This paper addresses the problem of seeking generalized Nash equilibrium for constrained aggregative games with double-integrator agents who communicate with each other on an unbalanced directed graph. An auxiliary variable is introduced to balance the consensus terms in the designed algorithm by estimating the left eigenvector of the Laplacian matrix associated with the zero eigenvalue in a distributed manner. Moreover, an event-triggered broadcasting scheme is proposed to reduce communication loads in the network. It is shown that the proposed communication scheme is free of the Zeno behavior and the asymptotic convergence of the designed algorithm is obtained. Simulation results are demonstrated to validate the proposed methods.

When machine tool spindles are running at a high rotation speed, thermal deformation will be introduced due to the generation of large amounts of heat, and machining accuracy will be influenced as a result, which is a generalized issue in numerous industries. In this paper, a new approach based on machine vision is presented for measurements of spindle thermal error. The measuring system is composed of a Complementary Metal-Oxide-Semiconductor (CMOS) camera, a backlight source and a PC. Images are captured at different rotation angles during end milling process. Meanwhile, the Canny edge detection and Gaussian sub-pixel fitting methods are applied to obtain the bottom edge of the end mill which is then used to calculate the lowest point coordinate of the tool. Finally, thermal extension of the spindle is obtained according to the change of the lowest point at different time steps of the machining process. This method is validated through comparison with experimental results from capacitive displacement sensors. Moreover, spindle thermal extension during the processing can be precisely measured and used for compensation in order to improve machining accuracy through the proposed method.