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With the progressing autonomy of driving technology, machine is assuming greater responsibility for driving tasks to enhance safety. Leveraging this potential, this paper introduces a novel human-machine co-steering control strategy based on model predictive control. The strategy is designed to address the difficulties faced by drivers when driving on surfaces with low adhesion. Firstly, the proposed strategy utilizes a parallel human-machine co-steering framework with a weight allocation concept between the controller and the driver. Moreover, the nonlinear controller dynamics model and linear driver dynamics model are developed to characterize the interaction behaviors between human and machine under low-adhesion road surface conditions. And a nonlinear game optimization problem is formulated to capture the cooperative interaction relationship between human and machine.