Mobile Robots - Ørsted •DTU, Automation

Encoders• Encoders are used tomeasure the rotation ofthe wheels• Using two channelsenables detection ofdirection and four timesas many pulses can beused.

The displacement of the robot centrepoint∆U(i)=(∆U R+∆U L)/2Incremental change in orientation∆θ(i)=(∆U R-∆U L)/bb is the wheel distance

New pose of the robot is• x(i)=x(i-1)+∆U(i)cos(θ(i))• y(i)=y(i-1)+∆U(i)sin(θ(i))• θ(i)=θ(i-1)+∆θ(i)

Motor modelDC motors basically give speed inresponse to a speed command S i.Range [-128;127]ω w=K fS iV=(ω wR+ω wL)D/4ω=(ω wR-ω wL)D/2b

UMBmarkWhere am I: p. 14, pp. 19-20,and pp.130-142

Odometry errorsSystematic errors• Unequal wheel diameters• Average of actual wheel diameters differfrom nominal wheel diameter• Actual wheelbase differs from nominal• Misalignment of wheels• Finite encoder resolution• Finite encoder sampling rate

Odometry errorsNon-systematic• Uneven floors• Unexpected object on the floor• Wheel slippage• slippery floors• overacceleration• skidding• interaction with external bodies• castor wheels• non-point wheel contact with floor

UMBMark

Errors• Wheel base• Wheel diameterE =bE =dbbDDactualnomiRL

UMBMark

Calculating the Correctionsα =x + x 180c,g,cwc,g,ccw− 4Lπoβ =x − x 180c,g,cwc,g,ccw− 4LπoR =L 2sin( β 2)E d=RR+−bb22E b=o90 −α90o

CalibrationOn a straight line, calibrate the averagewheel diameterDo several cw and ccw experiments, notethat the x -axis is pointing in thevehicles direction at start and staysthere.Correct the odometery using Ed and EbIterate

Todays exercise1. Use the uncalibrated simulator2. Do UMBMark3. Work out calibration constants using Excelor Matlab4. Check when we put in the calibrationconstants in the simulator5. Real Robot test of UMBMark.