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The purpose of this paper is to look at how, in order to fit the practical environment, the scopes of the order‐quantity of a quantity discount contract are enlarged.

The contract feasible set (CFS) is discussed to extend the order quantity from a single point to an interval.

The application of the CFS can enlarge the scope of the contracts of the supply chain. The CFS can be used in the practice.

The CFS of the quantity‐discount contract only is discussed. The other contracts do not be involved.

A very useful advice for construction the parameters of the contracts.

The concept of the CFS is defined. The new approach that extend the parameters of the contracts from a single point to an interval is provided.

This paper aims to present a pose correction method based on integrated virtual impedance control for avoiding collision and reducing impact.

The authors first constructed the artificial potential field (APF) considering the geometric characteristics of the end-effector. The characteristics of the proposed field were analyzed considering the position and orientation misalignment. Then, an integrated virtual impedance control was proposed by adding resultant virtual repulsive force into traditional impedance control. Finally, the authors modified a correction trajectory for avoiding collision and reducing impact with virtual force and contact force.

The APF the authors constructed can get rid of a local minimum. Comparing with linear correction, this method is able to avoid collision effectively. When the capturing target has intrinsic estimation error, the pose correction can ensure smooth transitions among different stages.

This method can be implemented on a manipulator with inner position control. It can be applied to an industrial robot with applications on robotic assembly for achieving a softer and smoother process. The method can also be expanded to the kind of claw-shaped end-effectors for capturing target.

As the authors know, it is the first time that the characteristics of the end-effector are considered for avoiding collision in capturing application. The proposed integrated virtual impedance control can provide smooth transitions among different stages without switching different force/position controllers.