DE102008046348B4 - Method, device and a corresponding computer program product for computer-aided path planning of a movable device, in particular a medical device - Google Patents

Abstract

A method for computer-aided path planning of a movable device (1), in particular a medical device, in a space area (R), wherein the path planning takes place prior to the operation of the movable device, wherein: - the space area (R) is characterized by one or more activity volumes each comprising the spatial extent of at least a portion of the space area (R) and the probability of occurrence of one or more object types in the at least a portion of the space area (R); - One or more groups of tracks of the movable device (1) in the space area (R) are given, wherein a respective track by a plurality of transverse volumes (V1, ..., V10) is described, wherein a transverse volume (V1, .. ., V10) at a particular time of movement of the device (1) on the web comprises the volume which the device (1) will traverse anew from the respective point in time during a stopping and / or avoiding maneuver; A plurality of risk volumes is determined for a respective trajectory, wherein a risk volume is the spatial extent of the intersection between a respective activity volume and a respective transverse volume (V1,..., V10) of the trajectory and the probability of occurrence of one or more object types in accordance with the activity volume involved; Depending on the risk volumes of the respective lanes from each group of lanes, an overall risk of a collision of the device (1) with objects in the spatial area (R) is determined and with the aid of an optimization method an optimal set of lanes comprising one or more targets Web is determined from each group of webs, wherein at least one of the targets is a minimum overall risk of the corresponding web with respect to a collision of the moving device with objects in the space region; and; the optimization method takes account of parameters of a sensor arrangement comprising one or more sensors (7, 8,..., 12) in the spatial area (R), whereby the optimization method outputs the parameters of an optimal sensor arrangement with regard to the one or more targets.

Description

The invention relates to a method for computer-aided path planning of a movable device, in particular a medical device, in a spatial area. Furthermore, the invention relates to a corresponding computer program product and a corresponding movable device.

In a variety of technical applications, devices are automatically or semi-automatically moved to perform certain tasks. For example, in the field of medical technology for diagnosis or therapy - controlled by an operator and partly automatically - movements of medical devices are carried out, whereby the importance of automatically executed movements is always greater. The problem is that collisions of the moving device with other objects and persons may occur. In the case of moving medical devices, it is aggravating that the environments in which the devices are used often have high dynamics and limited space.

From the prior art, it is known to monitor the movement of a medical device by video cameras, thereby detecting collision hazards and initiate appropriate countermeasures. With a correspondingly high dynamics of the monitored movement, collision risks that occur relatively frequently can occur, which in turn lead to an interruption of the operation of the device, for example due to a braking or avoidance maneuver of the device. It is therefore desirable, even before the operation of the device, to plan the movement of the device in a computer-aided manner in order to avoid interruptions in operation.

The article "IEEE Transaction on Robotics and Automation", Vol. 14, No. 6, December 6, 1998, pages 912 to 925, discloses a method for planning the movement of a plurality of robots, wherein collisions between the paths of the robots based on the optimization of a functional can be avoided.

In the document EP 1 990 786 A1 For example, a method for predicting the motion trajectories of a plurality of objects is described, wherein a motion path is selected for a specific object, according to which the collision probability of the specific object with other objects is lowest.

In the publication "IT + IT Information Technology and Technical Informatics", 42 (2000) 1, pages 16 to 23, a navigation system of an autonomous robotic vehicle is disclosed in which obstacles in the vicinity of the vehicle are detected and avoided these obstacles in a suitable manner becomes.

The document DE 10 2005 027 522 A1 describes a control method for a device having at least one movable member that includes a sensor for detecting an obstacle, wherein a danger area for the member is set dynamically over a detected sensor value.

In the document DE 10 2005 023 165 A1 For example, a medical imaging system including a patient-traversable member and a collision avoidance method are described wherein movement of the traveling member is stopped or slowed as the member enters an individual protection zone enveloping the patient.

The article "IEEE Transaction on Robotics and Automation", Vol. 18, No. 3, June 2002, pages 393 to 398, describes a method for collision avoidance and motion planning using a minimum translation distance.

The document "Proceedings of the 30th Conference on Decision and Control", December 1991, pages 698-703, discloses the control of a mobile robot between movable objects using a Kalman filter to estimate the motion of the mobile objects.

In the publication DE 10 2007 036 583 A1 A method for reconstructing a body map of a patient's body is described, wherein distances between a detector of an X-ray device and the patient's body are measured. In this case, the velocities of the moving parts of the X-ray device are automatically controlled and the X-ray dose or irradiation time is set.

The invention is based on the object of planning the movement of a movable device in a computer-aided manner in such a way that collisions with other objects are kept low.

This object is achieved by the method according to claim 1 or the computer program product according to claim 17 or the movable device according to claim 18. Further developments of the invention are defined in the dependent claims.

In the method according to the invention, a computer-aided path planning is carried out prior to operation of the movable device, wherein the spatial area in which the device can move is characterized by one or more activity volumes, each of which is the spatial extent of at least a portion of the spatial area and the probability the occurrence of one or more object types in the at least one part of the space area. Furthermore, one or more groups of webs of the movable device are predetermined in space, with a respective web being described by a plurality of transversal volumes.

In this case, a transversal volume encompasses the volume at a particular point in time of the movement of the device on the track, which volume will be traversed anew by the device from the respective time point in a period of a stop and / or avoidance maneuver.

According to the invention, a plurality of risk volumes is determined for the respective lane from the one or more groups of lanes, wherein a risk volume is described by the spatial extent of the cut between a respective activity volume and a respective transverse volume. Thus, there are as many risk volumes for a respective transverse volume as there are activity volumes which overlap with the transversal volume. A risk volume is further characterized by the probability of occurrence of one or more object types according to the respective activity volume. The probability of occurrence can include several probabilities depending on the individual object types.

According to the invention, depending on the risk volumes of the respective webs from each group of webs, an overall risk of a collision of the device with objects in the spatial area is determined, wherein the respective webs of a group are preferably described parametrically. That is, for each lane group exists a parameter description by which a plurality of lanes are characterized by different choice of parameters. The overall risk of a collision represents a measure of the risk of collision as the device moves along the respective lanes of each group of lanes. With the aid of an optimization method, an optimal set of lanes is determined according to one or more targets comprising one lane from each group of lanes, wherein at least one of the targets is a minimum overall risk of the corresponding lane with respect to a collision of the moving device with objects in the region of space ,

According to the invention, a parameterization of the risk is achieved by a suitable definition of risk volumes via transversal volumes and activity volumes, it being possible, based on this parameterization with known optimization methods, to determine a set of paths with the lowest possible collision risk. Thus, before the actual operation of the device, suitable webs can be determined for different web groups, wherein in a preferred embodiment each web group characterizes a function or task to be performed by the device, for example certain diagnostic movements or transfer runs of a medical device. Preferably, the relative risk of using webs from the groups of webs is taken into account in the overall risk. That is, the less frequently lanes from a particular group are used, the less this lane group is included in the calculation of the overall risk.

The optimization method as part of the inventive method takes into account parameters of a sensor arrangement comprising one or more sensors in the spatial area, whereby the optimization method further outputs the parameters of an optimal sensor arrangement with regard to the one or more targets. In this way, with the method according to the invention, in addition to optimal paths, an optimal sensor arrangement is also determined with which the risk of collisions is reduced. Thus, a particularly low risk of collision is achieved in that not only the optimal paths are used during operation of the device, but also the sensors are positioned according to the determined optimal sensor arrangement.

In a further particularly preferred embodiment, a transversal volume further comprises one or more velocity vectors describing the speed and direction of the device as it traverses the transverse volume, a risk volume further being defined by the one or more Velocity vectors of the corresponding transversal volume is characterized, showing the risk volume by cutting with a volume of activity.

In a particularly preferred embodiment of the method according to the invention, a damage amount of a collision of the object type with the device is defined for a respective object type as a function of the velocity vector (s) of the respective risk volumes, the overall risk taking into account the damage levels for the risk volumes of the respective trajectory such that Overall risk increases with larger loss amounts. The collision risk thus depends not only on the collision itself, but also on the damage caused thereby. That is, in particular those collisions are avoided in which the damage caused is particularly high.

To parameterize the sensor arrangement, in a preferred variant of the invention, a respective sensor of the sensor arrangement is characterized by a detection probability of one or more object types, wherein the detection probability preferably depends on the location and / or speed of the respective object type relative to the sensor. If the sensors are arranged in a fixed position, the detection probability for each type of object can optionally be fixed. Preferably, a total detection probability for one or more object types from the individual detection probabilities is determined for a respective track. The individual detection probabilities along a path take into account, for sensors mounted on the device, their location and their speed according to the movement of the device, whereby the speed can be determined from the velocity vectors of the risk volumes. That is, from the parameters of the web can be closed on the detection probability of the individual sensors for different types of objects at the individual track positions. The determined total detection probability is taken into account as a parameter in the overall risk.

In a further, preferred embodiment of the method according to the invention, the overall risk further includes a damage reduction factor which models a reduction in the amount of damage in the detection of an object type by the sensor arrangement. The reduction in the amount of damage results from the fact that when detecting an object usually a corresponding braking operation or an evasive maneuver is triggered, so that the damage is less than if the device would continue to move regularly on its predetermined path.

In the method according to the invention, any desired sensor arrangements can be modeled. In particular, such sensor arrangements can be modeled with one or more active range-measuring sensors. An actively distance-measuring sensor is characterized in that it actively sends out and receives a signal, wherein the distance to corresponding objects is determined based on the change in the signal due to reflections or scattering of objects or based on the transit time of the signal. The signal can be configured as desired, for example electromagnetic waves (eg in the form of visible or non-visible light) or sound waves (in particular ultrasonic waves). Examples of such active range-measuring sensors are laser scanners or actively distance-measuring 3D cameras. The sensor arrangement may include sensors on the device and / or stationary mounted in the room sensors, the detection probability of one or more types of object for a sensor on the device depends on the mounting position of the sensor on the device and the speed at which the device moves.

In a particularly preferred embodiment of the invention, not the entire sensor array is parametrically taken into account, but there are predetermined predetermined positions for the sensors, but with adjustment parameters such. B. an angle of the sensor, incorporated into the parameterization of the sensor array.

In a further, preferred embodiment of the method according to the invention, a cost expenditure can be determined for each sensor arrangement, wherein a further goal of the optimization method is a minimum cost outlay. The cost in particular characterizes the monetary outlay required for the installation of the sensor arrangement. The cost can be z. B. consider the cost of the individual sensors or the cost of mounting the sensors at certain positions.

In the method according to the invention, any known optimization method can be used to solve the optimization problem. For example, analytical optimization methods, such. As the Newton method or method based on conjugated gradient used become. Preferably, however, probabilistic optimization methods are used, such. Eg genetic algorithms.

A preferred field of application of the method according to the invention is the planning of the movement of a medical device in a treatment room. The device can be, for example, an X-ray device, in particular a C-arm well known in the art.

In addition to the method described above, the invention further comprises a computer program product with a program code stored on a machine-readable carrier for carrying out each of the above-described variants of the inventive method when the program is run on a computer.

Moreover, the invention relates to a movable device, in particular a medical device, in which the optimal set of tracks, which was determined by the method according to the invention, stored in a memory of the device to operate the device based on the optimal set of tracks to move. In a preferred variant, the method has also been used to determine an optimum sensor arrangement, which is also stored in the memory of the device. Likewise, the sensors can already be arranged on the device according to the optimum sensor arrangement. The device is thus moved in operation based on the optimal set of paths and the optimal sensor arrangement.

Embodiments of the invention are described below in detail with reference to the accompanying drawings.

Show it:

1 a scenario in a medical intervention room with a movable C-arm and sensors for detecting objects in space, in which case optimal movement of the C-arm can be determined by the method according to the invention;

2 to 4 Side views of a C-arm to explain the traversed by the C-arm at different movements transverse volumes; and

5 a further view of a C-arm with sensors arranged thereon for detecting the environment of the C-arm, wherein the arrangement of the sensors can be optimized based on the inventive method.

1 shows a medical intervention space R in plan view, in which an X-ray measurement using a so-called. C-arm 1 to be carried out. The C-arm is a well-known in the art X-ray device, which can be moved via a (not shown) positioning means in different positions in the space for X-ray of body parts. The C-arm comprises a radiation source with collimater at one of its front ends 1a and at the opposite end a corresponding detection device 1b which are both suitably positioned according to the body parts of a patient to be X-rayed. In particular, a device of Siemens AG, for example AXIOM Artis dFA, can be used as the C-arm. However, the invention is also applicable to any other medical devices or non-medical devices, such as biplane systems with two C-arms, such. As the model AXIOM Artis dBC Siemens AG, or on Cartesian guided systems such. For example, the AXIOM Aristos FX Plus model from Siemens AG.

Next to the C-arm 1 is in 1 also a patient table 2 on which the patient to be X-rayed is lying. Furthermore, the space R contains schematically indicated monitors 3 on which the pictures taken by the C-arm are played back. In addition, as another medical device at the foot of the table 2 an EEG 4 provided (EEG = electro-encephalography). To protect the treatment personnel against X-rays is also an X-ray shield 5 present, which has a corresponding positioning device 6 , with which the protective shield is attached to the ceiling of the room R, can be moved in different positions. The current location of a doctor is in 1 indicated by an ellipse D and the current residence position of a wizard by an ellipse A.

In the scenario of 1 There is the problem that when performing movements of the C-arm, it may collide with the other objects or persons in the room. To one Therefore, to detect possible collision hazard early, are under the ceiling of the room R cameras 7 . 8th . 9 and 10 provided, with the cameras 7 and 8th on one long side of room R and the cameras 9 and 10 arranged on the other longitudinal side of the room. The viewing angles of the individual cameras are indicated by the angle α. The cameras enable a three-dimensional detection of a spatial area in which there is a risk of collisions. The cameras are 3D cameras, which preferably detect the spatial area in three dimensions based on an active distance measurement. The area covered by the cameras in 1 is an area of activity in which increased activity occurs due to movement of the C-arm or the treating staff or the patient. In addition to the cameras shown 7 to 10 can capture the immediate environment of the moving C-arm 1 Also cameras are provided directly to the C-arm, which move together with the C-arm.

Although the cameras can detect objects in the vicinity of the C-arm and thus avoid possible collisions of the C-arm with objects. Conventionally, however, the movement of the C-arm is not previously planned so that the risk of collisions is low. According to the invention, an optimal movement of the C-arm in the room can now be calculated in a computer-aided manner based on corresponding information about the intervention space and possible movement paths of the C-arm. The C-arm is then then suitably moved on the optimal paths. In addition, in a preferred embodiment, furthermore, an optimized arrangement of the cameras can be determined computer-assisted, in order to arrange the actual movement execution of the cameras according to the result of the optimization in space. One goal of the optimization carried out is to minimize the risk of collision, and as a further goal, the corresponding costs for the installation of cameras or sensors can be taken into account. The costs should be kept as low as possible.

When carrying out the optimization method, a large number of information and parameters are predefined, the optimization taking place based on this information or parameters. The information initially includes the already mentioned activity area in which activities are suspected. This area is divided into a plurality of activity volumes which are characterized by their spatial extent. An activity volume is characterized in the embodiment described here by further variables, which will be described in more detail below. Further, as further information possible web movements of the C-arm are known, the web movements are described with the help of so-called. Transverse volumes, which are explained below.

Some transversal volumes that result for different motions of the C-arm are in 2 to 4 played. 2 shows a diagnostic rotational movement of the C-arm around its center or isocenter. The center is the center of the 2 cross designated as C and the diagnostic rotational movement takes place about an axis perpendicular to the plane extending axis in this center. The cross C indicates the virtual patient tube, ie it essentially corresponds to the spatial extent of the patient to be X-rayed. The diagnostic rotational movement is further illustrated by the double arrow R. During this movement, transversal volumes are traversed by the C-arm, which are indicated as V1 to V4 in FIG 2 are indicated. A transversal volume describes in the embodiment of the invention described here at a particular point in time the path of movement of the C-arm, the volume which the C-arm will traverse anew after a stop command. This volume corresponds to the volume that the C-arm traverses after the stop command, minus the volume already occupied by the C-arm at the time of the stop command. The transverse volumes are further characterized by a field of velocity vectors, which will be explained in more detail below. One recognizes in 2 in that, in the diagnostic rotational movement, the machine traverses, depending on the direction of movement, corresponding volumes V1 or V2 on the back of the C-arm or volumes V3 and V4 respectively before the end of the C-arm.

3 shows two side views of the C-arm 1 with corresponding transverse volumes, which are traversed in a so-called. Anrückbewegung the C-arm. The approach movement describes the movement of the C-arm towards its working position. The direction of movement is indicated by the arrow P. Further, again, the virtual patient tube is represented by the cross C. It can be seen that a transverse movement V5 in the interior of the C-arm and two transversal volumes V6 and V7 are traversed before the C-arm during a return movement.

4 shows a view similar to 3 , now traversed transverse volumes are shown in a downward movement away from the working position of the C-arm. The Abrückbewegung is indicated by the arrow P ', in the opposite direction as the arrow P of 3 indicated. Further in turn, the virtual patient tube is indicated as a cross with reference symbol C. It can be seen that corresponding transverse volumes V8, V9 and V10 are traversed on the back of the C-arm during this reversing movement.

5 shows another side view of the C-arm 1 , the corresponding sensors 11 and 12 for immediate three-dimensional coverage of the environment before the C-arm. The sensors are again, for example, 3D cameras, which are preferably the cameras 7 to 10 according to 1 correspond. The essentially cone-shaped space area through the camera 11 is detected, is denoted by the reference numeral B1 and the likewise cone-shaped space area through the camera 12 is detected, denoted by the reference B2. The cameras are used in particular to detect areas in front of the C-arm during a rotational movement, which is again indicated by the double arrow R, which may be shadowed by the C-arm itself. In a preferred variant of the optimization method according to the invention, the arrangement of these cameras is taken into account in such a way that an optimal position of the cameras with regard to a collision avoidance is determined taking into account low costs.

In the following, embodiments of an optimization method according to the invention will be explained in detail. For optimum motion planning, the path of the device whose movement is planned must first be parameterized. A path of the device is described by the course of the positions of the joints of the device over time. It is assumed that {g _k } _{k = 1, .., N are} the movable joints of the otherwise rigid device, which are summarized in a vector q = (g ₁ , ..., g _N ) ^T , which is the Represents the configuration of the device. A pathway is determined both by the joint positions and by the passage of time, in which the joint positions are taken. The trajectory is therefore determined as a whole by a time interval [t ₀ , t ₁ ] and the configurations assigned to these times, that is, by the mapping q: [t ₀ , t ₁ ] → Q.

The webs of the device should each fulfill a specific purpose and thereby comply with certain conditions. For example, the purpose is to move the device from a configuration initially given to a particular end configuration. For example, with respect to the C-arm described above, the purpose could be to circularly move the collimator and detector of the C-arm around a body organ to be X-rayed. In the following, for movement planning, a plurality of groups of tracks are considered, each group corresponding to a task set in the application. The tasks are hereinafter referred to as {A _i , l = 1, ..., L}. The aim of the optimization process is to determine an optimal trajectory for each group of trajectories with regard to one or more objectives, in particular with regard to a minimal collision risk.

The lanes from each group of lanes are determined to a degree by the task at hand. For a transport journey, for example, a starting point q (t ₀ ) = q ₀ and an end point q (t ₁ ) = q _{1 are} defined or a plurality of end points Q1, where q (t ₁ ) ∈ Q ₁ , if a set of parking positions come into question. Further restrictions result from the obstacle landscape of the spatial area in which the device is to move. Configurations that lead to collisions with obstacles are prohibited. Each relevant obstacle leads to a set O _k of forbidden configurations, so that for the trajectories traversed by the device: q (t) ∉ O _k , t ∈ [t ₀ , t ₁ ], k = 1, ... K.

The paths are usually described by a sufficiently dense discrete set of individual times τ _i , i = 1, ..., T with τ ₀ = t ₀ and τ _T = t ₁ . A fixed orbit B is then given by the tuples {(τ _i , q _i ) | i = 1, ..., T}. These tuples are combined into a long parameter vector p = (τ ₁ , q ₁ , τ ₂ , q ₂ , ..., τ _T , q) that defines the trajectory. Restrictions on the web are thus given by limitations of this parameter vector, e.g. By the requirement q ₁ ∉ 0 _k , i = 1, ..., T, k = 1, ..., K due to obstacles or by the requirement q _i ∈ B ₁ , i = 1, .. ., T due to requirements for the task performed by the railway.

As already mentioned above, the tasks of the trajectories that can be carried out in one application area are defined as {A _i , l = 1, ..., L}. In this case, the set of paths A fulfilling a task A _{i is} represented by the parameter set P _i . In general, these sets contain several elements, ie the obstacle landscape and the requirement remain free parameters. In a transport journey z. As a rule, many different paths possible, as long as no obstacle is met and start and end points are met. From these free paths, an optimal path is selected according to the invention for each task, which is described with the corresponding optimum parameter set.

In a preferred embodiment of the invention, the optimization is carried out with regard to two goals. The first goal is to minimize the risk of collision with previously unknown obstacles, and the second objective concerns minimum costs for sensors to be mounted in the room, which cost may be fixed according to any given measure. In particular, the cost is higher, the more expensive a sensor is and the more difficult it is to attach it to positions in the room or on the device.

In addition to the goal of minimizing risk and costs, other optimization goals may also be taken into account. In particular, the optimization can also take place with regard to the fact that a web is to be traversed through the device in as short a time as possible or that the energy consumption when passing through the web should be minimal. Furthermore, in the optimization as a further requirement, a safety criterion can be taken into account, i. H. that the railway has to keep certain distances to obstacles.

In the method according to the invention, an activity area or activity volume is predetermined, it being possible for this volume to be subdivided into a plurality of individual volumes. The activity area describes a part of the space in which with certain probability a certain activity takes place. In the scenario according to 1 For example, the activity volume can be controlled by the cameras 7 to 10 be defined areas of space defined. The activity volume not only describes a spatial area but is also characterized by the context, ie whether the device for which a lane is being planned is currently in motion, how many people are present, how many independent activities of these persons take place in parallel and the like. In the following, such a context is considered by an a-priori probability of occurrence for objects and persons in the room. An activity volume is thus described by V _A = (G, {(h _j , p (h _j )) | j = 1, ..., J}), ie by the probabilities p (h _j ) of the occurrence of objects Class h _j in the space area G, where the space area is given with respect to a space-fixed world coordinate system W.

In the method according to the invention further transversal volumes are given, which have already been described in the foregoing. The transversal volumes describe areas of space which the device for which a movement is planned will traverse in the near future. The volumes depend on the geometry of the device, which is assumed to be fixed except for the joint positions. In addition, the transverse volumes depend on the trajectory, ie the trajectory B of the device during the respective movement. In the trajectory, joint positions and the corresponding time points are noted. It is assumed in the embodiment described here that the device does not evade but stops in the event of detection of an obstacle. That is, a transversal volume describes the volume that a device passes through in a given track position until it stops. In the following, T _i denotes the time interval which the machine requires to stop in the event of the detection of an obstacle at the instant τ _i . Similarly, a corresponding time interval can also be defined for an evasive movement if the device executes such a movement when an obstacle is detected.

Das heißt, das Transversalvolumen beschreibt die Menge aller Punkte im Raum, die im Anhaltezeitraum des Geräts noch durchquert werden, und zwar bis auf diejenigen, bei denen das Gerät am Anfang schon ist. Hierbei bezeichnet T_i die Zeitspanne des Anhaltevorgangs zum Zeitpunkt τ_i und q_i ist die entsprechende Konfiguration zum Zeitpunkt τ_i. Die Konfigurationen zu den Zeitpunkten τ_j im Anhalteintervall T_i sind dabei als q_j bezeichnet.The size of the transversal volume is defined based on the volume V _M (q), which is the volume that the machine occupies in space for a given configuration q. This volume is also given in the fixed world coordinates W. The transversal volume depends on the movement trajectory and the time and is defined as

That is, the transversal volume describes the amount of all points in the space that are traversed during the stopping period of the device, except for those where the device is already at the beginning. Here, T _i denotes the period of the stopping operation at the time τ _i and q _i is the corresponding configuration at the time τ _i . The configurations at the times τ _j in the stopping interval T _i are denoted as q _j .

welches ebenfalls von der Trajektorie B und dem Zeitpunkt τ_i abhängt. Durch dieses Geschwindigkeitsfeld werden die GeschwindigkeitenIn the embodiment of the invention described herein, a transverse volume is further specified by velocity vectors. In particular, each transverse volume also includes one more field

which also depends on the trajectory B and the time τ _i . This speed field makes the speeds

im Transversalvolumen erstmals durchqueren wird, wenn das Gerät der geplanten Trajektorie folgt.ν _T (B, τ _i ) (P) described by which the first part of the device a given point

traverse for the first time in the transversal volume when the device follows the planned trajectory.

In the optimization method according to the invention, the risk of a collision with the help of risk volumes is determined for the respective tracks. A risk volume is an average of an activity volume V _A = (G, {(h _j , p (h _j )) | j = 1,..., J}) and of a respective transverse volume V _T (B, τ _i ) the corresponding orbit B, ie V _R (B, τ _i ) = V _T (B, τ _i ) ∩ G. The risk volume inherits the velocity vector field of the respective transverse volume and the occurrence probabilities of the activity volume.

Die Wahrscheinlichkeit einer Kollision wird somit beschrieben als der Quotient aus dem jeweiligen Risikovolumen und dem Aktivitätsvolumen, multipliziert mit der Auftretenswahrscheinlichkeit des Objekttyps. Die Wahrscheinlichkeit einer Kollision ist dabei eine Funktion der Bahntrajektorie B und des Zeitpunkts τ_i.If, with the method according to the invention, a movement is planned for an application space which does not have sensors for detecting obstacles, then one can estimate the probability of a collision with an object of a specific type _hj under some equal distribution assumptions

The probability of a collision is thus described as the quotient of the respective risk volume and the activity volume multiplied by the probability of occurrence of the object type. The probability of a collision is a function of the trajectory B and the time τ _i .

In the embodiment of the invention described here, in the modeling of the risk of a collision, the severity of the collision occurring is included. This takes into account that not every collision is equally serious. In particular, it is considered to be more serious when a person is hit by the device at high speed than when a cable is torn off in a collision. The severity of a collision is taken into account here by a damage height d _j (h _j , ν) which describes the magnitude of the damage of a collision of an object type h _j with a velocity v.

With the aid of the amount of damage and the probability of a collision, a total risk of the device can be calculated during its movement. This risk is the product of the probability of occurrence of a collision and the amount of damage. For an object type h _j in a risk volume V _R (B, τ _i ) = V _T (B, τ _i ) ∩ G (represented as an average of an activity volume V _A = (G, {(h _j , p (h _j )) | j = 1, ..., J}) and a transversal volume V _T (B, τ _i )) there is thus the following risk of collision depending on the object type h _j , the time τ _i on the path B and the activity volume G:

These elementary risks are summed over a disjoint decomposition of the space into activity volumes V _{A, n} , the object types h _{j, n} in the respective activity volume V _{A, n} and the paths B _m according to the relative frequency b _{m of} their use. Thus, a total risk R can be estimated as follows:

In the above expression, a multiplicity of terms disappear because the intersection of activity volume and transverse volume is empty. In this estimation, most influencing variables are fixed, but the respectively selected representative P _m from each group of orbits B _m fulfilling a given task A _m is not yet determined. With the totality of these representatives P = (P ₁ , ..., P _m , ..., P _M ) over all tasks as degree of freedom one finally obtains the total risk as the following function:

Ohne Berücksichtigung der Sensoranordnung bei der Optimierung kann das Minimum für jeden Repräsentanten einzeln gebildet werden, d. h. es gilt:

If the cost of a sensor arrangement is not taken into account as an optimization target, the goal of the optimization is only to minimize the overall risk, with a suitable optimization method searching for the set of representatives P _min which minimizes the overall risk, ie searches for

Without taking into account the sensor arrangement in the optimization, the minimum for each representative can be formed individually, ie it applies:

Any optimization method known from the prior art can be used in the optimization just outlined. For example, analytical optimization methods such as the Newton method or the conjugate gradient method can be used. Preferably, however, probabilistic methods, such. As genetic algorithms used.

An embodiment of the method according to the invention is described below, in which, in addition to the determination of optimal paths, an optimum arrangement of sensors is also determined. The sensors are used in the movement of the device for the detection of obstacles. The sensors monitor the risk volumes to reduce the risk of collision. The sensors can be arranged fixed in space or else on the moving device. Any type of sensors may be used, preferably sensors with active range finding are used. Examples of usable sensors are single-beam optical rangefinders, actively ranging 3D cameras, such as MESA models, laser scanners, such as the Hokuyo URG 04-LX, ultrasound systems, capacitive sensors, and radar rangefinders.

A sensor S _{k of} an arrangement of several sensors is characterized by a detection probability. The probability of detection is the probability of recognizing a possible obstacle and is referred to below as p (S _k , h _j , o _j , ν _j ). It depends on the type h _{j of} the obstacle to be detected and on the location o _j and the speed v _{j of} the obstacle relative to the sensor. The corresponding probabilities are determined experimentally in advance in laboratory experiments. For such sensors, which are attached to the device itself, the location and speed of the obstacle are additionally to be understood as a function of the trajectory and the mounting location on the machine. Thus, the probability of detection becomes p (S _k , h _j , o _j (B _m , q _{s, k} ), ν _j (B _m , q _{s, k} )). In this case, q _{s, k} denotes the mounting location of the sensor on the device.

From the detection probability of the individual sensors, a total detection probability can be calculated in a simple manner. For example, considering a volume covered by two independent sensors S ₁ and S ₂ , the probability of detecting an obstacle is given by: 1 - (1 - p (S ₁ , h _j , o _j (B _m , q _{s, 1} ), v _j (B _m , q _{s, 1} ))) · (1 - p (S ₂ , h _j , o _j (B _m , q _{s, 2} ), v _j (B _m , q _{s, 2} )))

Similarly, the probability of detecting an obstacle for a set of sensors S = (S _k , q _{s, k} ) can then also be calculated as p (S, h _j , B _m ).

With a, in the embodiment described here as firmly assumed probability α ∈ [0, 1] the collision with a detected obstacle is prevented, ie the probability that in spite of the sensors {S ₁ , ..., S _K } a collision takes place , is 1 - α =: β. This corresponds to a modeling such that the damage is reduced by the factor β ∈ [0, 1] in the detection of an imminent collision and corresponding initiated braking or avoidance maneuvers.

There can thus be two cases. Namely, with a probability p (S, h _j , B _m ), the obstacle is seen and the damage is reduced by the factor β, and with a probability 1-p (S, h _j , B _m ), the obstacle is not recognized and Damage not reduced. Thus, the overall risk as a function of the selected representatives P _{m of} the tracks and the selected sensor arrangement can be represented as follows:

After changing the mean factor, the total risk is as follows:

It can be seen from the above equation that the overall risk is reduced both with increasing β and with increasing p (S, h _j , B _m ). The above equation thus links the path planning and the sensor arrangement. Based on the above equation of the overall risk, an optimization with regard to a minimum risk can take place again, whereby now the parameters of the tracks and the parameters of the sensor arrangement are optimized at the same time.

In the embodiment described below, an optimization is also carried out involving the costs C (S) of the sensors of the sensor arrangement. The costs represent the additional expense of installing sensors in the room or on the device and should be as low as possible. It is thus carried out a multi-objective optimization with the aim of low cost and low risk of collision. This simultaneous optimization of the risk R (P, S) and the cost C (S) can be achieved by a common objective function, which is defined, for example, as follows: C _ges (P, S) = κ _r × R (P, S) + κ _s C (S). Depending on the application, the weights κ _R and κ _{S are} defined appropriately. The sought optimum is then

In a further variant of the method according to the invention, an optimization is carried out in such a way that maximum limits for risk or costs are determined and only with regard to one of the remaining components selected from risk and costs is minimized. Optionally, any other multiple-number optimization strategies may be used.

Since the overall risk derived above, which takes into account both the trajectories and the sensor arrangement, is difficult to describe closedly over the entire range of variations of the independent variables, the optimization is preferably carried out using simulation techniques and probabilistic optimization methods, such as eg. B. genetic algorithms. The simulation proceeds to model the environment of use, the obstacles (i.e., the type of obstacles, the probability of occurrence, the speed, and the like), as well as the device, the movement of the device, and the sensor array sensors. Through experiments, the probabilities of detecting obstacles of a particular type by sensors of a particular type are known in advance. Thus, the risk can be determined for a given trajectory and sensor arrangement.

Diese Optimierungsaufgabe wurde bereits im Vorangegangenen in Bezug auf ein Gerät ohne Sensoren beschrieben und kann wiederum mit geeigneten Optimierungsverfahren gelöst werden.The joint optimization of the path movement and sensor selection or sensor placement is based on a set of paths of the device which are characteristic of the field of application considered. Often, for freely programmable devices so many paths or tasks are possible that not all can be taken into account in the optimization. Thus, there remain tasks for which the corresponding tracks are not yet optimized, but the sensors are fixed. The optimal track is then found as

This optimization task has already been described above in relation to a device without sensors and can in turn be solved with suitable optimization methods.

und kann wiederum mit bekannten Optimierungsverfahren gelöst werden.In a further embodiment of the method according to the invention, a basic configuration of the sensor arrangement for detecting obstacles is predetermined and only a relative configuration q _{s of} the sensors to the volume to be monitored can be set within certain limits. In this case, for a given task, the optimal settings of both the particular trajectory P _m and the configuration of the sensors q _s are found. This optimization task thus finds the optimum

and can in turn be solved with known optimization methods.

As can be seen from the preceding explanations, with the method according to the invention an optimal trajectory of a device in a given environment can be determined, the objectives of the optimization taking into account a minimal risk of collision or minimum costs for the sensors used. The method thus provides optimal paths for various tasks and optionally also an optimal sensor equipment. These quantities can be stored in a memory of the device, so that the optimal path through the device is carried out during the execution of the corresponding task. Likewise, when using the device, the sensors may be attached to the device or in space in accordance with the optimum sensor arrangement.

Claims (19)

Method for computer-aided path planning of a movable device ( 1 ), in particular a medical device, in a spatial area (R), wherein the path planning takes place prior to the operation of the movable device, in which: - the spatial area (R) is characterized by one or more activity volumes, each of which is the spatial extent of at least one part the space area (R) and the probability of occurrence of one or more object types in the at least a part of the space area (R); One or more groups of webs of the movable device ( 1 ) in the space area (R), a respective track being described by a plurality of transversal volumes (V1, ..., V10), a transversal volume (V1, ..., V10) at a respective moment of movement of the device ( 1 ) on the web comprises the volume which the device ( 1 ) will be traversed anew from the respective time in a period of a stop and / or avoidance maneuver; A plurality of risk volumes is determined for a respective trajectory, wherein a risk volume is the spatial extent of the intersection between a respective activity volume and a respective transverse volume (V1,..., V10) of the trajectory and the probability of occurrence of one or more object types in accordance with the activity volume involved; Depending on the risk volumes of the respective lanes from each group of lanes, an overall risk of a collision of the device ( 1 ) is determined with objects in the space region (R) and with the aid of an optimization method an optimal set of orbits is determined according to one or more targets comprising one lane from each group of lanes, at least one of the targets having a minimum overall risk of the corresponding lane is a collision of the moving device with objects in the space area; and; the optimization method comprises parameters of a sensor arrangement comprising one or more sensors ( 7 . 8th , ..., 12 ) in the space area (R), whereby the optimization method outputs the parameters of an optimal sensor arrangement with respect to the one or more targets. Method according to claim 1, in which, through each group of tracks, one through the device ( 1 ) is characterized. Method according to claim 1 or 2, wherein the overall risk takes into account the relative frequency of use of webs from the groups of webs. Method according to one of the preceding claims, in which a transverse volume (V1, ..., V10) further comprises one or more velocity vectors which determine the speed and direction of the device ( 1 ) when crossing the transversal volume (V1, ..., V10), wherein a risk volume further comprises the velocity vector (s) of the transversal volume (V1, ..., V10), from which the risk volume results by intersection with an activity volume. Method according to Claim 4, in which, for a respective object type, a damage amount of a collision of the object type with the device ( 1 ) is defined as a function of the velocity vector (s) of the respective risk volumes, the overall risk taking into account the damage levels for the risk volumes of the respective trajectories in such a way that the overall risk becomes greater for larger loss levels. Method according to one of the preceding claims, in which a respective sensor ( 7 . 8th , ..., 12 ) of the sensor arrangement is characterized by a detection probability of one or more object types, the detection probability preferably being determined by the location and / or the speed of the respective object type relative to the sensor ( 7 . 8th , ..., 12 ) depends. Method according to one of the preceding claims, in which a total detection probability for one or more object types from the individual detection probabilities is determined for a respective track, the total detection probability of the respective paths being taken into account as parameters in the overall risk. Method according to one of the preceding claims, in which the overall risk includes a damage reduction factor which models a reduction in the amount of damage in the detection of an object by the sensor arrangement. Method according to one of the preceding claims, in which the sensor arrangement comprises one or more actively distance-measuring sensors ( 7 . 8th , ..., 12 ), in particular one or more laser scanners and / or actively distance-measuring 3D cameras. Method according to one of the preceding claims, in which the sensor arrangement comprises sensors ( 11 . 12 ) on the device ( 1 ) and / or stationary in the space area (R) mounted sensors ( 7 , ..., 10 ), wherein the detection probability of one or more object types for a sensor ( 11 . 12 ) on the device ( 1 ) from the mounting position of the sensor ( 11 . 12 ) on the device ( 1 ) and the speed at which the device ( 1 ) emotional. Method according to one of the preceding claims, in which the sensor arrangement is arranged by setting parameters of sensors (30) arranged at predetermined positions. 7 . 8th , ..., 12 ) is parameterized. Method according to one of the preceding claims, in which a cost can be determined based on the parameters of the sensor arrangement, wherein a further objective of the optimization method is a minimum cost outlay. Method according to one of the preceding claims, wherein the optimization method comprises an analytical optimization method, in particular a Newton method or a method based on conjugate gradients. Method according to one of the preceding claims, in which the optimization method comprises a probabilistic optimization method, in particular a genetic algorithm. Method according to one of the preceding claims, in which the movement of a medical device ( 1 ) in a treatment room (R) is planned. The method of claim 15, wherein the medical device ( 1 ) is an X-ray device, in particular a C-arm. Computer program product with a program code stored on a machine-readable carrier for performing a method according to at least one of the preceding claims, when the program runs on a computer. Movable device, in particular a medical device, wherein the optimal set of tracks, which was determined by a method according to at least one of claims 1 to 16, in a memory of the device ( 1 ) to move the device in operation based on the optimal set of paths. Apparatus according to claim 18, wherein further the optimal sensor arrangement, which was determined by a method according to one of claims 1 to 12, is stored in the memory and / or sensors on the device ( 1 ) are arranged according to the optimum sensor arrangement to move the device in operation based on the optimal set of tracks and the optimal sensor arrangement.

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