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The point-foot biped robot is highly adaptable to and can move rapidly on complex, non-structural and non-continuous terrain, as demonstrated in many studies. However, few studies have investigated balance control methods for point-foot sliding on low-friction terrain. This article presents a control framework based on the dual-objective convergence method and whole-body control for the point-foot biped robot to stabilize its posture balance in sliding. In this control framework, a dual-objective convergence equation is used to construct the posture stability criterion and the corresponding equilibrium control task, which are simultaneously converged. Control tasks are then carried out through the whole-body control framework, which adopts an optimization method to calculate the viable joint torque under the physical constraints of dynamics, friction and contact forces. In addition, this article extends the proposed approach to balance control in standing recovery. Finally, the capabilities of the proposed controller are verified in simulations in which a 26.9-kg three-link point-foot biped robot (1) slides over a <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow><mn>10</mn></mrow><mo>∘</mo></msup></semantics></math></inline-formula> trapezoidal terrain, (2) slides on terrain with a sinusoidal friction coefficient between 0.05 and 0.25 and (3) stands and recovers from a center-of-mass offset of 0.02 m.