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This paper analyzes track-stair interactions and develops an online tipover prediction algorithm for a self-reconfigurable tracked mobile robot climbing stairs, which is vulnerable to tipping-over. Tipover prediction and prevention for a tracked mobile robot in stair climbing are intractable problems because of the complex track--stair interactions. Unlike the wheeled mobile robots, which are normally assumed to obey the nonholonomic constraints, slippage is unavoidable for a tracked mobile robot, especially in stair climbing. Furthermore, the track-stair interactive forces are complicated, which may take the forms of grouser-tread hooking force, track--stair edge frictional force, grouser-riser clutching force, and even their compositions. In this paper, the track--stair interactions are analyzed systematically, and tipover stability criteria are derived for a tracked mobile robot climbing stairs. An online tipover prediction algorithm is also developed, which forms an essential part for autonomous and semiautonomous stair-climbing control. The effectiveness of the proposed algorithms are verified by experiments.