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Performing a stable and robust surface landing on small celestial bodies is essential for future scientific exploration and planetary defense missions. However, in practical missions, due to the weak gravity and complex surface topography, the widely adopted rigid landers are prone to rebound or overturning upon touchdown. This paper reviews a novel landing mode, namely the flexible landing, and highlights the most recent developments in the fields of flexible landing guidance and navigation. The flexible landing employs a flexible lander composed of a soft structure and several embedded rigid nodes to execute the landing mission. Compared with rigid landers, the soft structure, which is made of intelligent materials, increases the contact area between the lander and the surface and dissipates kinetic energy during touchdown, thereby reducing the risks of rollover or rebound.
Despite the advantages in enabling reliable and adaptable surface landing, the flexible lander is inherently an infinite-dimensional system, presenting challenge for the design of guidance, navigation, and control methods. To overcome this challenge, the concept of “equivalent plane” is introduced to establish a state representation model, where the state of the flexible lander is represented by the state of the equivalent plane center, including the center position, velocity and tilt angle. Since the state of the equivalent plane center can be derived from the states of the nodes, autonomous navigation, guidance and control of the flexible lander can be achieved through the estimation and control of the finite-dimensional node states. Building upon this, a cooperative flexible landing navigation method is proposed. During the landing process, the state of the nodes satisfies the flexible deformation constraints. By incorporating such nonlinear inequality constraints to refine the state estimates, a constrained filtering algorithm with theoretically guaranteed performance is developed. Further, the geometric characteristic of the landing trajectory is considered. The curvature guidance is then designed to enable the flexible lander follows a geometrically convex trajectory for landing, facilitating earlier observation of the landing site and improving obstacle avoidance performance.