Post-processing of a planned path by means of an acausal fir filter

Abstract

The invention relates to a method for post-processing a planned path (11) in the low speed range with the aid of an acausal FIR filter (10) having multiple filter steps (27). The invention also relates to a vehicle (30) for carrying out the method according to the invention, as well as well as to a use of said method.

Description

[0001] Description

[0002] Technical field

[0003] The present invention relates to a method for post-processing a planned path in the low-speed range using an acausal FIR filter with multiple filter steps. The invention also relates to a vehicle for carrying out the process and to the use of the method according to the invention.

[0004] State of the art

[0005] In automated parking, the vehicle's computers control the steering wheel, accelerator, and brakes so that the vehicle achieves a calculated target pose (pose = 2D position, orientation, and curvature) when parking in the space and when exiting in the desired direction on the road. Once a parking space is detected and selected by the driver, a target pose and a path to reach it are calculated based on the detected objects. To follow the calculated path precisely, it must be drivable, meaning the vehicle's kinematic limitations must be taken into account. To find runtime-efficient paths, generic path planners sometimes use motion primitives that only consider a portion of the limitations. In these cases, a post-smoothing filter is used to smooth the calculated path.

[0006] Savitzky and Golay (“Smoothing and Differentiation of Data by Simplified Least Squares Procedures”, Anal. Chem. 1964, 36, 8, 1627-1639) describe the analysis of digital data using numerical methods. They employ filtering and differentiation to process the data and prepare for further processing steps. They also present a simplified procedure using least squares calculations.

[0007] Similarly, Schafer ("What Is a Savitzky-Golay Filter?", IEEE Signal Processing Magazine 2011, 28, 4, 111-117) defines the so-called Savitzky-Golay (S-G) filters and their properties in the frequency domain, as well as their design using polynomial approximation of an impulse train. He also presents an approximation formula for the 3 dB cutoff frequency as a function of the polynomial order N and half the length M of the impulse response.

[0008] Matute-Peaspan et al. (C. Lateral-Acceleration-Based Vehicle-Models-Blending for Automated Driving Controllers, Electronics 2020, 9, 10, 1674) describe model-based trajectory tracking as a widely used technique for automated driving systems. A critical factor is the correct selection of a vehicle model to achieve the best compromise between real-time capability and robustness. A combination of multiple vehicle models is also possible.

[0009] Disclosure of the invention

[0010] According to the invention, a method for post-processing a planned path in the low-speed range is proposed using an acausal FIR filter with multiple filter steps. In this method, a section processed within a filter step is shorter than the length of the path, and each filter step is performed using polynomial approximation and its evaluation.

[0011] The planned path, which is present at the beginning of the method according to the invention, is a path pre-calculated and sampled by a conventional path planner using a generic path planning algorithm, which specifies a planned driving maneuver for a vehicle. In the method proposed according to the invention, a filter is applied to the discontinuous sampled curvature profile of a pre-planned path and post-processed in such a way that the necessary smoothness is achieved in the curvature profile of the path to enable precise control. The curvature profile specifies the corresponding curvature at each point on the path. The curvature profile is usually parameterized via the arc length (distance along the path). The curvature itself denotes, at a specific point on the path, the inverse of the curve radius at that point. (A straight line with curve radius °°, for example, would consequently have a curvature of 0.)) Accordingly, the curvature profile of a path can also be understood as a mathematical function that provides the corresponding curvature at a given point on the path for a given distance.

[0012] The smoothness of the curvature profile achievable in the inventive method refers to its property as a mathematically "smooth function" that is arbitrarily differentiable. For example, when referring to a "sufficiently smooth" function or "sufficient smoothness," the requirement is that the function is differentiable multiple times (e.g., n times) depending on the specifications. In this context, the smoothness resulting from the method corresponds to the resulting differentiability of the curvature profile. In the inventive method, the polynomial order used particularly influences how often the resulting filtered function is differentiable and, consequently, the degree of smoothness achieved.

[0013] Control engineering is used to influence the behavior of a physical system, such as a vehicle, based on specific input variables and associated technical components, or to impose a desired behavior. "Control" or "smoothing" refers specifically to the system's ability to technically implement an input signal. As described above, a generically planned path does not account for all the kinetic constraints of a system, meaning that without any post-processing (so-called "post-smoothing filters"), a vehicle could not travel along the path. A controller would be unable to keep the vehicle on the path. Therefore, the necessary smoothness of the path, enabling the controller to steer the vehicle along it, is achieved through the technical capability of control.The vehicle for which the planned path is intended is primarily a passenger car, but other vehicles, e.g. trucks, buses, commercial vehicles, are also included.

[0014] According to the invention, an acausal FIR filter is used. This is a digital filter for processing a signal. The technical implementation is achieved, for example, using logic devices (such as ASICs or FPGAs) or in the form of program sequences with a signal processor. An FIR filter operates with a finite impulse response (FIR) and allows a linear phase response during filtering steps. An acausal FIR filter is also numerically more stable and its function is not solely dependent on past values. The acausality of the filter can be utilized because the entire signal path is available at the time of filtering.

[0015] The section processed within a filter step can also be referred to as the "filter window" and specifies which data points from the path are considered for the current filter step. According to the invention, the length of the processed section must be shorter than the length of the path, resulting in multiple filter steps within the method. For each subsequent filter step, the filter window, i.e., the section to be processed, is shifted further along the path, and the filter step is performed again. This is repeated until the filter window reaches the end of the path. Each filter step, or its execution, comprises a polynomial approximation within the filter window and its evaluation to obtain a filtered curvature value. The resulting smoothness is determined, among other things, by the polynomial order used and the chosen length of the filter window.

[0016] In an advantageous embodiment of the method according to the invention, the polynomial approximation is carried out using the least squares method in the processed section.

[0017] In a preferred embodiment, a Sawitzky-Golay (SG) filter, known in the field of digital data processing, is used as the acausal FIR filter. In principle, SG filters are possible in both causal and acausal variants. Since the entire curvature profile is already known at the beginning of the filtering process in the method according to the invention, the advantage of the numerically stable acausal variant can be utilized, and an acausal SG filter is used according to the invention.

[0018] In a further advantageous embodiment of the method according to the invention, the low speed range includes speeds up to 5 m / s, preferably up to 4 m / s, particularly preferably up to 3 m / s, especially parking maneuvers. Parking maneuvers include, in addition to maneuvering in a parking lot, a parking area, a parking garage or comparable parking environments, in particular driving into or out of a parking space, i.e. a parking area for parking the vehicle.

[0019] In a further advantageous embodiment of the method according to the invention, the polynomial order and / or the length of the processed section are individually determined for each execution of the method. These determine the filter dynamics and the resulting smoothness of the curvature profile and can be adjusted and changed independently of each other or in a predetermined relationship. The parameters are always individually selected to achieve the desired properties. In particular, they depend on the kinematic properties of the system, especially a vehicle, and can therefore have different advantageous settings.

[0020] In a further advantageous embodiment of the method according to the invention, the assumed safety distances remain above a defined threshold value in the planned path after reworking. Such safety distances relate to the distances of the vehicle during the execution of the path to static or moving objects in the environment, e.g., other vehicles, infrastructure components, road users, building parts, plants, and can vary.

[0021] In a further advantageous embodiment of the method according to the invention, a speed profile is calculated in a subsequent process step by deriving a curvature along the resulting path. This profile indicates a preferred or a maximum speed at which the respective sections or points of the path should be traversed. The derivation of the curvature is therefore directly correlated with the respective speed. In a further advantageous embodiment of the method according to the invention, a filtered profile of a vehicle orientation and a vehicle 2D position is calculated in a subsequent process step by integration. This allows a complete check of the state of a vehicle, e.g., at the end of a maneuver, which can then be used as the starting point for a subsequent maneuver.Vehicle orientation refers in particular to the current direction of travel, while the vehicle 2D position refers to its classification in the environment, e.g. in the surrounding infrastructure, from a top-down perspective.

[0022] In a further advantageous embodiment of the method according to the invention, monitoring is carried out to ensure that deviations between the original and filtered path points remain below a defined threshold. This also serves, in particular, to avoid collisions with static and moving objects in the environment. Preferably, when deviations above the defined threshold are detected, an acausal FIR filter with an adapted filter dynamic, in particular a higher filter dynamic, is applied. The filter dynamic is determined by the polynomial order and the selected length of the filter window and, in turn, influences the deviations between filtered and original data points. The filter dynamic can be described as the responsiveness to the input signals, i.e., how quickly the filter output changes in response to a change at the input.Thus, the filter dynamics depend on the filter's parameterization. For example, low filter dynamics mean that a change at the input results in a very slow change at the filter's output, whereas with high filter dynamics, the output reacts much faster to the (same) change at the input. Within the scope of the present invention, increasing the polynomial order, as well as decreasing the window width (i.e., the length of the processed section), increases the filter dynamics and thus results in a faster output response to the filter's input signals.

[0023] In a further advantageous embodiment of the method according to the invention, a suitable vehicle model is integrated in a final process step using a classical numerical integration method, such as is typical for model-based trajectory tracking. This is used, for example, to determine the associated angular profile as well as the profiles of the x and y coordinates. Common methods for a numerical integration procedure, which is to be understood as a numerical method for the approximate calculation of the solution of a model, are widespread in the field and include, for example, the explicit Euler method, the implicit Euler method, the Runge-Kutta family of methods, the Adams-Bashforth family of methods, the Adams-Moulton family of methods, and many more.

[0024] The method according to the invention involves, for example, the integration of a single-track model (also known as a "bicycle model") of a vehicle, which is valid and common in the low speed range up to 5 m / s or 18 km / h. In such a model, the vehicle under consideration is simplified in such a way that it has only one wheel per axle and is therefore single-track.

[0025] Furthermore, the invention relates to a vehicle with an assistance system for carrying out the method according to the invention. Such a vehicle is in particular a passenger car, but other vehicle types such as trucks, buses, or commercial vehicles are also included. The vehicle according to the invention includes, in particular, the means for carrying out the method according to the invention and for subsequently executing the planned path in a corresponding driving maneuver.

[0026] Furthermore, the invention relates to the use of the inventive method for performing an automated parking maneuver of a vehicle. Its application is particularly relevant in the field of path following control.

[0027] Advantages of the invention

[0028] In the method proposed according to the invention, an acausal FIR filter is applied to the discontinuous sampled curvature profile of a pre-planned path. This ensures that the path pre-calculated and sampled by a path planner possesses the necessary smoothness in its curvature profile, allowing for precise control during the execution of a driving maneuver. The application of filter-based approaches in the field of vehicles and driving maneuvers, particularly parking applications, is not previously known. A key advantage is that the filter used functions as a low-runtime post-smoothing filter, enabling rapid post-processing of the planned path.Furthermore, it can be exploited that the path to be processed is already completely available at the time of filtering and that the future curvature values ​​can be included in the filter application, thus enabling an acausal formulation and therefore the use of an acausal filter variant. Thus, according to the invention, an acausal FIR filter is used. This results in significantly improved performance compared to conventional filter applications.

[0029] The resulting smoothness can be influenced in the inventive method by the polynomial order used and / or the length of the filter window. Thus, for example, the result and the time required can be weighed against each other, coordinated, and adjusted.

[0030] Adjusting the resulting smoothness of the filtered curvature profile, which is directly possible via the polynomial order of the filter, has the added advantage of guaranteeing precise alignment of the resulting path. This ensures the path's suitability for the system, such as the desired vehicle. The required smoothness, for example, for a specific vehicle model, can be directly specified using the polynomial order. For instance, a vehicle with a trailer (car-trailer combination) would require a higher degree of smoothness than a single vehicle. Furthermore, the process allows for monitoring safety distances based on threshold values ​​and, if necessary, adjustments to the process parameters.

[0031] Since many parts of the filter's calculations depend only on the window width and the filter's polynomial order, they can be performed at system startup, for example, when a vehicle is started. This means that a large portion of the calculations are already completed. In a further development, it is even possible to store the results of these calculations in read-only memory (ROM), allowing the calculations to be performed before the system even starts. In both implementations, this results in very fast execution of the actual calculations required during the process's runtime. The window width and polynomial order of the filter also provide information about other properties of the resulting filtered curvature profile, such as the maximum slope or potential overshoot.Therefore, the two parameters can be chosen to fulfill the desired properties. Consequently, a very high degree of control over the resulting system behavior is ensured. At the same time, the overall complexity of the method is very low, since the filter's behavior is determined solely by the two parameters of window width and polynomial order. Thus, in comparison to alternative post-smoothing methods for path planning, a procedure is proposed that combines simple design and low complexity with a reliably adjustable resulting path.

[0032] Furthermore, adjusting the filter dynamics allows direct influence on the resulting vehicle movement and thus on user comfort. Similarly, the steering behavior can be influenced by using various filter parameters. For example, settings such as "Steering while stationary is not permitted," "Steering while stationary is permitted," or "Depending on the parking situation, one of the previous categories must be selected" can be taken into account. This allows parameter sets to be selected according to the driving situation, and switching between the aforementioned options is possible. The same applies to other parameter sets and options.

[0033] Thus, the method according to the invention enables a resulting path that can be driven without jerky behavior of the vehicle or without short, rapid steering wheel movements, without a significantly increased calculation time being necessary, and is perceived as pleasant by the driver in terms of user comfort.

[0034] A further advantage is that the method according to the invention is independent of the method used for the preceding, generic path planning and can, in principle, be applied to any planned path. Thus, easy integration of the method into existing and all common systems is readily possible.

[0035] Brief description of the drawings: Embodiments of the invention are explained in more detail with reference to the drawings and the following description.

[0036] They show:

[0037] Figure 1 shows a schematic representation of the principle of the acausal FIR filter in the method according to the invention, and

[0038] Figure 2 shows the execution of a parking maneuver using the method according to the invention.

[0039] Embodiments of the invention

[0040] In the following description of embodiments of the invention, identical or similar elements are designated by the same reference numerals, and repeated descriptions of these elements are omitted in individual cases. The figures represent the subject matter of the invention only schematically.

[0041] Figure 1 shows a schematic representation of the principle of the acausal FIR filter 10 in the method according to the invention. The acausal FIR filter 10 is used to perform post-processing over the entire length LP 12 of a planned path 11 with a discontinuous sampled curvature profile 23, starting at its beginning 13. For this purpose, a section 17 to be processed, also referred to as the filter window 18, is selected, the length LA 16 of which must be shorter than the length LP 12 of the path 11. The selected section 17 to be processed specifies which data points from the path 11 are considered for the current filter step 27. The acausal FIR filter 10 is applied spatially over these path points 19 within the filter window 18. To perform a filter step 27, a polynomial approximation 26, e.g., using the least squares method, is carried out in the filter window 18. This polynomial is then evaluated to obtain a filtered curvature value 22.The filter window 18 is then moved along path 11 to select the next section 17 to be processed and to repeat the described filter step 27 consisting of polynomial approximation 26 and evaluation. During this process, it is also monitored that the deviations 28 between the original and filtered path points 19 do not exceed a threshold value. This is carried out until the end 14 of path 11 is reached, at which point the entire path 11 has been processed and is available as a filtered path 15 with improved smoothness 24. In this context, the smoothness 24 of the filtered path 15 resulting from the procedure corresponds to a resulting differentiability of the curvature profile 23. The resulting smoothness 24 is determined by the polynomial order and the length LA 16 of the filter window 18. A velocity profile can then be derived from the curvature 21 of the filtered path 15.

[0042] In a final step, a suitable vehicle model, e.g., a single-track model (also known as a "bicycle model") valid for low-speed applications, can be integrated using a classical numerical integration method, as is typical for model-based trajectory tracking. This is used, for example, to determine the associated angular profile as well as the x- and y-coordinate profiles.

[0043] Common methods for numerical integration, which can be understood as numerical methods for approximating the solution of a model, are widespread in the field and include, for example, the explicit Euler method, the implicit Euler method, the Runge-Kutta family of methods, the Adams-Bashforth family of methods, the Adams-Moulton family of methods, and many more.

[0044] Figure 2 shows the execution of a parking maneuver using the method according to the invention. The method according to the invention can be used in particular in the field of path following control for automated (parking) maneuvers at low speeds, i.e., for speeds up to 5 m / s or 18 km / h, preferably in the parking sector.

[0045] In automated parking, the steering wheel, accelerator, and brake are actuated by the assistance system 31 of the vehicle 30 in such a way that the vehicle 30 reaches a calculated target pose 34 on a parking space 35 when parking and, when exiting, in the desired direction of travel on a road 36. When carrying out the method according to the invention, an automated parking maneuver can be performed in which the resulting path 15 can be traversed without jerky behavior of the vehicle 30 or without short, rapid steering wheel movements. For this purpose, the initially conventionally planned path 11 is post-processed with an acausal FIR filter 10, and its curvature 21 is smoothed over the entire length LP 12.The system monitors that deviations 28 from the original and filtered path points 19 do not exceed a defined threshold, and that safety distances 37 to objects 38 – whether static or moving – are not undercut to avoid collisions with these objects 38. Using the filtered curvature profile 23 and a speed profile, the filtered vehicle orientation 33 and the vehicle's 2D position 32 can be calculated via the path parameter. The vehicle orientation 33 relates in particular to the current direction of travel, while the vehicle's 2D position 32 relates to its position in the environment, e.g., in the surrounding infrastructure, as viewed from above.

[0046] The invention is not limited to the embodiments described here and the aspects highlighted therein. Rather, within the scope specified by the claims, a multitude of modifications are possible that fall within the bounds of what is considered skilled in the art.

Claims

Claims 1. Method for post-processing a planned path (11) in the low speed range using an acausal FIR filter (10) with multiple filter steps (27), wherein a section (17) processed within a filter step (27) is shorter than a length LP (12) of the path (11) and wherein a filter step (27) is performed by means of polynomial approximation (26) and its evaluation.

2. Method according to claim 1, characterized in that the polynomial approximation (26) is carried out using the least squares method in the processed section (17).

3. Method according to claim 2, characterized in that a Sawitzky-Golay (SG) filter is used as the acausal FIR filter (10).

4. Method according to one of claims 1 to 3, characterized in that the low speed range includes speeds up to 5m / s, in particular parking maneuvers.

5. Method according to one of claims 1 to 4, characterized in that the polynomial order and / or the length LA (16) of the processed section (17) is individually determined for an execution of the method.

6. Method according to one of claims 1 to 5, characterized in that the safety distances (37) assumed by the rework in the planned path (11) remain above a defined threshold value.

7. Method according to one of claims 1 to 6, characterized in that in a subsequent method step a velocity profile is calculated by deriving a curvature (21) along the resulting path (15).

8. Method according to one of claims 1 to 7, characterized in that in a subsequent method step a filtered progression of a vehicle orientation (33) and a vehicle 2D position (32) is calculated by integration.

9. Method according to one of claims 1 to 8, characterized in that monitoring is carried out such that deviations (28) from original and filtered path points (19) remain below a defined threshold.

10. Method according to claim 9, characterized in that, upon detection of deviations (28) above the specified threshold, an acausal FIR filter (10) with an adapted filter dynamic is applied.

11. Method according to one of claims 1 to 10, characterized in that in a final method step a suitable vehicle model is integrated by a classical numerical integration method.

12. Vehicle (30) with an assistance system (31) for carrying out the method according to one of claims 1 to 11 .

13. Use of the method according to any one of claims 1 to 11 for performing an automated parking maneuver of a vehicle (30).

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