Mobile & Service Robotics Mobile & Service Robotics Sensors for Robotics Sensors for Robotics – 3 Sensors for Robotics Sensors for Robotics 3
Laser sensors � Rays are transmitted and received coaxially � Rays are transmitted and received coaxially � The target is illuminated by collimated rays � The receiver measures the time ‐ of ‐ flight (back and forth) � It is possible to change the rays direction (2D or 3D measurements) D ′ D Transmitter L Receiver R i θ ′ ′ λ λ = = + + + + = = + + + + λ λ c f c f ( ( L L D D ) ) 2 2 D D ( ( L L D D ) ) π 2 Basilio Bona 2 ROBOTICA 03CFIOR
Laser sensors λ plitude Amp θ 0 Transmitted Reflected Phase Basilio Bona 3 ROBOTICA 03CFIOR
Laser sensors METHODS � Pulsed laser: direct measurement of time ‐ of ‐ flight: one shall be � Pulsed laser: direct measurement of time of flight: one shall be able to measure intervals in the picoseconds range � Beat frequency between a modulating wave and the reflected � Beat frequency between a modulating wave and the reflected wave � Ph � Phase delay d l � It is the easiest implementable method Basilio Bona 4 ROBOTICA 03CFIOR
Laser sensors θ c ′ λ = = + = + λ ; D L 2 D L π f 2 c = speed of light = f frequency of the moduling wave ′ = D D total distance total distance = λ λ = f f 5 5 60 60 MHz; MHz; m m The confidence on distance estimation is inversely proportional to The confidence on distance estimation is inversely proportional to the square value of the received signal amplitude Basilio Bona 5 ROBOTICA 03CFIOR
Laser sensors A typical image from a rotating mirror laser scanner. S Segment lengths are proportional to the measurement uncertainty t l th ti l t th t t i t Basilio Bona 6 ROBOTICA 03CFIOR
Triangulation Triangulation is the process of determining the location of an i l i i h f d i i h l i f object by measuring angles from known points to the object at either end of a fixed known baseline either end of a fixed known baseline The point can be chosen as the third point of a triangle with one known side and two known angles In practice: � Light sheets (or other patterns) are projected on the target � R fl � Reflected light is captured by a linear or 2D matrix light t d li ht i t d b li 2D t i li ht sensor � Simple trigonometric relations are used to compute the distance Basilio Bona 7 ROBOTICA 03CFIOR
Triangulation Triangulation concepts baseline d d l = + ⇒ = l ; d α β β tan tan 1 1 + + α β tan tan Basilio Bona 8 ROBOTICA 03CFIOR
Triangulation α β γ sin sin sin = = BC BC AC AC AB AB ⋅ β ⋅ α AB sin AB sin = = AC ; BC γ γ γ γ sin sin sin sin = ⋅ α RC AC sin = ⋅ β RC BC sin ⋅ α ⋅ β AB sin sin = RC γ sin ⋅ α ⋅ β AB sin sin = RC α α + + β β sin( sin( ) ) Basilio Bona 9 ROBOTICA 03CFIOR
Triangulation D D f f Transmitter Transmitter L x L = = D D f f x f f Basilio Bona 10 ROBOTICA 03CFIOR
Structured light Basilio Bona 11 ROBOTICA 03CFIOR
Structured light = α H D tan Basilio Bona 12 ROBOTICA 03CFIOR
Structured light � Monodimensional � di i l D α − f cot u case u f D Du = x α α − f u cot Df = z α − f f cot u Basilio Bona 13 ROBOTICA 03CFIOR
Vision � Vision is the most important sense in humans � Vision includes three steps � Vision includes three steps � Data recording and transformation in the retina � Data transmission through the � Data transmission through the optical nerves � Data elaboration by the brain Basilio Bona 14 ROBOTICA 03CFIOR
Natural vision R ti Retina Basilio Bona 15 ROBOTICA 03CFIOR
Natural vision Optic chiasm fMRI shows the brain areas interested by neural activity associated to vision Basilio Bona 16 ROBOTICA 03CFIOR
Artificial vision � C � Camera = retina ti � Frame grabber = nerves � CPU = brain Basilio Bona 17 ROBOTICA 03CFIOR
Vision sensors: hardware CCD ( Co pled Charge De ice light sensiti e discharging capacitors of 5 to CCD ( Coupled Charge Device, light ‐ sensitive, discharging capacitors of 5 to 25 micron ) CMOS ( Complementary Metal Oxide Semiconductor technology ) Basilio Bona 18 ROBOTICA 03CFIOR
Artificial vision � Projection from a 3D world on a 2D plane perspective � Projection from a 3D world on a 2D plane: perspective projection (transform matrix) � Discretization effects due to transducer pixels (CCD or � Discretization effects due to transducer pixels (CCD or CMOS) � Misalignment errors � Misalignment errors Pixel discretization Parallel lines Converging lines Basilio Bona 19 ROBOTICA 03CFIOR
Artificial vision π ′ π F π 3D object Optical axis Reversed image plane Focal Plane Principal image plane Principal image plane Basilio Bona 20 ROBOTICA 03CFIOR
Artificial vision Geometric parameters P ′ i ′ x O R m ′ x x i i m m i i i ′ R Optical axis O O f f C x i i ′ j x c m i R c i t c c c O i P P R R j j i i π π F Image plane Focal plane Focal plane Basilio Bona 21 ROBOTICA 03CFIOR
Artificial vision T A R c c Several rigid and perspective transformations P P R R are involved are involved m T B ′ π ′ R R R R i i Optical Rescaling correction Basilio Bona 22 ROBOTICA 03CFIOR
Artificial vision ′ ′ x x x = ⇒ = c i z f c ′ c z f x c c i i i c P ′ P z z c x ′ k C A i c c C i P ′′ x c c π π π ′ F f ′ f f f P P Basilio Bona 23 ROBOTICA 03CFIOR
Artificial vision x R R i i ′ x R y y Basilio Bona 24 ROBOTICA 03CFIOR
Artificial vision Image parameters p i ′ j x O O i i p i y t i ′ c i C i j j i Basilio Bona 25 ROBOTICA 03CFIOR
Artificial vision Aberration types Ab i Pincushion distortion Pi hi di i Barrel distortion B l di i Non radial distortion (tangential) Radial distortion Radial distortion is modelled by a function D ( r ) that affects each point v in the projected plane relative to the principal point p , where D(r) is normally a non ‐ linear scalar function and p is close to the midpoint of the projected image. Barrel projections are characterized by a positive gradient of the distortion function , whereas pincushion by a negative gradient = − + + v D v ( ( p p v ) ) p p d d Basilio Bona 26 ROBOTICA 03CFIOR
Artificial vision Image errors Errors are due to the imperfect alignment of pixel elements Basilio Bona 27 ROBOTICA 03CFIOR
Vision sensors Distance sensors • Depth from focus • Stereo vision Stereo vision Motion and optical flow Basilio Bona 28 ROBOTICA 03CFIOR
Depth from focus The method consists in measuring the distance of an object evaluating the focal length adjustment necessary to bring it in focus the focal length adjustment necessary to bring it in focus Short distance focus Medium distance focus Far distance focus Basilio Bona 29 ROBOTICA 03CFIOR
Depth from focus 1 1 1 = + f f D D f f D D e L L D ( , , ) x y z i image plane l ( , x y ) i i + + L d L d ( ( e e ) 1 ) 1 1 1 1 1 focal plane f l l = − − b x ( ) D δ e + 2 f ( d e ) s x ( ) blur radius shape Basilio Bona 30 ROBOTICA 03CFIOR
Depth from focus Near focusing Far focusing Basilio Bona 31 ROBOTICA 03CFIOR
Stereo disparity ( ) x y z , , x left lens right lens f z image plane ( ) ( ) x , y x , y r r � � b baseline (known) Basilio Bona 32 ROBOTICA 03CFIOR
Stereo disparity x x x x + + − x x b b / 2 / 2 x x b b / 2 / 2 = = � , r f z f z − x x x x b b = � r f z Idealized camera ( ( ) / 2 ) + + x x x x / 2 geometry for f � r = x b stereo vision − x x � r ( ( ) ) / 2 + y y � r = y b − y y y y � � r r f = z b x − x x x � � r Disparity between two images → Depth g p computation Basilio Bona 33 ROBOTICA 03CFIOR
Stereo vision Distance is inversely proportional to disparity closer objects can be measured more accurately closer objects can be measured more accurately Disparity is proportional to baseline For a given disparity error, the accuracy of the depth estimate increases with increasing baseline b However, as b is increased, some objects may appear in one camera, but not in the other , A point visible from both cameras produces a conjugate pair conjugate pair Conjugate pairs lie on epipolar line (parallel to the x ‐ axis for the arrangement in the figure above) Basilio Bona 34 ROBOTICA 03CFIOR
Stereo points correspondence Th These two points are corresponding: i di how do you find them in the two images? Left image Right image Disparity Disparity Ri ht Right Left Basilio Bona 35 ROBOTICA 03CFIOR
Epipolar lines corresponding points P stay on the epipolar lines π τ τ τ τ 1 2 q q 1 2 � � � 1 1 2 e 1 e C C 2 2 C 1 2 R t , epipolar lines these two points are known and fixed (they are called epipoles) Basilio Bona 36 ROBOTICA 03CFIOR
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