Spherical and Flat Surface Motion Sensing using Laser Mouse Sensors

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2 2 2 Spherical and Flat Surface Motion Sensing using Laser Mouse Sensors KUMAGAI Masaaki, Tohoku Gakuin Universit, Tagajo, Miagi Ralph L. Hollis, The Robotics Institute, Carnegie Mellon, Pittsburgh, PA, USA This paper describes a sensing method for motion of a spherical surface. The method uses two or more optical mouse sensors, detects circumferential speeds of the surface, and transforms those speeds into angular velocit of the sphere. It can be also applied to a flat surface sensing b assuming that the radius is infinit. With weighted average of multiple combinations of sensor outputs, the eperimental result showed onl 1% error in sensing. A particle filter based absolute estimation method was also introduced. It compensates the position error b using pattern-filled surface and reflection sensing of mouse sensors. The method was eamined through simulation on a flat surface, which showed effectiveness of the improved method. Ke Words : Motion detection, Spherical surface, Laser mouse sensor, Particle filter 1 ballbot (1) BallIP (2) (3) (4) (5) 2 (3) ( 9 ) ( ) 3.8 m/s 5 μm 2.1 ( ) N l(l =...N 1) l ( n =2N ) 2l, 2l +1 P i(i =...n 1(= 2N 1)) p i s i ( ) 1 p 2l = p 2l+1 s 2l s 2l+1 = s ( ) n v si,v sj,v sk (i, j, k =...n 1)! P i v i v i =! p i (1) s i v si = s i v i = s i (! p i ) =! (p i s i) (2) j, k v si p i s i ω v sj = p j s j ω = A! (3) v sk p k s k ω A(i, j, k) A (v si,v sj,v sk ) T! v si!(i, j, k) =A 1 (4) v sj v sk N. Pr d n f th 2 J nf r n n R b t nd h tr n,, J p n, 26 28, 2 2 2(

3 s s 1 Optical mouse sensor P, P 1 Detection aes r s i sensor P i (p i ) s i s i+1 P i (p i ) Fig. 1: Eample arrangements of mouse sensors around a ball N n =2N C(n, 3) = n(n 1)(n 2)/6 w 1(i, j, k) = A ( ) A = A A 1 A 1 (4) ω (or,) = a 1v si + a 2v sj + a 3v sk (5) (a 1,a 2,a 3 A 1 ) w 2(,) (i, j, k) = a1vsi + a2vsj + a3v sk (6) a 1v si + a 2v sj + a 3v sk 1 w 1(i, j, k)w 2(i, j, k) ω (i, j, k) ω = i,j,k w 1(i, j, k)w 2(i, j, k) i,j,k (ω ω ) () R T s R R new = R (Δθ ) R (Δθ ) R (Δθ ) R old (8) R, R, R,, Δθ = T sω, Δθ = T sω, Δθ = T sω Δθ, Δθ, Δθ T s (7) Fig. 2: Three mouse sensor boards with fiing frame and drive unit Fig. 3: Eperimental result of ball motion sensing while the ball was rotated b hand. Points with lines indicate trajectories of unit vectors fied at the center of the ball Microsoft Avago.5 N. Pr d n f th 2 J nf r n n R b t nd h tr n,, J p n, 26 28, 2 2 2(2

4 ADNS-61 dspic PC 1 H BallIP (2) ballbot (1) 2mm ( ) 3 ( (3) ) (R ).5deg 3deg 1% 2.2 r (,,r) v = rω v = rω ω ω ω (3) v si p i s i ω v sj = p j s j ω = v sk p k s k ω p is i p is i p is i p is i p is i p is i p js j p js j p js j p js j p js j p js j p k s k p k s k p k s k p k s k p k s k p k s k ω (9) ω ω p i(j,k) = r s i(j,k) = ( ) rω = v rω = v v si v sj v sk = s iv +s iv +(p is i p is i)ω s jv +s jv +(p js j p js j)ω s k v +s k v +(p k s k p k s k )ω s i s i p is i p is i v = s j s j p js j p js j v s k s k p k s k p k s k ω v = Ã (1) v ω (v,v ) ω 4mm (3) 3 1% (PF) (6) ( Monte Carlo Localiation, MCL (7) ) 3.1 ( ) () 3.2 PF (6) (, ) θ (v ΔT,v ΔT,ω ΔT ) new = old + v ΔT cos θ v ΔT sin θ new = old + v ΔT sin θ + v ΔT cos θ θ = θ old + ω ΔT/2 θ new = θ old + ω ΔT (11) PF () (1) (2) (3) mm (b) ( ) (b) (a) ( ) v = d/dt PF 2% (b) (b)(c), (2/47, 2/61)mm, or N. Pr d n f th 2 J nf r n n R b t nd h tr n,, J p n, 26 28, 2 2 2(

5 Vel.(mm/s), Ang.vel.(deg/s) d/dt d/dt dθ/dt Time(s) S3 S2 S1 S (a) Input for the estimation; (v,v,ω ) and four sensor readings. (mm) (mm) (mm) (b) Ideal trajector (black outline with gra dashed line) and estimated (red outline) (mm) (c) Distribution of particles (n=1) Fig. 4: Simulated results using particle filter for absolute measurement. (a) ( on ) (a) (b) PF 1 5ms N(,2) N(,(π/1) 2 ) [, 1] {,1,2,3,4} {+5,, 1, 25, 5} PF (c) [ 1, 1] [ π, π] ( 5 ) Sensor state (off<->on) (c) 25ms( 5 ) 1s(2 ) 2s(4 ) 3s 7s 19s (3s ) 3s PF PF PF (1) ()(2) (3) 4, 1% Microdnamic Sstems Laborator (ballbot) (1) U.Nagarajan, M.Anish Mampetta, G.Kantor, R.Hollis, State Transition, Balancing, Station Keeping, and Yaw Control for a Dnamicall Stable Single Spherical Wheel Mobile Robot, Proc. ICRA 29, pp , 29 (2) M.Kumagai, T.Ochiai, Development of a Robot Balanced on a Ball First Report, Implementation of the Robot and Basic Control, Journal of Robotics and Mechatronics, vol.22 no.3, pp , 21 (3) M.Kumagai, R.L.Hollis, Development of a Three-Dimensional Ball Rotation Sensing Sstem using Optical Mouse Sensors, Proc. ICRA 211, 211 ( ) (4) K.M.Lee, D.Zhou, A real-time optical sensor for simultaneous measurement of three-dof motions, IEEE/ASME Trans. on Mechatronics, vol.9 issue.3, pp , 24 (5) D.Stein, E.R.Scheinerman, G.S.Chirikjian, Mathematical Models of Binar Spherical-Motion Encoders, IEEE/ASME trans. on Mechatronics, vol.8 no.2, pp , 23 (6),, vol.88 no.12, pp , 25 (7) D.Fo, W.Burgard, F.Dellaert, and S.Thrun, Monte Carlo Localiation: Efficient Position Estimation for Mobile Robots, Proc. AAAI 99, 1999 N. Pr d n f th 2 J nf r n n R b t nd h tr n,, J p n, 26 28, 2 2 2(4

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