The stair-climbing apparatus has a series of articulating wheel sets extending below the platform. All of the wheel sets are vertically adjustable to negotiate stairways and similar changes of elevation. The lead wheel set is fixed longitudinally relative to the platform, while following wheel sets are longitudinally adjustable to adjust for the pitch or slope of different stairways. The apparatus uses sensors (e.g., mechanical, infrared, ultrasonic, etc.) to detect the presence of the stair risers and their height, control of the assembly being accomplished by a control circuit on board the machine. The wheel sets are raised and lowered independently of one another by pantograph mechanisms extending between the platform and the wheel sets. The horizontally adjustable wheel sets are positioned by a longitudinally disposed rack on the platform.