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This paper analyzes the effect of towing a single-axle trailer on static tip-over stability for field mobile robots on slopes. For this purpose, this study defines altered supporting polygons (ASP) for both tractor and trailer. These ASPs are based on a force-torque static equilibrium analysis that reshapes the corresponding ground contact supporting polygons. In this way, it is possible to estimate tip-over stability for each unit separately by projecting its center of gravity onto its ASP, even in the case that both bodies have different inclinations. Online implementation issues and simulation results are discussed. Moreover, a case study is presented for the Alacrane mobile manipulator, which carries a trailer for power generation.