By J. C. Alexander, J. H. Maddocks (auth.), Ingemar J. Cox, Gordon T. Wilfong (eds.)

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1) provides an underdetermined set of equations for y that reduce to the condition where the scalar angular velocity reduces to n is arbitrary. 2) which is minimized when n __ (al - a2)' (Xl - X2) IXI - x21 2 . 3) that was predicted by the ideal rolling model. Notice that the second wheel undergoes ideal rolling in such a manner that the slippage of the first wheel is minimized. Furthermore, the minimal dissipation is strictly positive unless al - a2 is parallel to Xl - X2. In this last case the compatibility condition for ideal rolling of both wheels is satisfied, P = 0, and no slippage occurs.

We compute the least-squares solution 4a) = ( 4u (BT B )-1 BT A R. j2/2 -I. 0. 4. Composite Robot Equation for U The motion of Uranus results from the simultaneous motions of the wheels. To model the motion, we combine the equations-of-motion of the four wheels in (5)-(8) to form the composite robot equation-of-motion: Otherwise 0 OJ RpR= C J2 Js 0 = Bo4 AoRpR or Dm (9) 4. 1. Actuated Inverse Solution We compute the actuated inverse solution by calculating the actuated wheel velocities in (10) from the robot velocities.

K. 1973. Planning considerations for a roving robot with arms. Proc. of the 3rd IJCAI. Stanford, California. pp. 308-316. Lord Rayleigh 1894-1896. The Theory of Sound 2nd edition, two volumes. London: McMillan. reprinted by Dover, 1945, New York. Marrs, T. 1985. The Personal Robot Book. Blue Ridge Summit, Pennsylvania: Tab Books, Inc .. Moravec, H. P. 1980. Obstacle avoidance and navigation in the real world by a seeing robot rover. Ph. D. thesis. Stanford University Department of Computer Science.

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