10/21/2009. d R. d L. r L d B L08. POSE ESTIMATION, MOTORS. EECS 498-6: Autonomous Robotics Laboratory. Midterm 1. Mean: 53.9/67 Stddev: 7.
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1 1 d R d L L08. POSE ESTIMATION, MOTORS EECS 498-6: Autonomous Robotics Laboratory r L d B Midterm 1 2 Mean: 53.9/67 Stddev:
2 Today 3 Position Estimation Odometry IMUs GPS Motor Modelling Kinematics: Differential Drive 4 Two driven wheels plus a passive caster Mechanically simple, robust. Very common! Basic geometry d R d L r L d B 2
3 Kinematics: Tank Drive 5 No way to make all wheels be on tangents of circles with same origin Wheels must slip. Lots of torque required Kinematics: Bicycle Model 6 d Each wheel moves along a circle π/2-θ θ Not necessarily the same circle But they have the same center Total straight angle = π r 1 r 2 Total triangle angle θ We can measure the baseline Pick back wheel as frame of reference Solve for r 1 3
4 Kinematics: Ackerman Vehicle 7 In a car, front two wheels must be at different angles in order for all wheels to be on circles with a common origin. Main complication for us: Curvature determined by front wheels Coordinate system usually defined by back wheels Extra geometric busy-work. Kinematics: Omni/ Mecanum/Swedish Drive 8 Idea: instead of infinite lateral friction force, how about zero? Allow wheels to slip so that robot can move in any direction Wheels on top of wheels Kinematics: Think force diagram 4
5 Kinematics: Rocker-Bogie 9 NASA s favorite design Front pair/rear pair can turn in place. (Ackerman type geometry: single origin but with 6 wheels.) Rockers and bogies freely pivot Good obstacle handling All 6 wheels stay on the ground Motion of robot chassis is minimized Encoders 10 Single channel encoders Provide speed Direction is ambiguous Quadrature phase encoders Provide speed and direction 5
6 Encoders 11 Advantages Great quality data Not dependent on motor parameters Disadvantages Expensive Don t get torque information Don t tell you about slippage Odometry: quality 12 Robot started/stoppped in same place This is a very good odometry result Very carefully optimized parameters Consider this an upper bound on quality of odometry Good odometry Very carefully tuned odometry 6
7 IMUs 13 Gyros measure angular velocity Integrate to obtain angular position Errors accumulate over time Accelerometers measure acceleration Integrate twice to obtain position Errors accumulate really fast almost useless. However: can measure acceleration due to gravity! Roll/Pitch can be measured directly assuming no other accelerations no integration required! Gyros 14 Coriolis effect An object in a rotating coordinate frame experiences a force proportional to its velocity Idea: move a mass around a lot and see if there s a force acting on it. Orientation is integral of angular motion error accumulates. Fiber-optic Gyro (FOG) Shoot photons in a circle. If we re rotating CCW, the CW photons will complete a circuit faster than those moving CCW. Measure arrival times using interferometry. More fiber = more circles = greater sensitivy. (km of fiber optic cabling!) 7
8 Coriolis Effect 15 IMU calibration 16 Null rate output: what is the output when the device is not rotating? Calibrate via holding device still Scale factor Calibrate via rotating by known amount Temperature compensation Calibrate via Axis alignment Calibrate via 8
9 Magnetometer/Compass 17 Always a popular idea Error doesn t integrate over time. Unfortunately, hard to make work reliably Many sources of interference Robot itself Buildings In fact, some have built maps of environments by using the local magnetic flux as a landmark! Gyro compassing With an accurate enough gyro, you can measure the Earth spinning beneath you (unless you re at the equator!) GPS 18 Launch some accurate clocks into orbit Satellites broadcast the time and almanac of satellite positions Want to measure distance from receiver to satellites dist = time * Assume receiver has atomic clock Each satellite observation gives a sphere that the receiver must be on Two spheres: circle Three spheres: a point Receiver doesn t have an atomic clock Use fourth satellite, add local time as unknown variable. Tricky GPS characteristic Error characteristic non-gaussian! GPS IIR-15 (M), launched September 25,
10 Global Coordinate Frames 19 Motor Model 20 Motor has winding resistance Lower = more current = more powerful motor R winding Motor generates voltage proportional to angular velocity A motor is always a generator too. V EMF = K EMF * rad/s Current through motor is proportional to torque torque = K torque * I R winding + V EMF - Motor Get R winding, K EMF, K torque from datasheet or measure yourself (how?) We re ignoring the inductance of the motor effects are relatively transient. 10
11 Motor Model 21 I = V eff / R winding + R winding V eff = V in - V EMF V in - Driver + V EMF - Motor Example: No Load 22 rad/s V in V EMF Power Time Large V eff : lots of current, lots of torque. Motor accelerates quickly. Motor is spinning pretty fast, generating large VEMF. Consequently, Veff is smaller, less current, less torque, less acceleration. Motor is at constant velocity. VEMF is almost equal to Vin. Difference creates a torque just enough to balance losses in the system. Almost no power used. 11
12 Example: Under Load 23 Similar as before, only it takes more torque to achieve the same acceleration. V in Power rad/s V EMF Time What happens in a stall? Example: Change Direction 24 Power V in Time V EMF rad/s 12
13 Driving Motors 25 In theory: Drive motor with some voltage [0, V max ] More voltage More current More torque In reality, hard to generate low-impedence analog signals. Solution: Pulse width modulation Pulse-Width Modulation 26 Alternate input voltage between V max and 0. What is the right period? 13
14 H Bridge 27 We generate these voltages with an H-Bridge Four BIG transistors, S1-S4. S1 + S4 = Forward S2 + S3 = Reverse S1 + S3? S2 + S4? S1 + S2? S3 + S4? None? Measuring Current 28 Simple way of measuring motor current Measured voltage is positive regardless of direction of motor. If we know Vin, I, V sense = I R sense and R winding we can To analog-to-digital estimate V EMF converter R sense 14
15 Measuring Current 29 Advantages Not very expensive (a resistor and ADC port) Allows estimation of Back EMF too Disadvantages Noisy PWM waveform can be seen in current Measuring Back EMF Directly 30 Open all H-bridge switches, measure voltage across motor Advantages Direct measurement Disadvantages Motor must periodically coast: limits maximum power Potentially high voltages 15
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