B.5.MPC.R:5.4 - A motion command changes its unit and starting point

In C.29.3’s robot case, the effective wheel radius is 0.05 m, ten motor revolutions turn the wheel once, and the interface counts 1,000 increments per motor revolution. A two-metre displacement requires a total of 63,662 motor increments after rounding. C.29.3 handles sending that total through the available command field.

Now change the radius to 0.06 m and the interface to an absolute wheel-position target. It counts 1,000 units per wheel revolution, currently reads 3,000 and admits targets from 0 to 65,535. The requested forward displacement remains 2 m. Assume rolling without slip and completion at the commanded count.

Recover the count’s new meaning before reusing the calculation. If q is the target, the wheel travels (q−3,000)/1,000 revolutions, so the model gives:

d=(q−3,000)/1,000 * 2π * 0.06 m.

The new scale already counts wheel revolutions; use that scale to obtain the needed increment:

Δq=2/(2π*0.06) * 1,000 ≈ 5,305.16477.

Round to 5,305 and add the initial count, giving target q=8,305. This target is admitted. Its modeled displacement is approximately 1.99993788 m. Nearest-integer rounding contributes at most half a count, corresponding to π*0.06/1,000 m ≈ 0.00018850 m; compare that contribution with the receiving accuracy requirement.

Reusing the former total 63,662 as the absolute target would pass the new range check but give approximately 22.8690 m under this model. The value has changed from a relative motor increment to an absolute wheel position. The repair therefore changes the physical parameter, the count-to-motion correspondence and the computational use of initial state together.

The useful return is the new command with its displacement and rounding consequence. A changed starting count requires recomputing the target; a changed radius or count scale reopens their correspondence. A slip or incomplete motion requires the relevant physical or execution repair. C.29.3’s preparation and completion comparison can then use this revised command.