EE Mobile Robots

Transcription

1 Electric Electronic Engineering Bogazici University December 27, 2017

2 Introduction Motion Sensing Absolute position measurement Environmental Sensing

3 Introduction Motion Sensing Environmental Sensing Robot Topologies Manipulator type robot systems Mobile robot type robot systems Differential wheeled (2 actuated wheels) 3 wheeled systems Insect-like wheels (2 groups) Legged Mobile robot with manipulators

4 Introduction Motion Sensing Environmental Sensing Wheel in Planar Motion- Radius r Wheel on a plane with position [x y] T and orientation ϕ Note 3 possible movements: Linear ( θ) - Going forward/backward (φ remains same) Rotational ( φ) - Changing orientation φ Both -

5 Linear velocity - Due to θ Outline Introduction Motion Sensing Environmental Sensing Linear velocity v = r θ

6 Introduction Motion Sensing Environmental Sensing Linear Movement ( θ) - Top-down view

7 Introduction Motion Sensing Environmental Sensing Linear Velocity Velocity components wrt to coordinate axes X and Y r θ = ẋ sin(ϕ)+ẏ cos(ϕ) Velocity component wrt to perpendicular wrt to X and Y 0 = ẋ cos(ϕ)+ẏ sin(ϕ)

8 Rotational Movement ( φ) Outline Introduction Motion Sensing Environmental Sensing A circular trajectory with radius R - Orientation φ changes!

9 Introduction Motion Sensing Environmental Sensing Rotational Movement Considering Orientation φ Arc distance in global coordinates - s = R φ Linear velocity v = s t Rotational velocity ω = φ t κ = 1 R = φ s Change in initial position x = R(cos( φ) 1) y = R sin( φ)

10 Introduction Motion Sensing Environmental Sensing Rotational Velocity Change in initial position via considering an initial orientation of φ x = R(cos( φ) 1)cos(φ) R sin( φ)sin(φ) y = R(cos( φ) 1)sin(φ) R sin( φ)cos(φ) Assuming orientation change is very small cos( φ) 1 and sin( φ) φ Simplified equations x = R φsin(φ) y = R φcos(φ) s = R φ x = ssin(φ) y = scos(φ) Dividing both sides by t ẋ = v sin(φ) ẏ = v cos(φ) Rotational velocity ω = φ

11 Jacobian Model Outline Introduction Motion Sensing Environmental Sensing ẋ ẏ φ = sinφ 0 cosφ [ v ω ] Note that the first two equations yield: ẋ cosφ+ẏ sinφ = 0 tanφ = ẋ ẏ

12 Differential Wheel Outline Introduction Motion Sensing Environmental Sensing

13 Introduction Motion Sensing Environmental Sensing Assumptions Movement on planar surface with z-axis perpendicular to floor No slippage Rigid robot links For small t, change in orientation φ is very small.

14 Robot Model Outline Introduction Motion Sensing Environmental Sensing Seperation of two wheels b Wheels with radius r Angular velocities of right and left wheels ω r and ω l - Linear velocities of right and left wheels e 1 v r and e 1 v l Note v r = r ω r and v l = r ω r Linear velocity of mid point u = 1 2 (v r +v l ) Angular velocity of midpoint ω = 1 b (v r v l ) = r b (ω r ω l ) Path curvature κ = 2 b v r v l v r+v l If v l = v r, κ - Turn on the spot In order to minimize stress on mechanical structures, avoid commanding wheel speeds of different sign Note that v l,v r [0,V m ] κ [ 1 b, 1 ] b and u V m2

15 Velocity Kinematics Outline Introduction Motion Sensing Environmental Sensing ẋ ẏ φ = r 2 sin(φ) r 2 sin(φ) r 2 cos(φ) r 2 cos(φ) r b r b [ ωr ω l ]

16 Unicycle Robot in Path Following Introduction Motion Sensing Environmental Sensing

17 Introduction Motion Sensing Environmental Sensing Mathematical Notation Center of mass - Q A point on the path to be followed - P Intrinsic frame (Serret-Frenet) - F Inertial frame I Curvilinear abscissa (horizontal coordinate) of P along path - s The vector to Q - q = (X,Y,0) in frame I or q = (s 1,y 1,0) in frame F The vector to P is p Rotation matrix from I to F - R = R(θ c )

18 Introduction Motion Sensing Environmental Sensing Kinematic Modelling Curvature κ c c (s) = dθ ds ω c = θ c = c c (s)ṡ ċ c (s) = g c (s)ṡ where g c (s) = dcc(s) ds

19 Velocity Computations Outline Introduction Motion Sensing Environmental Sensing Velocity of P in I dp dt F = [ ṡ 0 0 ] T Velocity of Q in I Since q = p +R 1 r, dq dt I = dp dt I + dr dt F r +R 1dr dt F After simplification and multiplying both sides by R R dq dt I = dp dt F +r ω c + dr dt F

20 Velocity Computations (cont) Introduction Motion Sensing Environmental Sensing Using dq dt I = [ ẋ ẏ 0 ] T and dr dt F = [ ṡ 0 0 ] T s 1 0 r ω c = y θ c Using ω c = θ c = c c (s)ṡ R ẋ ẏ 0 = ṡ(1+c c (s)y 1 )+ṡ 1 ṡc c (s)s 1 +ẏ 1 0

21 Kinematic Model Outline Introduction Motion Sensing Environmental Sensing Solving for ṡ 1 and ṡ 1 [ ] [ ṡ1 cosθc sinθ = c ẏ 1 sinθ c cosθ c ][ Ẋ Ẏ ] [ ṡ(1+cc (s)y 1 ) ṡc c (s)s 1 ]

22 Kinematic Model Outline Introduction Motion Sensing Environmental Sensing Using the dependence of Ẋ and Ẏ on v Let θ = θ m θ c ṡ 1 ẏ 1 θ = cosθ 0 sinθ [ v ω m ] ṡ(1+c c (s)y 1 ) ṡc c (s)s 1 c c (s)ṡ

23 Introduction Motion Sensing Environmental Sensing Dynamic Model R - Radius of wheels Let τ 1 and τ 2 are the control inputs F = τ 1+τ 2 R N = L(τ 1+τ 2 ) R v = F m ω = ω c c c s g c ṡ 2 = N I c c s g c ṡ 2

24 Introduction Motion Sensing Environmental Sensing Kinematic Based Only Kinematic control laws ṡ = vcosθ +k 1 s 1 θ = δ γy 1 v sinθ sinδ k 2 (θ δ) θ δ V 1 = 1 2 lim t v(t) 0 δ(0,v) = 0 y 1,v y 1 v sinδ(y 1,v) 0 Then V 1 0 ( s 2 1 +y 2 1) + 1 2γ (θ δ(y 1,v))

25 Introduction Motion Sensing Environmental Sensing Dynamics Based Kinematic control laws where F = mf 2 k 4 (v v d ) ξ = δ γy 1 v sinθ sinδ θ δ N = If 1 k 3 ɛ k 2 (θ δ) where ξ - desired θ f 1 = ξ 1 γ (θ δ)+c c s +g c ṡ 2 f 2 = v d ɛ = θ ξ V 2 = V lim t v(t) 0 ( ɛ 2 +(v v d ) 2) V 2 0 δ(0,v) = 0

26 References Outline Introduction Motion Sensing Environmental Sensing D. Soetanto, L. Lapierre, and A. Pascoal. Adaptive, Non-Singular Path-Following Control of Dynamic Wheeled Robots. In Proceedings of the 42nd IEEE Conference on Decision and Control (CDC 03), pp: , USA, G.Indiveri,A. and K. Lingemann. High Speed Differential Drive Mobile Robot Path Following Control With Bounded Wheel Speed Commands. In Proceedings of the 2007 IEEE International Conference on Robotics and Automation, pp: , Italy, 2007

27 Motion Odometry Inertial systems Environmental Tactile Proximity Sensing Ground-Based RF Beacons and GPS Cameras and vision Kinect

28 Approaches Dead Reckoning - Determining the present location of based on some previous position through known course and velocity info over a given length of time Displacement along the path of travel - derived from some onboard instrumentation - some type of encoders directly coupled to the motor armatures or wheel axles Odometry Inertial systems

29 Encoders that accurately quantify angular position and velocity Available sensors: Brush encoders. Potentiometers. Synchros. Optical encoders. Magnetic encoders. Inductive encoders. Capacitive encoders

30 Encoders (cont.) Types: Incremental vs Absolute Positive features: Self-contained and always providing an estimate Negative issues: Errors accumulate

31 Incremental Optical Encoders

32 Simplest type - Single-channel tachometer encoder Tradeoff here - resolution versus update rate: Used as velocity feedback sensors in medium- to high-speed control systems, but noise and stability problems at extremely slow velocities due to quantization errors Cannot detect the direction of rotation and thus cannot be used as position sensors. Improved transient response Faster update rate Phase-quadrature incremental encoders: Overcome this via adding a second channel, Incremental nature of the phase-quadrature output signals: Angular position can only be relative to some specific reference, as opposed to absolute.

33 Absolute Optical Encoders Typically used for slower rotational applications when potential loss of reference from power interruption is not acceptable Best suited for slow and/or infrequent rotations such as steering angle encoding, as opposed to high-speed continuous rotations Instead of the serial bit streams of incremental designs, parallel word output with a unique code pattern for each quantized shaft position!

34 Absolute Optical Encoders

35 Gray-Code Encoding

36 Approaches Active beacons: Measuring the direction of incidence of 3 or more active transmitting beacons Artificial landmark recognition: Distinctive artificial landmarks Natural landmarks Model matching

37 Heading Help to compensate accumulation of error Detect orientation errors Gyroscropes & Accelerometers Compasses

38 Gyroscropes & Accelerometers To measure rate of rotation and acceleration Measure the angular velocity of the system in the inertial reference frame. Integrating the angular velocity, compute the system s current orientation Mechanical gyroscopes - ( USD) Piezoelectric gyroscopes - Around 300 USD Optical gyroscopes Geomagnetic sensors Positive features: Self-contained Negative issues: Not suitable for accurate positioning over extended period of time and price

39 Proximity Aimed at detecting presence rather than actual profile! Can operate in rugged environments reliably Magnetic Ultrasonic Optical Inductive Capacitive

40 Optical Proximity Outline

41 Tactile (Haptic) Sensing Outline Last resort indication of collisions Force sensing: Direct physical contact btw sensor and object of interest Sensor Typles Contact closure Magnetic Piezoelectric Photoelectric Magnetoresistive Piezoresistive Ultrasonic

42 Passive Feeler

43 Contact Closure Fleers Passive: A simple wire that when rel. motion occurs, closes a loop Active: Incorporate a search strategy for increased coverage

44 Active Feelers

45 Tactile Bumpers Touch-based microswitches

46 Distributed Surface Array Embedded tactile arrays to provide 2D profile Skin-like sensor array that is placed above the manipulator arm

47 Doppler

48 Doppler Actual ground velocity along path V a Measured doppler velocity V d Angle of inclination α Observed Doppler shift F d Transmitted frequency F t V a = cf d 2F t cosα

49 Doppler - Problems Errors in detecting true ground - Side-lobe interference, Vertical velocity components introduced by vehicle reaction to road surface anomalies, Uncertainties in the actual angle of incidence due to the finite width of the beam. Around 500 USD/sensor

50 TOF Time-of-flight range sensors d = vt Ultrasonic Laser Phase-shift measurement or Frequency modulation Reliability issues: Variations in the speed of propagation, particularly in the case of acoustical systems. Uncertainties in determining the exact time of arrival of the reflected pulse. Inaccuracies in the timing circuitry used to measure the round-trip time of flight. Interaction of the incident wave with the target surface.

51 Laser-Based TOF Laser-based TOF ranging systems, also known as laser radar or lidar, Laser energy - emitted in a rapid sequence of short bursts aimed directly at the object being ranged. Time required for a given pulse to reflect off the object and return is measured and used to calculate distance to the target based on the speed of light. Accuracies - Few centimeters over the range of 1 to 5 meters Price Expensive!

52 Cameras Camera types 1. Analog 2. Digital Interface electronics Required in case of analog cameras

53 Kinect 1. Kinect Sensor: An RGB camera, infrared laser projector combined with a monochrome CMOS sensor and multi-array microphone running proprietary software

54 Typical Configurations Encoders Cameras Targeting camera Laser range finder Tactile sensing

55 References H.R. Everett. for Mobile Robots: Theory and Application. A.K. Peters, J. Borenstein, H.R. Everett and L. Feng. and Methods for Mobile Robot Positioning, Technical Report, The University of Michigan, 1996.