  This paper addresses the problem of pushing manipulation with nonholonomic
mobile robots. Pushing is a fundamental skill that enables robots to move
unwieldy objects that cannot be grasped. We propose a stable pushing method
that maintains stiff contact between the robot and the object to avoid
consuming repositioning actions. We prove that a line contact, rather than a
single point contact, is necessary for nonholonomic robots to achieve stable
pushing. We also show that the stable pushing constraint and the nonholonomic
constraint of the robot can be simplified as a concise linear motion
constraint. Then the pushing planning problem can be formulated as a
constrained optimization problem using nonlinear model predictive control
(NMPC). According to the experiments, our NMPC-based planner outperforms a
reactive pushing strategy in terms of efficiency, reducing the robot's traveled
distance by 23.8\% and time by 77.4\%. Furthermore, our method requires four
fewer hyperparameters and decision variables than the Linear Time-Varying (LTV)
MPC approach, making it easier to implement. Real-world experiments are carried
out to validate the proposed method with two differential-drive robots, Husky
and Boxer, under different friction conditions.
