Method for generating a laterally offset trajectory

Abstract

It is suggested a method for generating a lateral offset trajectory for an at least partially automated mobile platform, the method having the following steps: providing a target lateral offset; inverting a provided dynamics model of the mobile platform; providing at least one limit of a system variable of the dynamics model for determining the lateral offset trajectory; determining a time sequence of lateral offset trajectory points for the inverted dynamics model based on the at least one limit of the system variable, using a state variable filter and using the target lateral offset as an input signal; wherein each point of the time sequence of the lateral offset trajectory is determined in an analytical manner by means of the state variable filter; and determining a time sequence of values of at least one controlled variable of the mobile platform by means of the inverted dynamics model and by means of the time sequence of lateral offset trajectory points as an input signal of the inverted dynamics model for generating the lateral offset trajectory.

Description

TECHNICAL FIELD

[0001] The present application relates to a method for generating a lateral offset trajectory for at least partially automated mobile platforms, a control device and a corresponding computer program product. BACKGROUND

[0002] In general, emergency evasion maneuvers for avoiding accidents in road traffic are triggered at very late points in time, that is to say shortly before a potential collision, with the result that high demands are made on the dynamics of the maneuver. On the one hand, in many cases the participating objects are only sensorically detectable at very late points in time, for example because a pedestrian steps out onto the carriageway from a line-of-sight obstruction; on the other hand, the sum of sensor uncertainties and uncertainties of other processes of the detected situation is often very high, because for example sudden changes in movement of intersecting pedestrians can be difficult to predict.

[0003] It is therefore worthwhile to pursue the full utilization of the dynamics available, in particular the vehicle dynamics. SUMMARY

[0004] In planning the design of interventions in the lateral dynamics of a vehicle for a driving assistance function, a corresponding vehicle trajectory is mostly chosen such that an optimal change process is derived in relation to the comfort of the intervention, in which for example a lateral acceleration limit and / or a lateral sway limit (Querruckbeschraenkung) is controlled. In order to observe the controllability limit values, the trajectory is chosen such that the global yaw rate maximum coincides with the controllability yaw rate limit value.

[0005] A yaw rate change process with a global maximum is thereby produced. In order to guarantee the controllability of the vehicle by means of manual intervention by the driver when the vehicle dynamics are automatically intervened (these interventions potentially being faulty), limit values of the dynamics intervention are observed, which have been determined in the scope of experimental investigations for various actuators and vehicles.

[0006] It has been shown that these system-independent limit values relating to the lateral dynamics of a vehicle in relation to the actuators can be transferred to system-independent limit values for a corresponding vehicle, for example the yaw rate.

[0007] In developing such a driving assistance function, the system-specific actuator limit values are usually derived from the system-independent controllability limit values, such as for example the yaw rate.

[0008] However, the setting of the limits of the controlled variables (Stellgroessen) corresponding to the actuators and, if necessary, other required restrictions on the behavior of the system, which can be described by means of so-called state variables, are usually not taken into account directly in the trajectory planning, but rather are only fed into the functional implementation downstream by corresponding application of the trajectory planning. This increases the application outlay.

[0009] If the actuator-specific controlled variable limits have to be derived from the yaw rate limits, it can be problematic to take the yaw rate limits into account directly within the functional implementation. This cannot be done without simplification due to the differential or nonlinear relationship. However, this simplification can lead to significant deviations between the vehicle dynamics assumed thereby and the real vehicle dynamics. In turn, this can result in the exceedance of controllability limits during the yaw rate change of the maneuver, which then have to be prevented with increased downstream application outlay.

[0010] The development of such a driving assistance function that enables the direct consideration of restrictions within the trajectory planning is usually based on optimization methods and, as a result, can only be conditionally integrated into the control device of a mobile platform for mass production in the usual case due to the high computing power required.

[0011] Thereby, according to the prior art, the potential for avoiding accidents is not utilized, since the maximum yaw rate or the yaw rate limit is only reached at a few points in time within the change process of the trajectory.

[0012] According to aspects of the present application, a method for generating a lateral offset trajectory, a method for providing a control signal, an application of the method, a control device, a computer program product and a machine-readable storage medium are suggested according to the features of the independent claims. Advantageous design solutions are the dependent claims and the subject matter of the following description.

[0013] In the entire description of the present application, the order of the method steps is indicated such that the method can be easily understood. However, the person skilled in the art will recognize that many of these method steps can also be traversed in other orders and lead to the same or corresponding results. In this sense, the order of the method steps can be changed accordingly. Several features are equipped with counting words in order to improve readability or make the assignment more explicit, but this does not mean that there is a certain feature.

[0014] A method for determining a lateral offset trajectory for an at least partially automated mobile platform is suggested, which has the following steps:

[0015] In one step, a target lateral offset is provided. In another step, a provided dynamic model of the mobile platform is inverted. In another step, at least one restriction of a system variable of the dynamic model is provided to determine a lateral offset trajectory. In another step, a time sequence of lateral offset trajectory points for the inverted dynamic model is determined with a state variable filter (based on the at least one restriction of the system variable) and with the target lateral offset as an input signal, wherein each point of the time sequence of the lateral offset trajectory is determined analytically. In another step, a time sequence of values of at least one controlled variable of the mobile platform is determined with the inverted dynamic model and with the time sequence of the lateral offset trajectory points as an input signal for the inverted dynamic model to generate the lateral offset trajectory.

[0016] According to one aspect, the state variable filter has an unlimited desired dynamics (Wunschdynamik).

[0017] In other words, in this method, the controlled variables are determined with the inverted dynamic model, which are then used as input signals for a real dynamic system, such as for example a mobile platform. The lateral offset trajectory can be executed by the mobile platform from the time sequence of values of the at least one controlled variable.

[0018] The following is to be interpreted broadly in relation to the analytically determined features and in particular to be determined by approximation methods and optimization methods: Each point of the time sequence of the lateral offset trajectory is determined analytically with the state variable filter. In particular, the analytically determined at least includes determining integrals with fixed step size during runtime and at any point in time. The analytically determined thus in particular does not include a recursive determination of the individual points in the sense of optimization methods. In particular, the analytically determined includes traversing a chain of n integrators, wherein n describes the order of the system, which characterizes the dynamic model. Such an analytically determined point of the time sequence of the lateral offset trajectory can be carried out for example with a computer and a correspondingly configured computer program.

[0019] In particular, with the determined time sequence of values of the at least one controlled variable, an expected setpoint (Sollvorgabe) for another control loop can be generated to control the mobile platform, for example by a setpoint of a steering angle or a steering angle rate, the lateral offset trajectory (corresponding to a feedforward control).

[0020] This method enables online trajectory planning with direct consideration of at least one system variable restriction, in particular controlled variable restrictions and / or state variable restrictions, based on a differential flat system for describing a dynamic model of a mobile platform and a state variable filter, wherein in particular controlled variable restrictions and / or state variable restrictions can be directly considered when performing the online trajectory planning.

[0021] Here, by using the flat coordinate w z The target lateral offset is differentiated n times in time and used as a state variable filter for online trajectory planning to determine the time series of the lateral offset trajectory points. Furthermore, using this method, by providing a time series of values ​​for at least one controlled variable, feedforward control and / or regulation based on flatness can be achieved. That is, by providing at least one controlled variable in the form of a value series, the mobile platform can be controlled and / or regulated using this value series.

[0022] By using a differentially flat system to describe the dynamic model and, in particular, state variable filters, all theoretical system variables can be parameterized, and the dynamic model of the moving platform can be inverted to establish control and / or regulation for the platform. This is particularly applicable to linearly controllable dynamic models of the moving platform, and especially to nonlinear dynamic models if the nonlinear dynamic model is differentially flat. Here, the linearly controllable model is always differentially flat; in the nonlinearly controllable model, the flatness property must be proven separately.

[0023] Advantageously, this approach can directly consider all existing state-controlled variable constraints of the mobile platform's dynamic model as integral components of the online trajectory planning; and / or can provide flatness-based feedforward control to maximize the functional utility of the automatic avoidance function. As a result, closed-loop planning of avoidance or lateral deviation trajectories can be performed with optimal utilization of the controllability limits of state variables (e.g., yaw rate) and / or controlled variables (e.g., steering angle rate).

[0024] Additionally, other state and controlled variable constraints can be implemented without having to solve the optimization problem during runtime, and therefore the method does not need to be compatible with the computational capabilities of the serial control device set up to execute the method.

[0025] In other words, this method leads to the conclusion that:

[0026] - By maximizing the controllability limits of the mobile platform's state variables (e.g., yaw rate) and / or controlled variables (e.g., steering angle rate), the functional utility of the avoidance function with the corresponding generated lateral offset trajectory is optimized.

[0027] - A closed, model-based approach for directly and systematically considering state and controlled variable constraints without requiring numerical solutions to the optimal control problem during runtime.

[0028] - guarantees the feasibility of the computed trajectory, since existing state- and controlled variable limits have been taken into account when generating the lateral offset trajectory.

[0029] - does not decisively increase the computation time or real-time capability, since a numerical on-line solution of the optimal control problem can be omitted, since the computation is performed by means of a non-recursive algorithm.

[0030] - generates a trajectory on-line, which is able to realize an adaptive behavior with respect to the necessary lateral offset, since a situation change, which has led to an adaptation of the evasion trajectory, can be directly taken into account by the method in the next computation step.

[0031] - additional advantage, since the dynamics model used when generating the lateral offset trajectory can directly provide an actuator-specific feedforward control part to realize the evasion maneuver.

[0032] In this method, the dynamics model of the mobile platform can be described by a linear model, which is described in state space representation by equations 4.1 and 4.2:

[0033]

[0034] y = Cx + Du (4.1) c T · x 4.2

[0035] Herein, x(t) e Rn x (t) e R n denotes the state vector of the dynamics model, and denotes the time derivative of x(t) e Rn x (t) e R 1 denotes the input variable, and y(t) e R 1 denotes the output variable of the dynamics model.

[0036] A denotes a system matrix characterizing the dynamic behavior of the dynamics model, b denotes the input vector of the system, c denotes the output vector of the corresponding system or dynamics model, and y denotes the output variable of the corresponding system or dynamics model.

[0037] In particular, the dynamics model of the mobile platform can be a dynamics model for the lateral dynamics of the mobile platform, which is characterized in explicit form by equations 4.3 and 4.4.

[0038]

[0039] Equations 4.3 and 4.4 for the lateral dynamics model of the mobile platform are based on an extended linearized single-track model. In addition to the standard single-track model, the lateral dynamics model is extended according to equations 4.3 and 4.4 using state variables such as sideslip angle (β) and yaw rate d / dtψ(t), along with the yaw angle ψ(t) and lateral offset y. L The state variables are δ(t) and the steering angle δ(t).

[0040] To describe the lateral dynamics model, the steering angular rate can be selected in this method used to generate the lateral offset trajectory. Instead of choosing the steering angle δ(t) as the controlled variable, this model uses the steering angle δ(t) to describe the system's state, while the steering rate is used instead. The controlled variable that represents the system.

[0041] The parameters in matrix A indicate: forward tilt stiffness (Schraeglaufsteifigkeit vorne)c v Back tilt stiffness c h The mass of the mobile platform is m; the vehicle speed is v; the distance from the center of gravity of the mobile platform to its rear axle is l. h The distance l between the center of gravity of the mobile platform and its front axle v ; and the moment of inertia J of the mobile platform related to the longitudinal axis z .

[0042] By inverting the dynamic model of the moving platform, the process of changing pre-given output variables (such as, for example, lateral offset y) from a model that has not been inverted is obtained. L In the time correlation of (t), the changes in input variables of a model without inversion can be directly calculated, such as the steering angle rate.

[0043] To invert the dynamic models 4.1 and 4.2, firstly, using transformation rules 4.5 to 4.8, and according to equations 4.9 and 4.10, the dynamic models 4.1 and 4.2 can be transformed into linear registrar normal form or into (differential) flat coordinates z. For the transverse dynamic model according to equations 4.3 and 4.4, this yields the system of equations 4.11 and 4.12.

[0044] z =T· x 4.5

[0045] A R =T·A·T -1 4.6

[0046] b R =T·b 4.7

[0047] c R T c T ·T -1 4.8

[0048] Equations 4.1 and 4.2, transformed to flat coordinates, can be described according to the following equations 4.9 and 4.10.

[0049]

[0050] y= c R T · z 4.10

[0051] Here, the variable z represents the variable of the (flat) output of the dynamic model for the lateral dynamics.

[0052] The transformation matrix T (4.5b, 4.5a) is used to transform the state described in original coordinates x to flat coordinates z . The matrix A R characterizes the system of the dynamic model in flat coordinates or in the regulation canonical form; b R The input vector of the transformed system is described by c R The output vector is described by y and i describes the corresponding input variable of the dynamic model in flat coordinates.

[0053]

[0054] T = [t, A T ·t,...,(A T ) n-1 ·t] T 4.5b

[0055] Here, Q S is the controllability matrix and β is a scaling factor, and t is β times the last row of the inverted controllability matrix.

[0056]

[0057] Here, z (x) is the (x)th time derivative of z(t).

[0058] With the parameterization chosen according to equation 4.3 of the lateral dynamic model of the mobile platform, A​R and c R T The fact that several elements of the equation are zero significantly reduces the complexity of solving the system of equations.

[0059] a0=a1=a2=0 4.13

[0060] c R,4 =c R,5 =0 4.14

[0061] In response, the last line of the extended monorail model of the lateral dynamics of the mobile platform is simplified to 4.15, which can be inverted in flat coordinates z according to equation 4.16.

[0062]

[0063] Therefore, according to Equation 4.16, the expected change process of the controlled variable (e.g., steering angular rate) can be directly calculated using the corresponding derivative of the flat output z of the dynamic model. ).

[0064] To determine the time series of the lateral offset trajectory points, the spatial coordinates w y The target's lateral offset (corresponding to the reference variable) can be transformed into a reference signal w in flat coordinates. z The corresponding conversion is performed by filtering according to Equation 4.10, and leads to filter Equation 4.17.

[0065]

[0066] For online executable generation of lateral offset trajectories, the target lateral offset trajectory w can be pre-defined. y (t), and then transform the target's lateral offset trajectory w according to filter equation 4.17. y (t).

[0067] In particular, for the online executable generation of lateral offset trajectories, a target lateral offset value w can be pre-defined, for example. y and target time t end The target lateral offset is then calculated, and the target lateral offset value w is transformed according to filter equation 4.17. y and target time t end .

[0068] For online trajectory planning, when using a state variable filter, the target lateral offset w from filter 4.17 is used. z The nth time derivative is used to determine the time series of the lateral offset trajectory points for the inverted dynamic model according to the feedforward control equation 4.16.

[0069] For this, a state variable filter with order (n = 5) of the extended single-track model 4.3 and 4.4 in flat coordinates can be used, which can be described with equation 4.18.

[0070] In other words, the state variable filter plans a time series of lateral offset trajectory points for the inverted extended single-track model. Thus, in the case considered n = 5, the state variable filter has the same system order as the assumed road section or vehicle model. In addition, according to 4.18, no further model variables / information from the single-track model enters the unrestricted state variable filter.

[0071] According to Then it follows:

[0072]

[0073] By correspondingly designing the filter coefficients (a F，0 ,..., a F，4 ) via pole assignment (Polvorgabe) for example according to the prior art, or by designing a linear quadratic regulator (LQR) in consideration of the road section dynamics, that is to say the moving platform and the assumed system limits, the desired dynamics for the trajectory planning can be predefined with the aid of the state variable filter.

[0074] In the case of a predefined desired dynamics for the state variable filter, the generated lateral offset trajectory can be adapted to the behavior of the moving platform.

[0075] In other words, in order to carry out online trajectory planning in the case of a predefined target lateral offset w y (t) or w z (t), the flat outputs of the dynamics model and their time derivatives are used according to:

[0076] z *(1) ,..., z *(5) ; z * = [z * , z *(1) , z *(2) , z *(3) , z *(4) ],

[0077] The trajectory change process z *(t) to determine a time series of lateral offset trajectory points which are then used as input variables of the inverse model for calculating the manipulated variable change process in order to calculate the expected manipulated variable change process according to equation 4.16

[0078] Based on state system variable limits, like e.g. a yaw rate limit, by means of polyhedral state limits (as shown below), a time series of lateral offset trajectory points for the inverted dynamics model can be determined and thus can be an integral part of the trajectory planning.

[0079] A set of k polyhedral state limits corresponding to equation 4.19 describes the restriction by a separating interface (hyperplane) in the state space as follows:

[0080]

[0081] F x · x (t)- g x ≤ 0 4.19.

[0082] In this case, the set of all state vectors passes exactly on the separating interface x |F x · x = g x} is given. And F x is a matrix defining a linear combination of states which is restricted; x (t) is the state vector in the original coordinates; and the vector g x illustrates the value of the respective limit.

[0083] For the yaw rate limit case considered here, the polyhedral state limit reduces to a Box state limit according to equations 4.20 and 4.21, and directly represents the limit value of the state .

[0084]

[0085] According to equations 4.22 and 4.23, these limits can be transformed into flat coordinates by applying the transformation rule in flat coordinates with the transformation matrix T described above for the transformation.

[0086]

[0087] In the transformation, in case of the chosen parameterization of the system model 4.3, The number of elements of z according to 4.24 is zero.

[0088]

[0089] These restrictions are taken into account within the trajectory planning by restricting the highest order, i.e. the n-th derivative of the flat output z * In order to generate a correlation between the highest order derivative z *(5) and the state restrictions, an approximation of the state z * is performed by a Taylor series over a small time range At.

[0090] The necessary restrictions of z *(5) can be calculated by equations 4.25 and 4.26 for the upper and lower bound of the yaw rate.

[0091]

[0092] In this case, A p and b p are given by equation 4.26b.

[0093]

[0094] In order to ensure that an evasive trajectory has been achievable in the trajectory planning, the manipulated variable restrictions can additionally be considered as restrictions of the system variables when determining the time sequence of the lateral offset trajectory points for the steering angle rate.

[0095] According to equations 4.15, 4.27 and 4.28, the steering angle rate is limited as a manipulated variable of the system by calculating the maximum allowed highest order derivative of the flat output z * with the provided manipulated variable restrictions and from the last line of the system equation 4.3 in flat coordinates.

[0096]

[0097] In this method for generating a lateral offset trajectory, it is particularly advantageous that the state- and manipulated variable restrictions can be considered as integral components of the overall construction of the generated lateral offset trajectory. By this, a compliance with the above described controllability limit values, for example a state variable restriction, such as for example the yaw rate, can be introduced.

[0098] Therefore, the consideration of the restrictions of the state variables and / or the manipulated variables within the trajectory planning can be performed by restricting the highest order, i.e. the n-th derivative of the flat output z * .

[0099] According to the approach shown here, other state- and controlled variable limits can be implemented. Then, the system of differential equations 4.18 can be solved during runtime by a numerical integration, for example by a numerical integration with fixed step size, in order to perform an online trajectory planning, wherein, as described, the highest order derivative of the flat output can be limited.

[0100] That is, based on at least one limit of the system variables, the time sequence of lateral offset trajectory points for the inverted dynamics model with state variable filter can be viewed as corresponding to a switched system, since the saturation element 4.29 can be parameterized in the case of using the proposed boundary functions 4.25, 4.26, 4.27 and 4.28 (cf. Figure 3 As an example is advantageous):

[0101]

[0102] Here, The unrestricted desired dynamics describing the time sequence of lateral offset trajectory points is interrelated with the boundary functions 4.25, 4.26, 4.27 and 4.28, such that the allowed, i.e. limited, trajectory change process is derived in view of the assumed system limits

[0103] For selected limits of the controlled variables and state variables, according to equation 4.29, a prioritization can be freely chosen and the order thereof is implemented via a series connection of saturation elements. This prioritization offers the advantage that if it is physically not possible to comply with a limit, then the limit with the next lower priority is automatically used in order to nevertheless provide a solution.

[0104] According to one aspect it is proposed to determine and / or calculate the respective points of the time sequence of lateral offset trajectories in an analytical manner by means of an online numerical solution of a differential equation and / or a system of differential equations.

[0105] According to one aspect it is proposed that the state variable filter has a pre-given target dynamics and in particular the pre-given target dynamics is characterized by an extended single-track model of the mobile platform. The advantage of a pre-given target dynamics is that the desired dynamic behavior of the system can be parameterized and pre-given. The extended single-track model can be used in order to take into account all relevant states of the system. Here, the single-track model is in addition extended by the state 'lateral offset', since a trajectory of the lateral offset is planned for the evasion maneuver.

[0106] According to an aspect it is proposed to transform the dynamics model of the mobile platform into flat coordinates; and in particular, the system of the state variable filter and the system of the dynamics model have the same system order.

[0107] Wherein the state variable filter with constraints can be described by equations 4.18 and 4.29.

[0108] According to an aspect it is proposed to determine the respective points of the time series of the lateral offset trajectory analytically by means of a numerical solution of the differential equation.

[0109] Advantageously, the time series of the lateral offset trajectory and in particular of the lateral offset trajectory points can be determined by numerically solving, that is to say by online integration, the system of differential equations in short time with less computational effort (compared to an optimization solution).

[0110] According to an aspect it is proposed to constrain at least one system variable of the dynamics model based on flatness by means of a polyhedral state constraint of at least one system variable of the state variable filter.

[0111] Advantageously, with the polyhedral state constraint, not only box constraints, that is to say x < x max , can be considered, but arbitrary linear combinations of states can thereby be constrained, for example velocity constraints related to the position can be mapped or considered.

[0112] According to an aspect it is proposed that the unconstrained desired dynamics are characterized by the time series of the lateral offset trajectory points and are pre-given by means of the filter coefficients (a F,0 ,..., a F,4 ) of the state variable filter by pole pre-setting and / or by designing a linear quadratic regulator.

[0113] In particular, the desired dynamics can consider, for example, the track dynamics of a mobile platform, like for example a vehicle. That is to say, the poles / time constants are chosen manually and / or by means of the mentioned design methods, such that the planned trajectory has the desired dynamics without constraints.

[0114] By explicitly considering the constraints of the system variables, the desired dynamics can be set substantially more dynamically in the method for generating the lateral offset trajectory, since the desired dynamics are constrained downstream taking into account the constraints and thereby guarantee the realizability.

[0115] According to an aspect it is proposed that the target lateral offset prescribes a target lateral offset value within a defined time interval.

[0116] According to one aspect it is suggested that at least one of the limits on the system variables of the flatness-based dynamics model relates to at least one limit on the controlled variables and / or at least one limit on the state variables of the flatness-based dynamics model. The advantages of the thus constructed method have been set out above.

[0117] According to one aspect it is suggested that the state variable filter is limited according to the order of prioritization based on the limits on the controlled variables of the dynamics model and / or based on the limits on the state variables of the dynamics model.

[0118] In other words, the selected limits on the controlled variables and the state variables can be selected according to the order of prioritization and the order thereof can be implemented via the series connection of the saturation elements. This order of prioritization provides the advantage that if it is physically not possible to comply with the limits in the order of prioritization, then the limit with the next lower priority is automatically limited in order to nonetheless provide a solution.

[0119] According to one aspect it is suggested that at least one of the limited controlled variables of the flatness-based dynamics model is a controlled variable of at least one actuator influencing the lateral dynamics of the mobile platform and / or the gradient of the controlled variable and / or the acceleration of the controlled variable. By means of this, the method can be adapted to different requirements for controlling and / or regulating or operating the mobile platform.

[0120] According to one aspect it is suggested that the at least one actuator controls the steering angle and / or at least one brake pressure and / or at least one wheel damper.

[0121] By controlling different actuators, the type of mobile platform or the determined manner of the dynamics behavior of the mobile platform can be adapted.

[0122] According to one aspect it is suggested that at least one of the limits on the state variables of the dynamics model is the side slip angle and / or the yaw angle and / or the yaw rate and / or the lateral acceleration and / or the steering angle and / or the lateral offset of the mobile platform.

[0123] By means of this, the method can be adapted to different requirements for controlling and / or regulating the dynamics of the mobile platform.

[0124] It is suggested a method, wherein based on a time series of values of at least one controlled variable, a control signal for maneuvering an at least partially automated vehicle is provided; and / or, based on a time series of values of at least one controlled variable, a warning signal for warning a vehicle occupant is provided.

[0125] With this control and / or warning signal, a higher safety can be achieved at the mobile platform operated at least partially automatically.

[0126] The wording "based on" is to be broadly construed in relation to the feature that the control signal is provided based on a time series of values of the at least one controlled variable. The wording is to be construed such that the time series of values of the at least one controlled variable is considered for each determination or computation of the control signal, wherein it is not excluded that also other input variables are considered for such determination of the control signal. This applies correspondingly for the provision of the warning signal.

[0127] The above described method is suggested for use in the application of avoiding accidents in road traffic.

[0128] A control device is suggested which is set up to perform one of the above described methods for generating a lateral offset trajectory for an at least partially automated mobile platform.

[0129] According to one aspect, a computer program is described which comprises instructions which, when the computer program is executed by a computer, cause the computer to carry out one of the above described methods. Such a computer program enables the described methods to be employed in different systems.

[0130] A machine readable storage medium is described on which the above described computer program is stored. By means of such a machine readable storage medium, the above described computer program is portable.

[0131] A mobile platform can be understood as an at least partially automated system which is mobile and / or can be understood as a driving assistance system. Examples can be at least partially automated vehicles and / or vehicles with driving assistance systems. That is, in the present context, at least partially automated systems encompass mobile platforms in relation to at least partially automated functions, but mobile platforms also encompass vehicles and other mobile machines including driving assistance systems. Other examples of mobile platforms can be driving assistance systems or multi-sensor mobile robots with a plurality of sensors. BRIEF DESCRIPTION OF DRAWINGS

[0132] REFERENCE Figure 1 Embodiments of the invention are illustrated and embodiments of the invention are set forth in more detail in the following.

[0133] Figure 1 A data flow diagram of the method for generating a lateral offset trajectory is illustrated;

[0134] Figure 2 A data flow diagram of online trajectory planning with a limited state variable filter is illustrated;

[0135] Figure 3 A cascade of two saturation elements for considering state- and controlled variable limits in a prioritized manner within trajectory planning is illustrated;

[0136] Figure 4 a time course of the restricted highest order derivative of the flat output of the dynamic model is shown;

[0137] Figure 5a b a time course of the steering angle and the restricted steering angle rate is shown;

[0138] Figure 6a a comparison of the evasion trajectories is shown;

[0139] Figure 6b a comparison of the yaw rate time courses is shown; and

[0140] Figure 7 a simulation of a scenario with lateral offset trajectories of the evasion function is shown. DETAILED DESCRIPTION

[0141] Figure 1 A flow chart of a method 100 for generating lateral offset trajectories 620 for at least partially automated mobile platforms is schematically sketched. In step S1, the method is provided with a target lateral offset w y (t) 110. In step S2, the target lateral offset w y (t) 110 is transformed into flat coordinates w z (t) by means of a filter 130. For the online trajectory planning 140, the online trajectory planning 140 is provided with the target lateral offset in flat coordinates w z (t) as an input variable for a state variable filter 142 of the online trajectory planning 140, and the limits and the limits of the controlled variable 120 are provided in step S4 as input variables. Further, in step S3, a time sequence of lateral offset trajectory points z * (t n ) and the fifth time derivative z 5* (t) are determined as input variables for the inverted flat-based dynamic model 150 for determining a time sequence of lateral offset trajectory points, and the time sequence of lateral offset trajectory points z * (t n ) and the fifth time derivative z 5* (t) are provided to the inverted dynamic model in step S5. By means of the time sequence of lateral offset trajectory points z * (t n ) and the fifth time derivative z 5*(t) in step S6 by the inverted flatness-based dynamics model 150 160. a time series of values 160 of at least one controlled variable of the mobile platform 160 can be used for feedforward control for trajectory control of the mobile platform.

[0142] Figure 2 The information flow of the online trajectory planning 140 in flat coordinates is schematically sketched Figure 1 where the online trajectory planning 140 with an extended on-off state variable filter 140 with unrestricted filter desired dynamics 142 has a limiter 144 and an integrator chain 146.

[0143] Here, from the target lateral offset in flat coordinates w z (t) 130, with the help of the predefined desired dynamics of the state variable filter 142, the highest order time derivative of the flat output for the dynamics model unrestricted desired signal is limited by the limiter 144 and integrated by the integrator chain 146, thereby generating the trajectory z * and z *(1) ,..., z *(n) and their n time derivatives, in order to provide a time series of lateral offset trajectory points as input variables for the flatness-based inverse dynamics model of the mobile platform 150. Here, the input variables are both fed back into the limiter 144 and into the dynamics of the state variable filter 142 for the next calculation step. The output signal of the online trajectory planning 140 is provided to the flatness-based inverse dynamics model 150, for example for the calculation of a feedforward control Here, in this method, the system variables are dynamically limited, that is to say the dynamics of the filter are limited in a time- varying manner, according to the boundary functions 4.25, 4.26, 4.27 and 4.28.

[0144] Figure 3A prioritization of the limits of the state variables and / or of the controlled variables by means of a first saturation filter 144b and a second saturation filter 144d arranged in series behind the first one is schematically sketched, wherein the first saturation filter 144b can limit a state variable, such as, for example, the yaw rate, and the second saturation filter 144d arranged in the information flow direction behind the first saturation filter 144b can limit a controlled variable, such as, for example, the steering angle velocity, so that the fifth derivative of the input variable, i.e. z, is limited by means of the first saturation filter 144b and / or by means of the second saturation filter 144d. Here, the yaw rate limit 144a is provided both with the trajectory change process z * (t) of the flat output of the dynamic model, with the limit of the yaw rate, and with the time derivative thereof or the filter state of equation 4.18. The steering angle velocity limit 144c is provided both with the trajectory change process z * (t) of the flat output of the dynamic model, with the limit of the steering angle velocity, and with the time derivative thereof.

[0145] Thus, the prioritization of the limits can also be achieved by a sequential concatenation of the two limiters.

[0146] Figure 4 A curve diagram 400 is shown, in which the fifth derivative of the trajectory change process of the flat output z is plotted with a curve 450 against time t. Here, the limit of the fifth derivative is sketched both by the curve change process through the limit of the state variable 410 and by the curve change process through the limit of the controlled variable 420. It can be seen here that, by maximum utilization of the state variable 410, the fifth derivative is specified within the upper and lower limits of the controlled variable 420.

[0147] Figure 5a An exemplary change process of the controlled variable of the steering angle 510 over time is sketched with a curve diagram 500a.

[0148] Furthermore Figure 5b A corresponding change process of the steering angle velocity 520 with upper and lower limits 525 is sketched with a curve diagram 500b.

[0149] In Figure 6a , the lateral offset trajectory 620 generated with this method is compared in a curve diagram 600a with a differently generated lateral offset trajectory 610, wherein the latter has been generated according to the prior art without maximum utilization of the state limits for determining the trajectory.

[0150] Here, the lateral offset y of the mobile platform is plotted in the curve diagram 600a over the same road section x, and it can be seen that an increase in the lateral offset of about 20% can be achieved with the new method.

[0151] WithFigure 6b This is explained by the graph 600b in which, with respect to the time t, both the yaw rate 640 for the method described here and the yaw rate 630 according to the prior art are plotted. It becomes clear that by maximally utilizing the maximum possible yaw rate within the time range of the trajectory, an improved course of the trajectory can be achieved according to the described method.

[0152] Figure 7 A traffic scenario was sketched in which the evasion function with a laterally offset trajectory was simulated, which was triggered by a person on the carriageway.

Claims

1. Method for generating a lateral offset trajectory for an at least partially automated mobile platform, having the steps of: providing a target lateral offset (110); inverting a provided dynamic model of the mobile platform; limiting a state variable filter based on a limit of a controlled variable of the dynamic model and based on a limit of a state variable of the dynamic model according to a prioritized order, wherein the dynamic model is extended by a yaw angle, a steering angle and the lateral offset as state variables in addition to a side slip angle and a yaw rate; determining a time sequence of lateral offset trajectory points for the inverted dynamic model (150) using the state variable filter (142) and using the target lateral offset (110) as an input signal; wherein each point of the time sequence of the lateral offset trajectory is determined analytically; and determining a time sequence of values of at least one controlled variable (160) for the mobile platform using the inverted dynamic model (150) and using the time sequence of lateral offset trajectory points as an input signal for the inverted dynamic model (150) to generate the lateral offset trajectory. The state variable filter (142) has a pre-given target dynamics and the pre-given target dynamics is characterized using an extended single-track model of the mobile platform. The dynamic model of the mobile platform is transformed into a flat coordinate; and the system of the state variable filter and the system of the dynamic model have the same system order. The respective points of the time sequence of the lateral offset trajectory are determined analytically using a numerical solution of a differential equation. At least one system variable of the dynamic model (150) based on flatness is limited by means of a polyhedral state limit of at least one system variable of the state variable filter (142). At least one limit of a system variable of the dynamic model relates to at least one limit of a controlled variable and / or at least one limit of a state variable of the dynamic model. The at least one limited controlled variable of the dynamic model is a controlled variable of at least one actuator influencing the lateral dynamics of the mobile platform and / or a gradient of the controlled variable and / or an acceleration of the controlled variable.

2. The method of claim 1, wherein, The at least one actuator controls a steering angle and / or at least one brake pressure and / or at least one wheel damper.

3. The method of claim 1, wherein, The at least one limit of the state variable of the dynamic model is a side slip angle and / or a yaw angle and / or a yaw rate and / or a lateral acceleration and / or a steering angle and / or a lateral offset of the mobile platform.

4. The method according to any of the preceding claims 1 to 3, wherein, Based on the time sequence of values of the at least one controlled variable (160), a control signal for maneuvering the at least partially automated vehicle is provided; and / or, based on the time sequence of values of the at least one controlled variable (160), a warning signal for warning a vehicle occupant is provided.

5. The method according to any of the preceding claims 1-3, wherein, 11. The method according to any one of claims 1 to 3, which is used to avoid accidents in road traffic.

6. The method according to any of the preceding claims 1-3, wherein, ​ 7. The method of claim 6, wherein, ​ 8. The method of claim 7, wherein, ​ 9. The method of claim 6, wherein, ​ 10. The method according to any of the preceding claims 1-3, wherein, ​ ​ 12. Control device having a memory and a processor, wherein a computer program comprising instructions is stored on the memory, which instructions are set up to perform the method according to any one of claims 1 to 11 when the computer program is run on the processor.

13. Computer program product having a computer program comprising instructions which, when the computer program is executed by a computer, cause the computer to carry out the method according to any one of claims 1 to 11.

14. Machine-readable storage medium on which a computer program comprising instructions is stored, which instructions, when the computer program is executed by a computer, cause the computer to carry out the method according to any one of claims 1 to 11.

Images