Force-Closure Condition for Cooperative Multi-robot Pushing of Rectangular Objects

This research presents a necessary and sufficient closed-form condition for achieving planar force closure when pushing rectangular objects using four frictionless contacts. The derived condition, which depends on contact locations relative to object dimensions, is independent of the center of mass and serves as a geometric feasibility check before force allocation. When the condition is not met, the method identifies which opposing contact pair requires adjustment. The approach is integrated into a full-pose trajectory-tracking framework, where static wrench feasibility tests and narrow-passage floating-body simulations demonstrate that maintaining force-closure configurations significantly reduces root-mean-square (RMS) tracking errors in position and orientation compared to baseline methods.