A robotic vehicle is provided with improved traction and mobility via a specially designed wheel apparatus including a relatively rigid wheel structure formed from two circular, coaxial sprocketed wheel plates separated by a central hub. The sprockets on the wheel plates are circumferentially aligned with one another, with axially facing sprocket pairs being received in areas defined between circumferentially adjacent pairs of tread links in a series of tread links, equal in number to the number of sprocket pairs, arranged in a circular array around the periphery of the wheel structure. The sprocket pairs are sized and configured in a manner such that substantial relative axial and circumferential movement between the wheel structure and the tread link array are blocked, with the axially facing sprockets in each sprocket pair being axially and resiliently deflected toward one another by surface portions of their associated tread link area.