This paper presents a quadratic programming (QP) form algorithm to realize on-line planning of mobile manipulators with consideration for improving the stability level. With Lie group and screw tools, the general tree topology structure mobile robot dynamics and dynamic stability attributes were analysed. The stable support condition for a mobile robot is constructed not only in a polygonal support region, but also in a polyhedral support region. For a planar supporting region, the tip-over avoiding requirement is formulated as the tip-over prevent constraints with the reciprocal products of the resultant support wrench and the imaginary tip-over twists, which are constructed with the boundaries of the convex support polygon. At velocity level, the optimized resolution algorithm with standard QP form is designed to resolve the inverse redundant kinematics of the Omni-directional Mobile ManipulatorS (OMMS) with stability considerations. Numerical simulation results show that the presented methods successfully improve the stability level of the robot within an on-line planning process.
