**1. Introduction**

The moon is the hub and bridge between mankind and the universe, while lunar exploration is the premise and basis of deep space exploration. Nowadays, the separated design of an immovable lander and rover is still the core method of zero-distance exploration on the moon. Many countries have made world-renowned achievements such as the Soviet/Russian Luna-9 [1], the first lander to achieve lunar soft-landing, which absorbs impact energy using four airbags; American Surveyor-1 [2], the first legged lander to reach the lunar surface, which uses three three-branch buffered legs filled with aluminum honeycomb material, providing technical support for Apollo program [3]; Chinese Chang'e 4 [4] reaches the far side of the moon first, which utilizes four similar buffer legs. Notably, all these landers are immovable and are designed to help the rover finish landing, so their exploration capacity is restricted to around the fixed landing site. Two kinds of rover are applied to expand the exploration range, one is a manned lunar rover, like LRV [5], which can carry up to two astronauts, another is the unmanned wheeled rover, like Yutu 1&2[4,6], which can maneuver quickly with scientific instruments. However, the separated design of the lander and rover creates a heavy and complex prober system. The rover only executes exploration in a circle district with the lander as the center and the safety distance as the radius.

Thanks to excellent traversing performance on irregular terrain [7,8], legged robots are promising to accomplish lunar exploration compared with a wheeled rover. On the

**Citation:** Yin, K.; Zhou, S.; Sun, Q.; Gao, F. Lunar Surface Fault-Tolerant Soft-Landing Performance and Experiment for a Six-Legged Movable Repetitive Lander. *Sensors* **2021**, *21*, 5680. https://doi.org/10.3390/ s21175680

Academic Editor: Javier Cuadrado

Received: 28 July 2021 Accepted: 20 August 2021 Published: 24 August 2021

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one hand, the leg form is utilized in most existing landers, though they lack mobility on the lunar surface. On the other hand, legged robots are well designed in many fields such as running robots, Bigdog [9], Cheetah-3 [10] and Anymal [11,12]; underwater robots, Crabster [13,14]; heavy-duty robots, Octopus [15]; and exploration robots, Athlete [16], Spaceclimber [17] and Spacebok [18,19]. Furthermore, to combine the excellent speed performance for wheeled robots on even terrain and a great adaptive capacity for legged robots on irregular terrain, the wheel-legged robot [20] adopted a hierarchical framework to control wheel and leg motions; this has drawn a lot of researcher attention. Nevertheless, the current legged or wheel-legged robots are difficult to directly apply to lunar exploration. The hydraulic actuator is widely employed in HyQ2Max [21] or Bigdog [9] to obtain high explosive torque, which is infeasible for extraterrestrial exploration. The leg layout of a running robot cannot withstand the landing impact in all directions. The buffer capacity of the current robot is relatively weak, so the engine nozzle under the lander body will be easily damaged for colliding with the ground.

We have designed a six-legged movable repetitive lander "HexaMRL" in previous work to integrate the function of both lander and rover. IDUs are used to simulate the dynamic characters of an active dissipative system of spring and dampener by impedance control to achieve a buffered landing and protect the leg structure, different from the irreversible deformation of aluminum honeycomb material after landing [22–24]. Hence, the lander can still execute locomotion as a rover. After exploration at a current landing site, it can fly to the next landing site using the engine and repetitively perform buffered landing tasks. This new exploration mode will significantly increase the utilization rate of an individual prober on the moon and greatly extend the exploration district. However, the repetitive work mode has higher requirements for the quality and fault-tolerant landing capacity of the lander.

In the harsh lunar environment (i.e., intense radiation, large temperature difference and ultravacuum), it is hard to repair with the remote operation if some failures occur on the IDUs. Fault-tolerant control (FTC) for the robot has attracted great attention all over the world and is pivotal for the prober to execute exploration tasks. Nowadays, FTC is generally achieved by the following three methods. Firstly, multiple drives are used in the active joints; for example, Zhang et al. [25] employ dual-input/single-output (DISO) to drive the servo press machine. Secondly, the parallel robot could use a redundant drive [26] to eliminate singularities in the workspace. The third one is to increase the DoF of robot end-effector, such as the Canadian space station's remote manipulator system (SSRMS) [27], which adopted seven series joints to improve the workspace. However, the above FTC relies on more drives or more complex mechanisms, which will increase the system mass and complexity that are difficult for the lander to accept. Furthermore, fault-tolerant landing is not generally considered in current landers because most of the existing landers are three-legged or four-legged, which constructively lack fault-tolerant landing capacity when one leg fails. For a three-legged lander like Surveyor-1, the remaining two legs cannot support the lander. As for four-legged landers like Apollo 11 [3] or Chang'e 3, 4, & 5 [4,6,28], the center of mass of the lander will move to the side of the supporting triangle constructed by the remaining three legs, leading to a failed buffer landing on the uneven lunar surface. Therefore, hard strict standards are required for the manufacture and control of such landers and would be abandoned if any failures occur.

The six-legged design in HexaMRL makes the fault-tolerant soft-landing feasible without any supplement of drivers or mechanisms. In this paper, we have systematically studied the fault-tolerant soft-landing performance on the moon for HexaMRL. Firstly, we analyze the classification and stability of the landing configuration and establish the relationship between fault number and landing configuration by the synthesis equation. Secondly, regarding stable configuration, the corresponding fault-tolerant landing algorithms are designed to achieve a buffered landing, and a quasi-incentre stability optimization method is further proposed to increase the stability margin during supported operations. Thirdly, to verify the fault-tolerant landing on the moon, a series of experiments including five-legged, four-legged and three-legged soft-landing with a vertical landing velocity of −1.9 m/s and a payload of 140 kg are successfully carried out on a 5-DoF lunar gravity ground testing platform.

The rest of the paper is organized as follows. Section 2 introduces the lander system. The landing configuration is analyzed in Section 3. Sections 4 and 5 design the fault-tolerant algorithm and optimize the stability margin in supporting the operations, respectively. Section 6 clarifies the fault-tolerant landing experiments, and Section 7 discusses the experiment results. The last section is the conclusion and its expansion.
