Evidential grids use the theory of evidence and benefit from its properties like natural representation of the unknown and well-developed theoretical tools. e use of evidential grids allows the fusion of multiple sensors in a straightforward manner. A grid can be constructed for each data source and all grids can be combined together into oneSensorGridbefore further processing as described in the next chapter.
.. PerceptionGrid
One of the evidential grids used in the system is thePerceptionGrid(PG). is grid is unquestionably the most important of all evidential grids. It has been introduced to store the results of information fusion.PGis as well the output of the perception system and could be used in further steps of processing in an intelligent vehicle, e.g. for trajectory planning.
e choice of such afodis determined by the objectives we want to achieve. In our approach, respective classes represent:
D drivable free space, N non-drivable free space, M mobile moving objects,
¹is name, is general, used for grids containing information about dynamic objects.
. Perception grids for dynamic perception
(a) Camera view of the scene. (b)SourceGrid(SoG) in Cartesian coordinates.
Figure . – An example of an occupancy grid obtained using a multi-echo lidar sensor.
Grid colour code: white – occupied, black – free, grey – unknown.
S temporarily stopped objects,
I mapped infrastructure like buildings, walls, etc., U unmapped infrastructure.
Mass functions of each cell ofPGuse thereforeΩP G={D, N, I, M, S, U}as the frame of discern- ment (fod). From time to time, we will denote bymovablethe union{M, S}. An important note is to be done about the definition of drivable spaceD. In the following, we consider drivable the free space, such as road surface, where a vehicle can drive on, i.e. any of its parts (notably wheels) can be situated there. One must be reminded that some research works use the notion ofnavigablefree space. Such a free space can be seen as the drivable space reduced in order to take into account the geometric model of the vehicle. In other words, the centre of the vehicle is situated on the navigable space if and only if, aer applying any possible rotation, its bounding box (geometric model) is wholly situated on the drivable space. Since the drivable space, in contrast to the navigable space, is independent of the size and the shape of the vehicle, we opted for the use of the former.
ΩP G, besides describing the final result of the fusion process, is also a common, most refined, frame of discernment used in our information fusion system. Indeed, in the Dempster–Shafer theory (DST), two pieces of evidence need to be defined on the same frame of discernment in order to be combined¹.
When the frames of discernment in question differ during data processing, one has to transform them to a common frame. e transition between onefodand another is done by applying a refining function, cf. Definitionfor details.
As thePerceptionGrid(PG) retains the result of information fusion, the need to store previous data disappears. Otherwise, it would be necessary to store all the input grids for a given horizon of time.
Such an approach is obviously inefficient and can be envisioned only if the horizon is very limited.
.. SourceGrids
For each exteroceptive sensor, such as a lidar or a camera, an evidential grid calledSourceGrid(SoG) should be created. e system architecture permits equally the use of a single or multiple sensors.
When two or moreSoGs are used, they have to be combined into one grid before further processing or alternatively they can be fused at the time of their arrival. e manner in which such grids are combined is described in Chapter.
¹However, there may exist fusion operators that allow combining pieces of evidence defined on distinct frames.
Figure . – Paris th district city-hall. Le: a portion of the constructedGISGridobtained using data fromIGNmaps (Soheilian, Tournaire, et al.). Right: D view of the area (Googlea). Colour code: blue — buildings, dark yellow — roads, grey — intermediate space.
A newSourceGridis created for each incoming data acquisition. Each cell of theSourceGridstores a mass function mSi defined on the frame of discernmentΩSi. e frame can vary depending on the sensor in use. e higher the expressiveness of the sensing device, the more classes the corresponding grid will represent. Typically for a lidar,ΩSi ={F, O}, whereFrefers to the free space andOto the occupied space. e basic belief assignment depends on the model of the actual sensor. Details about the sensor model used in this dissertation are given further in this chapter in Section.onwards. Another sensor, for example camera, could be much more informative and comprehend detailed classes such as road surface, pavement, building, grass etc. An example of a simple occupancy grid is illustrated in Figure.. Other evidential grids based on a vision system are described in (Xu et al.).
e frame of discernmentΩSiis distinct fromΩP Gand a common frame for all sources has to be found.
Hence, a refiningrSiis defined as stated in Equation..
rSi: 2ΩSi →2ΩP G (.)
{F} → {D, N} {O} → {I, U, S, M}
A →
θ∈A
rSi({θ}) ∀A⊆ΩSiandA∈ {{/ F}, {O}}
Refining rSi makes it possible to perform the fusion of SourceGridi containing instantaneous grid obtained from sensoriwith other grids. Equation.expresses the refined mass function.
mΩSiP G(rSi(A)) = mΩSiSi(A) ∀A⊆ΩSi (.)
.. GISGrid
e purpose of theGISGrid(GG) is to contain all the data exploited from maps. In our approach, we limited the use of this data to geometrical information about the surface of the road and buildings. is grid allows us to perform contextual information fusion incorporating the meta-knowledge about the environment. Again, the meta-knowledge is related to the geometrical information furnished by maps.
We separated three different contexts for which the meta-information differs. Figure. juxtaposes a sample ofGISGridand a three-dimensional view on a building model.
. Perception grids for dynamic perception Urban scene contexts
ese contexts correspond to the classes of the frame of discernment used by theGISGrid. Namely,GG uses thefodΩGG={B, R, T}. ClassBcorresponds to the area occupied by buildings. Analogously, Rdefines the road surface. Finally, the classTmodels intermediate space that is not contained in either of the above. For example, the intermediate space contains pavements.
Each context has its proper characteristics. In the building context, the only classes we are supposed to detect are infrastructureI and non-drivable free spaceN. is last case is possible only if the map is faulty and depicts a non-existing building.
e road context is much more complicated and may contain any class except for mapped infrastructure Iand non-drivable spaceN. Indeed, one usually finds moving obstacles like cars or motorbikes on the road, but one cannot exclude the presence of pedestrians, especially on zebra crossings. Moreover, stopped vehicles are oen present on (the side o) the road. What concerns the infrastructure, one should allow the existence of small urban furniture (classU) such as lamps or barriers. Finally, an important assumption is made about the drivability of the road surface, supposing that the road is by definition drivable and thus excluding the non-drivable classD.
e last context, the intermediate spaceT should be understood as non-building and non-road en- vironment. Such a vague definition corresponds exactly to the knowledge possessed about this part of vehicle’s environment. In this context, mobileM and stationaryS objects as well as small urban infrastructureUcan be present. Obviously, one should disallow the vehicle to drive on the intermediate space unless in the case of emergency¹.
e GISGrid (GG) is created, for instance, by projecting map data onto a two-dimensional world- referenced grid. is is the step where the meta-information from maps is included. As stated above, this meta-knowledge can ban the existence of mobile objects where buildings are present and, con- versely, it indicates the possibility to find these objects on roads. e exact construction method of the GISGriddepends however on available geodata.
efodΩGG is different from the common frameΩP G. Some rules in the theory of evidence, such as Dempster’s rule, do not allow the direct combination of BBAs expressed on different frames of discernment, as this in the case with the SourceGrid. It is then necessary to express every belief assignment on a common frame of discernment before the combination. In our work, the mapping rGGis used when needed:
rGG: 2ΩGG →2ΩP G (.)
{B} → {I}
{R} → {D, S, M} {T} → {N, U, S, M}
A →
θ∈A
rGG({θ}) ∀A⊆ΩGGandA∈ {{/ B}, {R}, {T}}
Using this refining, one can compute the mass transfer as follows:
mΩGGP G(rGG(A)) = mΩGGGG(A) ∀A⊆ΩGG (.)
¹Please see perspectives for details.
exteroceptive sensor 3
SourceGrid3 (local)
mSoG3
SourceGrid3 (global)
mSoG3
exteroceptive sensor 2
SourceGrid2 (local)
mSoG2
SourceGrid2 (global)
mSoG2 exteroceptive
sensor 1
SourceGrid1 (local)
mSoG1
SourceGrid1 (global)
mSoG1
localisation system
vector maps GISGrid(global)
mGG
inputs
Figure . – Part of our perception system where the sensor models are applied.
e mappingrGG indicates that, for instance, building informationB fosters mass transfer to class I. On the road surfaceR, the existence of drivable free spaceDas well as stoppedSand movingM objects is possible. Lastly, on the intermediate areaT, the existence of mapped infrastructureIcan be excluded. Similarly, the free space is non-drivable therefore classDis disallowed as well. e presence of all other classes is however allowed.