Method for determining a posture of at least one free component in a reference environment of a motor vehicle

Abstract

The invention relates to a method for determining a posture of at least one free component in a reference environment (1) of a motor vehicle, said reference environment comprising at least one fixed component (2, 4), the method comprising steps of: - determining a three-dimensional representation and a posture of said fixed component, - for the mobile component, determining a three-dimensional representation, - discretizing the reference environment into a plurality of adjacent volume elements, - determining at least one orientation of the free component according to which the latter is completely encompassed in adjacent volume elements, - determining the set of possible positions for the free component, in the reference environment and according to the determined orientation, so as to have an index of superposition with the fixed component that is below a threshold, and - determining at least one posture of the free component.

Description

DESCRIPTION TITLE OF THE INVENTION: METHOD FOR DETERMINING A POSTURE OF AT LEAST ONE FREE COMPONENT IN A REFERENCE ENVIRONMENT OF A MOTOR VEHICLE TECHNICAL FIELD OF THE INVENTION

[0001] The present invention relates generally to the arrangement of components of a motor vehicle.

[0002] The invention relates more particularly to a method for determining a posture of at least one free component in a reference environment of a motor vehicle.

[0003] The invention finds a particularly advantageous application for the arrangement of components of a motor vehicle which are housed in the engine compartment of this vehicle. STATE OF THE ART

[0004] Motor vehicles have many components that must be positioned judiciously in order to respect various constraints such as available space constraints, access constraints, etc.

[0005] For example, the internal combustion engine of a motor vehicle comprises a multitude of components that must be housed in an engine compartment with limited space. The placement of the various components in such a space is generally carried out manually, using design software. It then requires the designer to have a method and great rigor to determine a combination of placement of all the components.

[0006] However, such a method does not guarantee that the resulting placement combination is optimal. Furthermore, it is quite time-consuming to implement. Finally, changing the placement of a component requires rethinking the entire placement of all the components concerned. PRESENTATION OF THE INVENTION

[0007] In order to overcome the aforementioned drawbacks, the present invention proposes to improve the determination of the placement of components in a motor vehicle.

[0008] More particularly, the invention proposes a method for determining a posture of at least one free component in a reference environment of a motor vehicle, said reference environment comprising at least one fixed component, the method comprising steps of: - for the fixed component, determination of a three-dimensional representation and a posture of said fixed component in the reference environment, - for the mobile component, determination of a three-dimensional representation, - discretization of the reference environment into a plurality of adjacent volume elements, - determination of at least one orientation of the free component according to which this free component is completely enclosed in adjacent volume elements, - determination of all possible positions for the free component, in the reference environment and according to the determined orientation, so as to present a superposition index with the fixed component lower than a predetermined threshold, and - determination of at least one posture of the free component by selecting a position from the set of possible positions determined for the determined orientation.

[0009] Thus, according to the present invention, all possible positions for placing the free component in the reference environment are determined. The final posture of the free component is then selected from all the possibilities by choosing the position (associated with the relevant orientation of the free component) which is optimal for the intended application and according to the imposed design constraints. The arrangement of the free component in the reference environment is therefore optimal because the method makes it possible to have all the posture possibilities and to choose the most suitable one.

[0010] The idea of ​​dividing the environment into a plurality of adjacent volume elements (of dimensions adjusted according in particular to the computing power available) makes it possible to reduce the computing time while ensuring that optimal positions are not left out.

[0011] Other advantageous and non-limiting characteristics of the method according to the invention, taken individually or in all technically possible combinations, are the following: - the predetermined threshold is less than or equal to 50%, and is preferably equal to 30%; - a step of optimization of the set of possible positions determined is planned, said optimization step being implemented for the possible positions having a superposition index with the non-zero fixed component, the optimization step comprising a displacement of each possible position concerned in the reference environment; - said displacement comprises a translation of the possible position concerned by a distance less than a characteristic dimension of a volume element; - said movement comprises a rotation of the possible position concerned by an angle of less than 10 degrees; - steps are provided for determining a plurality of orientations of the free component according to which the free component is completely encompassed in adjacent volume elements, and, for each determined orientation, determining all possible positions for the free component, in the reference environment, so as to present a superposition index with the fixed component lower than said predetermined threshold, said step of determining at least one posture of the free component being implemented for each determined orientation; - several free components are provided and the steps of determining a three-dimensional representation, determining at least one orientation and determining all possible positions are repeated for each free component; - said set of possible positions for a first of the free components forming a first group of possible positions and said set of possible positions for the other of the free components forming another group of possible positions, a step is provided for simultaneously determining a final posture for the first free component and another final posture for the other free component by comparing the possible positions of the first group and the possible positions of said other group, so that the final posture of the first free component and the final posture of the other free component do not overlap; - the simultaneous determination step is implemented by comparing, for each orientation of the first free component, the possible positions of the first group and the possible positions of said other group so that the final posture of the first free component and the final posture of the other free component do not overlap.

[0012] Of course, the various features, variants and embodiments of the invention can be combined with each other according to various combinations as long as they are not incompatible or mutually exclusive. DETAILED DESCRIPTION OF THE INVENTION

[0013] The description which follows with reference to the appended drawings, given as non-limiting examples, will make it clear what the invention consists of and how it can be implemented.

[0014] On the attached drawings:

[0015] - figure 1 represents a schematic perspective view of a reference environment of a motor vehicle;

[0016] - Figure 2 is a schematic top view of the reference environment of Figure 1;

[0017] - figure 3 is a schematic perspective view of a free component to be positioned in the reference environment of figure 1;

[0018] - figure 4 is a schematic view of a first orientation of the free component of figure 3;

[0019] - Figure 5 is a schematic view of a second orientation of the free component of Figure 3;

[0020] - figure 6 is a first representation of a plurality of positions of the free component according to the first orientation in the reference environment of figure 2;

[0021] - figure 7 is a second representation of a plurality of positions of the free component according to the first orientation in the reference environment of figure 2;

[0022] - figure 8 is a third representation of a plurality of positions of the free component according to the first orientation in the reference environment of figure 2;

[0023] - figure 9 is a representation of a plurality of positions of the free component according to the second orientation in the reference environment of figure 2;

[0024] - Figure 10 is a representation of a posture for the free component of Figure 3 and another posture for another free component in the reference environment of Figure 2.

[0025] A motor vehicle typically has a chassis that supports numerous pieces of equipment, including an internal combustion engine.

[0026] Taking the example of the internal combustion engine, typically, the vehicle has a plurality of components that are housed in an engine compartment. These components include, for example (and not limited to), an oil pan, a water pump, a fan, a starter, etc. All of these elements must be arranged in the engine compartment in order to occupy the minimum amount of space while ensuring optimal operation of the internal combustion engine.

[0027] The present invention therefore aims to enable the optimal placement of these components in defined spaces.

[0028] Figures 1 and 2 represent a reference environment 1 of a motor vehicle. This reference environment 1 defines the space in which a plurality of components 2, 4, 10, 11 will be positioned. The reference environment 1 here has a parallelepiped geometry but it can of course be of any shape (corresponding to the encompassing envelope of the space intended to accommodate the plurality of components).

[0029] For example, the reference environment 1 corresponds to the engine compartment of the internal combustion engine housing all of the components of this engine. In other words, this environment is delimited in particular by the chassis and the hood of the vehicle. More generally, the present invention of course applies to all the delimited spaces of a motor vehicle intended to accommodate a plurality of components.

[0030] Among the different components which are arranged in the reference environment 1, we distinguish the fixed components 2, 4 and the free components 10.

[0031] A fixed component is a component whose position and orientation in the reference environment 1 are already determined. In other words, each fixed component has a fixed posture. In this description, the term "posture" of a component will mean the positioning of this component, in the reference environment 1, in a predefined spatial position, and according to a predetermined orientation.

[0032] A moving component is a component whose position and / or orientation in the reference environment 1 must be determined.

[0033] Here we will consider that the reference environment 1 comprises at least one fixed component 2, 4. As shown in Figures 1 and 2, the reference environment 1 here comprises two fixed components 2, 4.

[0034] Each of these fixed components 2, 4 is therefore positioned in the reference environment 1 at a predefined spatial position and according to a predetermined orientation.

[0035] The reference environment 1 also houses at least one mobile component 10, 11 (the mobile component 11 is visible in Figure 10).

[0036] The method according to the invention described below aims to determine at least one possible posture for the arrangement of the mobile component 10, 11 in the reference environment 1.

[0037] This determination of at least one posture of the mobile component 10, 11 is carried out here using a computer processing unit, hereinafter called a calculator.

[0038] This calculator typically includes a processor, memory and various input and output interfaces.

[0039] Thanks to its input interfaces, the calculator is adapted to receive different data, typically data concerning the geometry of the reference environment 1 , the posture of fixed components, etc.

[0040] Thanks to its output interfaces, the calculator is adapted to transmit data concerning the possible postures for the mobile components 10, 11 to a vehicle designer.

[0041] Thanks to its memory, the computer stores a computer application, consisting of computer programs including instructions whose execution by the processor allows the computer to implement the method described below.

[0042] In general, the method according to the invention aims to make it possible to determine at least one possible posture of the mobile component 10, 11 for its arrangement in the reference environment 1. This determination takes into account the geometry of the reference environment 1 and the spaces authorized therein, a three-dimensional representation (i.e. the shape and dimensions) and the posture of each fixed component 2, 4 included in this reference environment 1. The method according to the invention then makes it possible to test a plurality of possible postures for the mobile component 10, 11 to be positioned, while taking into account its three-dimensional representation.

[0043] The different steps of the method for determining a posture of the mobile component 10 can now be described in more detail.

[0044] It is assumed at this stage that the geometry of the reference environment 1 in which the mobile component 10 must be positioned is known and recorded in the computer memory.

[0045] The process begins in a first step. In this step, the computer determines the three-dimensional representation and posture of each fixed component in the reference environment 1 .

[0046] During this first step, the computer also identifies an authorized zone 1A for the placement of the mobile component 10 in the reference environment 1. Here, the term “authorized zone 1A” means the parts of the reference environment 1 in which the mobile component 10 can be placed. Indeed, for example for reasons of optimal operation, thermal reasons or practical aspects, certain zones of the reference environment 1 are not suitable for receiving the mobile component 10 (zone 1B in FIGS. 1 and 2).

[0047] For example, if the moving component is a container containing a coolant, the coolant must be placed in an upper zone of the reference environment so that it is easily accessible for filling. The permitted zone of reference environment 1 is then, in this case, defined in an upper half of the reference environment.

[0048] All of this data then makes it possible to define constraints for positioning the mobile component 10 in the reference environment 1. In other words, at the end of this first step, the computer has a representation of the authorized zone 1A of the reference environment 1 to receive the mobile component 10, this authorized zone 1A also being delimited by the placement of the fixed components 2, 4.

[0049] It should be noted that this authorized area may in practice be different from one free component to another.

[0050] The process then continues during a second step during which the computer determines the three-dimensional representation (shape and dimensions) of the mobile component 10.

[0051] The method according to the invention then aims to determine the placement of this mobile component 10 in the authorized zone 1A of the reference environment 1. For this, during a third step, the authorized zone 1A of the reference environment 1 is decomposed according to a plurality of adjacent volume elements 5. In other words, the authorized zone 1A of the reference environment 1 is gridded with, as the unitary grid element, the volume element 5. In other words, the authorized zone 1A of the reference environment 1 is discretized into this plurality of adjacent volume elements 5.

[0052] As shown in Figures 1 and 2, the term "adjacent" refers to a juxtaposed and superimposed succession of volume elements 5 in the authorized zone 1A of the reference environment 1.

[0053] Here, each volume element 5 has a parallelepiped shape (here cubic) with a characteristic dimension of between 1 and 30 centimeters (cm). Alternatively, the shape of each volume element 5 may be different.

[0054] The characteristic dimension of a volume element is, for example, its largest dimension, or its average dimension, or more generally any measurable dimension. For a cube, it can be its width.

[0055] The method continues in a fourth step. In this step, the computer determines at least one orientation of the free component 10 according to which it is entirely enclosed in adjacent volume elements 5. All volume elements 5 in contact with the free component 10 participate in its enclosing.

[0056] In practice here, during this step, the calculator tests all the possible orientations for the mobile component 10 and identifies the one(s) for which the mobile component 10 is completely contained in adjacent volume elements 5. It is possible to select the orientation(s) for which the number of volume elements 5 encompassing the mobile component 10 is minimum.

[0057] Figures 4 and 5 represent two different orientations of the free component 10 according to which the latter is entirely enclosed in adjacent volume elements 5.

[0058] Then, during a fifth step, the calculator determines, for each identified orientation, all possible positions for the free component 10 in the authorized zone 1A. In other words, the pattern of adjacent volume elements 5 associated with the orientation concerned (namely the pattern of volume elements illustrated in FIG. 4 or 5, hereinafter called oriented pattern 5A) is tested in the authorized zone 1A in order to identify the possible positions of the free component 10 for which this pattern remains contained in the authorized zone 1A.

[0059] Figure 6 schematically represents all possible positions for the oriented pattern 5A associated with the first orientation (visible in Figure 4) of the free component 10.

[0060] Not all of the positions obtained are necessarily achievable in practice (i.e. during the manufacture and arrangement of these components) to position the free component 10 in the reference environment 1.

[0061] In fact, the calculator does not take into account the fixed components 2, 4 already present in the authorized zone 1 A of the reference environment 1. Thus, certain positions (denoted in the following prohibited positions 16) of the oriented pattern 5A overlap with the fixed components 2, 4.

[0062] The sixth step then constitutes a first “rough” selection of the possible positions for the free component 10 in the orientation concerned.

[0063] In order to determine realistic positions, the calculator proceeds to a classification of the positions obtained in the previous step.

[0064] It first distinguishes the “authorized positions 12”, in which the oriented pattern 5A is contained in the authorized zone 1A and does not overlap with a fixed component 2, 4. For these authorized positions 12, the superposition index between the free component 10 and at least one of the fixed components 2, 4 is zero.

[0065] Preferably, the calculator also identifies the “intermediate positions 14” for which the oriented pattern 5A is contained in the authorized zone 1A but partially overlaps with at least one of the fixed components 2, 4. For the intermediate positions 14, the superposition index is less than a predetermined threshold, preferably non-zero and less than 50%. This predetermined threshold is for example of the order of 30%. It could alternatively be zero.

[0066] The overlap index is calculated here by taking the ratio between: - the volume of the oriented pattern 5A which is superimposed on one (or more) fixed component, and - the total volume of the 5A oriented pattern.

[0067] The calculator finally identifies the “forbidden positions 16”, i.e. the remaining positions (for which the oriented pattern 5A is contained in the authorized zone 1A but largely overlaps with the fixed components 2, 4).

[0068] At the end of the sixth step, the calculator only keeps the authorized positions 12 and the intermediate positions 14 (figure 7 for the component 10 according to the first orientation). The prohibited positions 16 are eliminated and are no longer considered for the rest of the process because it is considered that the superposition index is too high to allow a realistic placement of the free component 10 in the reference environment 1A.

[0069] At this stage of the method, the computer has therefore identified the authorized positions 12, according to which the free component 10, in the orientation concerned, can be placed in the reference environment. In other words, the placement of the free component in the orientation concerned (here the first orientation) according to any one of the authorized positions 12 can be implemented in the reference environment 1 in a concrete manner (during the manufacture of the element of the motor vehicle associated with the reference environment 1).

[0070] On the other hand, the calculator also has the intermediate positions 14, for which the superposition index with at least one of the fixed components 2, 4 is considered low but for which this existing superposition potentially prevents concrete realization.

[0071] The method then comprises a seventh step of optimizing these intermediate positions 14. This optimization step is therefore implemented for all the positions identified in the fifth step and having a non-zero superposition index (but lower than the predetermined threshold).

[0072] This optimization step then aims to slightly correct these intermediate positions 14 and / or the orientation of the free component 10. In practice, the computer makes a correction to these intermediate positions 14 by subjecting them to a displacement. This displacement is for example a translation of the intermediate position 14 by a distance less than the characteristic dimension of a volume element 5. Preferably, this distance is less than half the characteristic dimension of the volume element 5.

[0073] Alternatively, this displacement may be a rotation by a predetermined angle around a center associated with the intermediate position concerned. This predetermined angle is, for example, less than 10 degrees.

[0074] Alternatively, the displacement may be a combination of translation and rotation as introduced above.

[0075] Concretely, during this seventh step, the calculator applies this displacement to the intermediate positions 14 in order to obtain resulting positions 12A, 16A (figure 8) and to identify those which could be authorized for the positioning of the free component 10. At this stage the resulting positions are considered as being authorized if the superposition index associated with them is zero. Thus here, as shown in figure 8, for the first orientation of the free component 10, the resulting positions 12A are authorized (and are therefore noted authorized positions 12) and the resulting positions 16A are eliminated (because the associated superposition index is not zero).

[0076] Finally, at the end of this seventh step, the computer has all the authorized positions 12 to position the free component 10 according to the first orientation in the authorized zone 1A of the reference environment 1 (figure 8).

[0077] The fifth, sixth and seventh steps are implemented for each orientation among the set of possible orientations of the free component 10 identified during the fourth step. Figure 9 represents for example the authorized positions 12 for positioning the free component 10 according to the second orientation in the authorized zone 1 A of the reference environment 1.

[0078] The method continues in an eighth step in which the computer selects one of the positions from among the authorized positions 12 for the free component 10 obtained in the previous step. This selection is for example implemented by taking into account constraints imposed by the designer, such as for example constraints aimed at limiting manufacturing costs or facilitating the assembly of the free component 10 in the reference environment 1.

[0079] During this step, the computer therefore has the selected position and the orientation of the free component 10 associated with it. In other words, at the end of this step, the computer has the selected posture of the free component 10 for its arrangement in the reference environment 1.

[0080] The calculator then transmits the manufacturing and placement instructions for the free component 10 according to the determined posture.

[0081] The various components 2, 4, 10 and the surrounding envelope corresponding to the reference environment 1 are then manufactured, before being installed in the motor vehicle according to the determined posture.

[0082] Thus, advantageously according to the invention, a large set of possible positions for the placement of the free component in the reference environment 1 is determined. The posture of the free component is then selected from all the possibilities by choosing the position (associated with the relevant orientation of the free component) which is optimal for the intended application and according to the manufacturing constraints imposed. This ultimate choice can be made by the computer or by an individual. The arrangement of the free component in the reference environment is therefore optimal because the process allows you to have all the posture possibilities and to choose the most appropriate one.

[0083] Optionally, after the seventh step, the method may comprise an optional step of forming groups among the determined authorized positions 12. These groups are for example formed by considering the authorized positions 12 relative to the corresponding volume elements 5.

[0084] Thus, as shown in Figure 8, for the first orientation of the free component 10, two groups C1, C2 of authorized positions 12 are formed during this optional step. As shown in Figure 9, for the second orientation of the free component 10, two groups C3, C4 of authorized positions 12 are formed during this optional step (the group C4 only comprises one authorized position, but it cannot be attached to the group C3 because the volume elements 5 which constitute it are not adjacent to the volume elements 5 of the authorized positions 12 of the group C3).

[0085] The present invention finds a particularly advantageous application for the simultaneous arrangement of the free component 10 and another free component 11 in the reference environment 1.

[0086] To implement this simultaneous placement, it is considered that the aforementioned steps (from the first to the seventh) have been previously implemented for each of the free component 10 and the other free component 11. Thus, at this stage, the computer has all the authorized positions 12 for positioning the free component 10 according to all the possible orientations (for this free component 10) in the authorized zone 1A of the reference environment 1 and all the authorized positions 12 for positioning the other free component 11 according to all the possible orientations (for this other free component 11) in the authorized zone 1A of the reference environment 1.

[0087] In other words, the computer has, on the one hand, all the possible postures of the free component 10 in the reference environment 1 and, on the other hand, all the possible postures of the other free component 11 in the reference environment 1.

[0088] A step of simultaneously determining a final posture of the free component 10 and a final posture of the other free component 11 is then implemented.

[0089] According to a first embodiment of this step, the calculator compares each possible posture of the free component with each possible posture of the other component 11 so as to determine a combination (of the final posture of the free component 10 and the final posture of the other free component 11) for which the superposition index between the two final postures is zero.

[0090] In this first embodiment, the computer can stop the execution of this step as soon as it has found a combination that satisfies the condition on the superposition index. This implementation is very fast but it is not necessarily optimal because it does not allow manufacturing constraints to be taken into account.

[0091] Alternatively, the calculator can determine the set of posture combinations of the free component 10 and the other free component 11 satisfying the condition on the superposition index.

[0092] This variant is particularly advantageous because it allows for a plurality of satisfactory combinations and for selecting the one that meets the manufacturing constraints imposed by the designer.

[0093] However, this is not the preferred implementation because determining all combinations satisfying the condition on the superposition index can be slow to implement.

[0094] In a second preferred embodiment, the optional step described above is implemented. Thus, the postures determined for the free component 10 are grouped into a plurality of groups and the postures determined for the other free component 11 are grouped into a plurality of other groups.

[0095] The calculator then proceeds to determine the possible combinations of the final postures by placing in parallel two by two, on the one hand, the groups of postures of the free component 10 and, on the other hand, the other groups of postures of the other free component 11.

[0096] This second embodiment makes it possible to simplify the determination of the final postures thanks to this comparison between the groups of postures of the free component 10 and the other groups of postures of the other free component 11.

[0097] In addition, it allows for a plurality of satisfactory combinations and to select the one that meets the manufacturing constraints imposed by the designer.

[0098] The final posture of the free component 10 and the final posture of the other free component 11 are then determined taking into account the constraints imposed by the designer, such as for example constraints aimed at limiting manufacturing costs or facilitating the assembly of the free component 10 in the environment of reference 1 as described in step eight.

[0099] Finally, in practice, the method according to the invention can be implemented in a loop. For example, considering that the mobile component 10 itself comprises a mobile sub-component to be positioned, the method is implemented initially to determine the final postures of the mobile component 10 and of the other mobile component 11 in the reference environment 1. Then, it is implemented to determine the posture of the mobile sub-component by taking as reference environment (for this mobile sub-component) the mobile component 10 (whose posture was determined during a first implementation of the method). Thus, a diagram that can be illustrated by a Russian doll organization is implemented to allow the arrangement of all the components included in the motor vehicle.

Claims

CLAIMS 1. Method for determining a posture of at least one free component (10, 11) in a reference environment (1) of a motor vehicle, said reference environment (1) comprising at least one fixed component (2, 4), the method comprising steps of: - for the fixed component (2, 4), determination of a three-dimensional representation and a posture of said fixed component (2, 4) in the reference environment (1), - for the mobile component (10, 11), determination of a three-dimensional representation, - discretization of the reference environment (1) into a plurality of adjacent volume elements (5), - determination of at least one orientation of the free component (10, 11) according to which this free component (10, 11) is completely enclosed in adjacent volume elements (5), - determination of all possible positions for the free component (10, 11), in the reference environment (1) and according to the determined orientation, so as to present a superposition index with the fixed component (2, 4) lower than a predetermined threshold, and - determination of at least one posture of the free component (10, 11) by selecting a position from the set of possible positions determined for the determined orientation.

2. Method according to claim 1, in which the predetermined threshold is less than or equal to 50%, and it is preferably equal to 30%.

3. Method according to claim 1 or 2, in which a step of optimizing the set of possible positions determined is provided, said optimization step being implemented for the possible positions having a superposition index with the non-zero fixed component, the optimization step comprising a displacement of each possible position concerned in the reference environment (1).

4. A method according to claim 3, wherein said displacement comprises a translation of the possible position concerned by a distance less than one dimension characteristic of a volume element (5).

5. A method according to claim 3 or 4, wherein said moving comprises rotating the relevant possible position by an angle of less than 10 degrees.

6. Method according to any one of claims 1 to 5, in which steps of: - determining a plurality of orientations of the free component (10, 11) according to which the free component (10, 11) is completely enclosed in adjacent volume elements (5), and - for each determined orientation, determination of all possible positions for the free component (10, 11), in the reference environment (1), so as to present a superposition index with the fixed component lower than said predetermined threshold, said step of determining at least one posture of the free component (10, 11) being implemented for each determined orientation.

7. Method according to any one of claims 1 to 6, in which several free components (10, 11) are provided and in which the steps of determining a three-dimensional representation, determining at least one orientation and determining all possible positions are repeated for each free component (10, 11).

8. Method according to claim 7, in which, said set of possible positions for a first of the free components (10, 11) forming a first group of possible positions and said set of possible positions for the other of the free components (10, 11) forming another group of possible positions, a step is provided for simultaneously determining a final posture for the first free component and another final posture for the other free component by comparing the possible positions of the first group and the possible positions of said other group, so that the final posture of the first free component and the final posture of the other free component do not overlap.

9. Method according to claim 8 taken in dependence on claim 6, in which the step of simultaneous determination is implemented by comparing, for each orientation of the first free component, the possible positions of the first group and the possible positions of said other group so that the final posture of the first free component and the final posture of the other free component do not overlap.

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