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SUMMARY:On the Stability and Control of Unicycles - Prof Robin Sharp (Univ
 ersity of Surrey)
DTSTART:20100312T160000Z
DTEND:20100312T170000Z
UID:TALK22433@talks.cam.ac.uk
CONTACT:Anita Clayson
DESCRIPTION:A mathematical model of a unicycle and rider\, with a uniquely
  realistic tyre force and moment representation\, is set up with the aid o
 f multibody modelling software. The rider’s upper body is joined to the 
 lower body through a spherical joint\, so that wheel\, yaw\, pitch and rol
 l torques are available for control. The rider’s bandwidth is restricted
  by low-pass filters. The linear equations describing small perturbations 
 from a straight-running state are shown\, which equations derive from a pa
 rallel derivation yielding the same eigenvalues as obtained from the first
  method. A nonlinear simulation model and the linear model for small pertu
 rbations from a general trim (or dynamic equilibrium) state are constructe
 d. The linear model is used to reveal the stability properties for the unc
 ontrolled machine and rider near to straight running\, and for the derivat
 ion of optimal controls. These controls minimize a cost function made up o
 f tracking errors and control efforts. Optimal controls for near-straight-
 running conditions\, with left/right symmetry\, and more complex ones for 
 cornering trims are included. Frequency responses of some closed-loop syst
 ems\, from the former class\, demonstrate excellent path-tracking qualitie
 s within bandwidth and amplitude limits. Controls are installed for path-f
 ollowing trials. Lane-change and clothoid manoeuvres are simulated\, demon
 strating good-quality tracking of longitudinal and lateral demands. Pitch 
 torque control is little used by the rider\, while yaw and roll torques ar
 e complementary\, with the former being more useful in transients\, while 
 the latter has value also in steady states. Wheel torque is influential on
  lateral control in turning. Adaptive control by gain switching is used to
  enable clothoid tracking up to lateral accelerations greater than 1ms−2
 . General control of the motions of a virtual or robotic unicycle will be 
 possible through the addition of more comprehensive adaptation to the cont
 rol scheme described. 
LOCATION:Cambridge University Engineering Department\, Oatley Seminar Room
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