refining braking curves as a train approaches its target, it does not offer the same level of computational efficiency and real-time adaptability as the present invention.

[0025] The invention's approach of combining pre-calculated common braking curves with real-time phase-in calculations represents a significant advancement over traditional methods that either rely solely on real-time calculations (which can be computationally intensive) or use static, pre-calculated curves (which may not adequately account for current operating conditions). This hybrid approach strikes an optimal balance between computational efficiency and real-time responsiveness, addressing the key challenges faced in implementing advanced train control systems for autonomous rail vehicles.

[0026] In the inventive method, the phase-in curve may be re-calculated every calculation cycle of the ATO device, which may be approximately 100ms long. This frequent recalculation allows the system to continuously adapt to the rail vehicle's current position and state, ensuring precise and up-to-date braking profiles. In contrast, the common braking curve can be re-used across multiple calculation cycles as long as the boundary conditions remain unchanged. This approach may significantly reduce the computational load on the ATO device, as the more complex and resource-intensive common braking curve calculations do not need to be performed in every cycle. By combining frequently updated phase-in curves with stable common braking curves, the system may achieve a balance between real-time responsiveness and computational efficiency.Description of Embodiments

[0027] In a first preferred embodiment of the inventive computer-implemented method, states of the common braking curve are stored at grid points only, wherein grid points are set where kinematic changes occur. This approach offers significant advantages in terms of data storage efficiency and computational performance. By storing braking curve states only at points where kinematic changes occur, the method reduces the amount of data that needs to be stored and processed without compromising the accuracy of the braking curve. This selective storage strategy allows for a more compact representation of the braking curve while still capturing all critical information needed for accurate train control. Alternative implementations could involve adaptive grid point selection based on the complexity of the track profile or the specific operational requirements of different train types.

[0028] In a further preferred embodiment of the inventive computer-implemented method, any point on the final braking curve connecting neighboring grid points is analytically calculated. This analytical calculation approach provides several benefits, including improved computational efficiency and enhanced accuracy of the braking curve. By using mathematical formulas to determine intermediate points between grid points, the method can generate a smooth and precise braking profile without the need for extensive data storage or interpolation. This technique allows for real-time adjustments to the braking curve with minimal computational overhead. Alternative implementations could explore different analytical methods, such as spline interpolation or polynomial fitting, to optimize the balance between accuracy and computational complexity for various operational scenarios.

[0029] In a further preferred embodiment of the inventive computer-implemented method, the phase-in curve intersects the common braking curve on the curve connecting two neighboring grid points. This intersection strategy offers a seamless transition between the real-time calculated phase-in curve and the pre-calculated common braking curve. By ensuring that the intersection occurs between grid points, the method maintains continuity in the braking profile while allowing for dynamic adjustments based on the current train state. This approach enhances the system's ability to respond to real-time changes in train position and speed while leveraging the efficiency of pre-calculated data. Alternative implementations could investigate adaptive intersection point selection based on factors such as train speed, track conditions, or safety margins.

[0030] In a further preferred embodiment of the inventive computer-implemented method, an envelope curve representing a minimum of all possible common braking curves is calculated. The envelope curve concept provides a powerful tool for optimizing train control and safety. By determining the minimum of all possible braking curves, the system establishes a conservative boundary that ensures safe deceleration across various scenarios. This approach allows for more efficient use of track capacity while maintaining robust safety margins. The envelope curve can serve as a reference for real-time decision-making, enabling faster response times in critical situations. The determined envelope curve is used in this embodiment as the common brake curve. Similar as the common brake curve also the states of the envelope curve may be stored at grid points only that, again, are set where kinematic changes occur.

[0031] In a further preferred embodiment of the inventive computer-implemented method, calculating the envelope curve comprises determining minimum values of multiple possible common braking curves for different targets. This comprehensive approach to envelope curve calculation enhances the system's ability to handle complex operational scenarios. By considering multiple targets and their associated braking curves, the method can generate an envelope that accommodates various potential stopping points or speed restrictions along the route. This multi-target consideration improves the flexibility and robustness of the train control system, allowing for efficient adaptation to changing traffic conditions or operational requirements. Alternative implementations could investigate dynamic target prioritization algorithms that adjust the envelope curve calculation based on real-time factors such as train spacing or energy optimization goals.

[0032] In a further preferred embodiment of the inventive computer-implemented method, calculating the phase-in curve comprises performing a straightforward calculation to determine a closest reachable intersection on the envelope curve that can be analytically determined between two neighboring grid points. This efficient calculation method for the phase-in curve offers several advantages, including reduced computational complexity and improved real-time performance. By focusing on the closest reachable intersection with the envelope curve, the system can quickly generate an optimal phase-in trajectory that ensures safe and efficient train operation. The analytical determination between grid points of the envelope curve further enhances computational efficiency while maintaining accuracy. Alternative implementations could explore adaptive calculation methods that adjust the complexity of the phase-in curve determination based on factors such as available computational resources or the criticality of the current operational phase.

[0033] In a further preferred embodiment of the inventive computer-implemented method, the method further comprises updating the pre-calculated common braking curve and / or envelope curve when environmental conditions or vehicle parameters change significantly. This dynamic updating capability ensures that the braking curves remain accurate and relevant in changing operational conditions. By incorporating real-time environmental data and vehicle parameter updates, the system can maintain optimal performance and safety across a wide range of scenarios. This adaptability is crucial for handling variations in weather conditions, track adhesion, power limitations, or changes in train configuration. Alternative implementations could investigate predictive updating algorithms that anticipate potential changes based on historical data or weather forecasts, allowing for proactive adjustments to the braking curves.

[0034] In a further preferred embodiment of the inventive computer-implemented method, the spatial and temporal restrictions include at least one of: speed limits, gradient information, track curvature information, adhesion information of a rail, and power restrictions. This comprehensive consideration of spatial and temporal restrictions allows for highly accurate and context-aware braking curve calculations. By incorporating a wide range of factors that influence train dynamics, the method can generate braking profiles that are optimized for specific track sections and operational conditions. This detailed approach enhances both safety and efficiency, enabling trains to operate closer to their performance limits while maintaining robust safety margins. Alternative implementations could explore the integration of additional data sources, such as real-time track condition monitoring or dynamic weather information, to further refine the spatial and temporal restrictions used in braking curve calculations.

[0035] Based on known devices for calculating braking curves, the invention further addresses the challenge of providing an Automatic Train Operation (ATO) device that enables efficient and accurate calculation of braking curves for autonomous rail vehicles while reducing computational load.

[0036] The invention solves this problem through an ATO device according to claim 10. Preferred embodiments result from the dependent claims 11 to 14, whereby the same advantages as initially explained for the inventive computer-implemented method apply analogously.

[0037] Based on known computer program products for calculation of braking curves, the invention further addresses the challenge of providing a computer program product that enables efficient and accurate calculation of braking curves for autonomous rail vehicles while reducing computational load. The invention solves this problem through a computer program product according to claim 15. The same advantages as initially explained for the inventive computer-implemented method apply analogously.Brief Description of the Drawings

[0038] Non-limiting and non-exhaustive examples are described with reference to the following figures.

[0039] For better explanation of the invention, the following schematic representations show: Figure 1a side view of an autonomous rail vehicle system comprising an exemplary ATO device according to the invention, Figure 2a graph depicting various braking curves for the autonomous rail vehicle of Figure 1, and Figure 3a flowchart for a method of calculation braking curves of the autonomous rail vehicle of Figure 1. Description of Examples

[0040] Figure 1 illustrates a side view of an autonomous rail vehicle system. The system comprises a train 1 consisting of a locomotive 2 and a passenger car 3 traveling on a rail 4. The train 1 is moving towards a target position 5 as indicated by the direction indicator 6. This target position 5 could represent a station stop, speed restriction point, or other significant location for the train's operation.

[0041] The locomotive 2 is equipped with an ATP (Automatic Train Protection) device 7 and an exemplary ATO (Automatic Train Operation) device 8 according to the invention. These devices are positioned on the underside of the locomotive 2, likely housing the control systems for autonomous operation. The ATP device 7 and ATO device 8 are part of a train control system 9 of the train 1 and are key components for the autonomous operation of the train 1. The ATP device 7 is basically designed as already known.

[0042] The ATO device 8 is responsible for performing the braking curve calculations and controlling the train's speed and position relative to the target position 5. During operation, the ATO device 8 calculates the braking curves for the train 1 and performs the method shown in Figure 3. Furthermore, the ATO device 8 is calculating the final braking curve shown in Figure 2. Figures 2 and 3 will be described later.

[0043] The passenger car 3 is coupled to the locomotive 2, representing a typical configuration for passenger rail transport. The rail 4 provides the track on which the train 1 operates, guiding its movement towards the target position 5.

[0044] Alternative embodiments could include different train configurations, such as multiple locomotives, freight cars, or specialized rail vehicles. The positioning of the ATP and ATO devices could also vary, potentially being distributed throughout the train or centralized in a single control unit.

[0045] Figure 2 depicts a graph illustrating braking curves for the train 1 shown in Figure 1 as an example for an autonomous rail vehicle. The graph shows velocity (V) on the vertical axis and distance (S) on the horizontal axis. A target position 5 is indicated at the bottom right of the graph, representing the final stopping point or speed restriction location. In the exemplary graph in Figure 2 the velocity in the target position 5 is zero but could also be above zero in alternative situations.

[0046] The graph includes multiple curves representing different aspects of the braking system. A braking curve 14 represents individual braking curves that could be calculated for various scenarios or conditions. These individual curves form the basis for the more complex calculations performed by the inventive ATO device 8.

[0047] An envelope curve 15 represents the minimum of all individual braking curves 14. This envelope curve 15 can provide a conservative boundary for safe deceleration across various scenarios. The envelope curve 15 is composed of multiple segments connected at grid points 12. These grid points 12 represent locations where significant changes in the boundary conditions occur, such as changes in track gradient or speed limits.

[0048] A current train position 10 is marked with a red X on the right side of the graph. From this point, a phase-in curve 11 is drawn in red, connecting the current train position 10 to the envelope curve 15. This phase-in curve 11 represents the real-time calculation performed by the ATO device 8 to adapt the pre-calculated braking curve to the train's current state.

[0049] The combination of the phase-in curve 11 and the relevant portion of the envelope curve 15 forms the final braking curve 16, which extends to the target position 5. This final braking curve 16 is what the ATO device 8 uses to control the train's deceleration.

[0050] Alternative implementations could explore different methods of representing and calculating the envelope curve, such as using more complex mathematical models or incorporating additional factors like real-time weather data or track condition information.

[0051] Figure 3 illustrates a flowchart for the method of calculating braking curves for the train 1 in Figure 1. The method begins with step 100, which involves performing a pre-calculation phase to pre-calculate a common braking curve for the train 1 based on spatial and temporal restrictions. The common braking curve can be the envelope curve 15 or one or more of the braking curves 14 shown in Figure 2. This step can also include storing states of the common braking curve 14 or the envelope curve 15 at grid points 12 only. Grid points 12 are set where kinematic changes occur. This step 100 is beneficial for reducing the computational load during real-time operations.

[0052] The process then moves to step 110, where a real-time calculation phase is performed. This step involves receiving the current train position 10 and state of the train 1. This information is likely gathered from various sensors and positioning systems onboard the train 1.

[0053] In step 120, the method calculates the real-time phase-in curve 11 from the current position 10 to the common braking curve 14, which could also be the envelope curve 15. This step adapts the pre-calculated curve to the train's current state, ensuring that the braking profile remains accurate and safe.

[0054] Step 130 involves using both the pre-calculated common braking curve 14 and the real-time phase-in curve 11 to determine the final braking curve 16 for the train 1. This step combines the efficiency of pre-computed data with the accuracy of real-time adjustments.

[0055] The method then proceeds to a decision point at step 140, where it checks if the target position and restrictions have changed. This step determines whether the pre-calculated common braking curve 16 can be reused for subsequent calculations.

[0056] If the target position and restrictions have not changed (No branch), the process moves to step 150. In this step, the common braking curve 14, which could also be the envelope curve 15, is re-used for the next braking curve calculation, potentially reducing computational load significantly. The next braking curve calculation is done for a changed position of the train 1, i.e. a new phase-in curve needs to be calculated anyway. Otherwise (not shown), if the target position and restrictions have changed, the common braking curve 14 needs to be updated.

[0057] Alternative implementations of this method could include additional steps for handling exceptional situations, such as emergency braking scenarios or unexpected obstacles on the track. The method could also be expanded to include more sophisticated decision-making processes at step 140, considering factors like energy efficiency or passenger comfort when determining whether to recalculate the common braking curve.

Claims

1. A computer-implemented method for calculating braking curves for an autonomous rail vehicle (1), comprising: performing a pre-calculation phase, including pre-calculating a common braking curve (14) for the autonomous rail vehicle (1) for a target position (5) based on spatial and temporal restrictions; performing a real-time calculation phase, including receiving a current position (10) and state of the autonomous rail vehicle (1); calculating in real-time a phase-in curve (11) from the current position (10) to the common braking curve (14); characterized in that a final braking curve (16) for the autonomous rail vehicle (1) uses both the pre-calculated common braking curve (14) and the real-time calculated phase-in curve (11); and the common braking curve (14) is re-used for the calculation of a next braking curve as long as the target position (5) and the spatial and temporal restrictions are unchanged.

2. The computer-implemented method of claim 1, characterized in that storing states of the common braking curve (14) at grid points (12) only, wherein grid points are set where kinematic changes occur.

3. The computer-implemented method of claim 2, characterized in that any point on the final braking curve connecting neighboring grid points (12) is analytically calculated.

4. The computer-implemented method of claim 2 or 3, characterized in that the phase-in curve (11) intersects the common braking curve (14) on the curve connecting two neighboring grid points (12).

5. The computer-implemented method of any of claims 1 to 4, characterized in that calculating an envelope curve (15) representing a minimum of all possible common braking curves (14).

6. The computer-implemented method of claim 5, characterized in that calculating the envelope curve (15) comprises determining minimum values of multiple possible common braking curves (14) for different targets.

7. The computer-implemented method of any of claims 5 to 6, characterized in that calculating the phase-in curve (11) comprises performing a straightforward calculation to determine a closest reachable intersection on the envelope curve (15) that can be analytically determined between two neighboring grid points (12, 13).

8. The computer-implemented method of any of claims 1 to 7, characterized in that the method further comprises updating the pre-calculated common braking curve (14) and / or envelope curve (15) when environmental conditions or vehicle parameters change significantly.

9. The computer-implemented method of any of claims 1 to 8, characterized in that the spatial and temporal restrictions include at least one of: speed limits, gradient information, track curvature information, adhesion information of a rail (4), and power restrictions.

10. An Automatic Train Operation (ATO) device (8) for calculating braking curves for an autonomous rail vehicle (1), comprising: a processor configured to perform a pre-calculation phase, including pre-calculate at least one common braking curve (14) for the autonomous rail vehicle (1) for a target position (5) based on spatial and temporal restrictions; perform a real-time calculation phase, including receive a current position (10) and state of the autonomous rail vehicle (1); calculate in real-time a phase-in curve (11) from the current position (10) to the common braking curve (14); characterized in that the final braking curve (16) for the autonomous rail vehicle (1) uses both the at least one pre-calculated common braking curve (14) and the real-time calculated phase-in curve (11); and the common braking curve (14) is re-used for the calculation of a next braking curve as long as the target position (5) and the spatial and temporal restrictions are unchanged.

11. The Automatic Train Operation (ATO) device (8) of claim 10, characterized in that the processor is further configured to store states of the common braking curve (14) at grid points (12, 13) only, wherein grid points are set where kinematic changes occur.

12. The Automatic Train Operation (ATO) device (8) of claim 11, characterized in that the processor is further configured to analytically calculate any point on the final braking curve connecting neighboring grid points (12, 13).

13. The Automatic Train Operation (ATO) device (8) of any of claims 10 to 12, characterized in that the processor is further configured to calculate an envelope curve (15) representing a minimum of all possible common braking curves (14).

14. The Automatic Train Operation (ATO) device (8) of claim 13, characterized in that calculating the envelope curve (15) comprises determining minimum values of multiple possible common braking curves (14) for different targets.

15. Computer program product comprising instructions that, when executed by a computer, cause the computer to perform a method according to any one of claims 1 to 9.

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