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In this article, a robust model predictive control method is investigated for settling the trajectory tracking problem of a bionic ankle–foot aided by a tensegrity mechanism. In order to achieve adaptive movement of the ankle–foot mechanism, a three-degrees-of-freedom spatial ankle–foot mechanism is designed by tensegrity, which is a spatial grid structure composed of springs and struts. Dynamic analysis is the basis of control algorithm research, and the dynamic model of the mechanism can be established by a Lagrangian equation. Then, a controller is proposed for tracking the trajectory of the ankle–foot mechanism under external disturbances. Combining rolling optimization and feedback correction, the controller can be defined as an optimization problem, by solving which the ankle–foot mechanism can be controlled to track the desired trajectory quickly. Furthermore, stability analysis is an essential part of predictive controller design, which can help to understand the operational mechanism of the control strategy. Numerical results demonstrate that the proposed approach improves trajectory tracking accuracy and avoids mechanism movement problems caused by disturbances. [ABSTRACT FROM AUTHOR]