A patient support apparatus includes a base having a length and including a plurality of caster wheels enabling movement of the patient support apparatus across a floor surface. An auxiliary wheel support structure is secured to the base and rotatably supports at least one non-castered auxiliary wheel. A drive mechanism including a motor may be configured to drive the auxiliary wheel. A braking system including at least one brake member may be configured to apply a braking force to decelerate the auxiliary wheel and is movable between a first position wherein the at least one brake member is disengaged from the auxiliary wheel and a deployed position wherein the at least one brake member is frictionally engaged with the auxiliary wheel to restrict rotation of the auxiliary wheel. The braking system may be configured to synchronize the braking forces applied to first and second auxiliary wheels.