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This paper analyzes tip-over stability and develops tip-over avoidance algorithms for a reconfigurable tracked mobile modular manipulator negotiating slopes, with consideration of track-terrain and vehicle-manipulator interactions. Integrating a tracked vehicle with an onboard manipulator, a tracked mobile manipulator is vulnerable to tipping over when negotiating slopes. Unlike the wheeled mobile robots, which are normally assumed to obey the nonholonomic constraints, slippage is unavoidable for a tracked vehicle negotiating slopes. The reconfiguration of the tracked vehicle, the motion of the onboard manipulator, together with the centrifugal forces during moderate or high-speed motion give rise to transfer of load distribution, thus complicating track-terrain interactions. In this paper, tip-over stability criteria are derived for a reconfigurable tracked mobile modular manipulator negotiating slopes, and a real-time tip-over avoidance algorithm is developed with online tracked vehicle reconfiguration or manipulator adjustment. The effectiveness of the developed algorithms has been verified through simulations and experiments, and the results are reported in this paper.