Soft-landing control for a six-legged mobile repetitive lander

doi:10.1007/s11465-024-0802-6

Front. Mech. Eng.

2024, Vol. 19

Issue (5) : 31 https://doi.org/10.1007/s11465-024-0802-6

Soft-landing control for a six-legged mobile repetitive lander

Qingxing XI¹, Zhijun CHEN¹, Ke YIN², Feng GAO¹(

)

¹. State Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
². National Key Laboratory of Aerospace Mechanism, Institute of Aerospace System Engineering Shanghai, Shanghai 201108, China

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Abstract

The primary mode of extraterrestrial exploration is a robotic system comprising a lander and a rover. However, the lander is immovable, and the rover has a restrictive detection area because of the difficulties of reaching complex terrains, such as those with deep craters. In this study, a six-legged mobile repetitive lander with landing and walking functions is designed to solve these problems. First, a six-legged mobile repetitive lander and its structure are introduced. Then, a soft-landing method based on compliance control and optimal force control is addressed to control the landing process. Finally, the experiments are conducted to validate the soft-landing method and its performances. Results show that the soft-landing method for the six-legged mobile repetitive lander can successfully control the joint torques and solve the soft-landing problem on complex terrains, such as those with steps and slopes.

Keywords six-legged mobile repetitive lander soft-landing method compliance control optimal force control complex terrains

Corresponding Author(s): Feng GAO

Issue Date: 29 October 2024

Cite this article:

Qingxing XI,Zhijun CHEN,Ke YIN, et al. Soft-landing control for a six-legged mobile repetitive lander[J]. Front. Mech. Eng., 2024, 19(5): 31.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-024-0802-6
https://academic.hep.com.cn/fme/EN/Y2024/V19/I5/31

Fig.1 Model of the six-legged mobile repetitive lander: (a) top view and (b) axonometric drawing. Six legs are labeled by numbers for identification purpose.

Fig.2 (a–h) Working mode of the six-legged mobile repetitive lander.

Tab.1 Dimensions of the leg mechanism

Fig.3 Leg mechanism and kinematic parameter: (a) composition of the leg mechanism, (b) kinematic parameter, and (c) portrait view of the leg mechanism.

Fig.4 Analysis of the passive spring.

Fig.5 Process of soft-landing.

Fig.6 (a–c) Change process from the landing state to the retracting state.

Fig.7 Supporting force in the retracting process.

Fig.8 Extended height of the body in the process of extending.

Fig.9 Control procedure for the entire soft-landing process.

Fig.10 Experiment scene for the lander.

Fig.11 Parameters of the terrains: (a) height of the step and (b) degree of the slope.

Tab.2 Grounded time of each leg on the terrain with a step

Fig.12 (a–h) Snapshots of the experiment on the terrain with a step.

Fig.13 Joint torques of the legs on the terrain with a step: (a) the torques of all six legs in the whole process and (b) the torques of the thigh motor and shank motor in the process of touching the ground.

Fig.14 Results of the experiment on the terrain with a step: (a) the average vertical value of the velocities of all six legs in BCF, (b) the average height of all six legs, and (c) the roll angle and pitch angle of the body.

Tab.3 Grounded time of each leg on the terrain with a slope

Fig.15 (a–h) Snapshots of the experiment on the terrain with a slope.

Fig.16 Order of the legs.

Fig.17 Joint torques of the legs on the terrain with a slope: (a) the torques of all six legs in the whole process and (b) the torques of the thigh motor and shank motor in the process of touching the ground.

Fig.18 Results of the experiment on the terrain with a slope: (a) the average vertical value of the velocities of all six legs in BCF, (b) the average height of all six legs, and (c) the roll angle and pitch angle of the body.

Tab.4 Grounded time of each leg on the terrain with a step for comparative experiment

Fig.19 (a–h) Snapshots for the comparative experiment.

Fig.20 Joint torques of the legs for the comparative experiment.

Abbreviations
BCF	Body coordinate frame
GCF	Ground coordinate frame
LCF	Leg coordinate frame
MPC	Model predictive control
RL	Reinforcement learning
Variables
B	Active damping of the compliance control
B_virtual	Virtual damping of the virtual compliance control
F_i	Supporting force of the ith leg
F_vi	Virtual foot-tip force in GCF
$F i L$	Force at the output end of the leg in LCF
F₁	Component of F_ki along line CD
F_ki	Force generated by the two passive springs in each leg
F_{vi_z}	Virtual vertical value
F_zi	Vertical foot-tip force
$F K i L (q i)$	Forward kinematic of the ith leg in LCF
g_earth	Gravitational acceleration of Earth
g_moon	Gravitational acceleration of the Moon
H₀	Average height of all six legs
H_init	Desired height of the body
i	Number to mark the legs of the robot (i = 1,2,...,6)
$I K i L (P i L)$	Inverse kinematic of the ith leg in LCF
$J F i L$	Force Jacobian matrix of the leg mechanism
$J v i L$	Velocity Jacobian matrix of the leg mechanism
K	Active stiffness of the compliance control
K_s	Stiffness of the spring
K_virtual	Virtual stiffness of the virtual compliance control
k_d	Control parameter of the derivative gain
k_i	Control parameter of the integral gain
k_p	Control parameter of the proportional gain
l_CF	Current length of the spring
L₀	Original length of the spring
m₁	Mass of the balancing weight
m₂	Mass of the lander
O_B-X_BY_BZ_B	Body coordinate frame, fixed to the body
O_G-X_GY_GZ_G	Ground coordinate frame, fixed to the ground
O_Li-X_LiY_LiZ_Li	Leg coordinate frame, fixed to the body
O_Li-X_LiY'_LiZ'_Li	Coordinate of the plane of the four-bar mechanism
$P L i B$	Coordinate of LCF in BCF
$P B G$	Coordinate of the body in GCF
$P i G$	Coordinate of the foot tip of the ith leg in GCF
$P i L$	Coordinate of the foot tip of the ith leg in LCF
$P i L ′$	Coordinate of $P i L$ in O_Li-X_LiY'_LiZ'_Li
$P ˙ i B$	Velocity of the foot tip of the ith leg in BCF
$P ˙ i L$	Velocity of the foot tip of the ith leg in LCF
$P ˙ z i B$	Vertical value of the foot tip of the ith leg
$P ˙ ¯ z B$	Average of the vertical value of all six legs
q_act,i	Actual joint angle
q_i	Kinematic parameters at the input end
q_init,i	Joint angle that should remain constant during the landing state
q_ref,i	Reference joint angle
q_{ref,i_last}	Reference joint angle in last control period
$q ˙ a c t, i$	Actual joint velocity
$q ˙ i$	Joint velocity of the ith leg
$q ˙ r e f, i$	Reference joint velocity
$L i B R$	Rotation matrix from LCF to BCF
$B G R$	Rotation matrix from BCF to GCF
r_i	Vector from the body to foot tip
t_extend	Total extending time
$w x B G$ , $w y B G$	Roll angle and pitch angle of the body
$w x B 0 G$ , $w y B 0 G$	Roll angle and pitch angle at the beginning of the extending state
$w ˙ x B G$ , $w ˙ y B G$	Velocity of the roll angle and the pitch angle
θ_ai, θ_ti, θ_si	Angle of the abduction, the thigh, and the shank motor of the ith leg
τ_body	Torque needed to control the body
τ_com,i	Torque generated by the compliance control
τ_i	Torque of the input end
τ_limit	Limited torque of the drive motor
τ_req,i	Required joint torque of each leg
τ_spring,i	Torque generated by the springs to the input end
τ_stab,i	Torque generated by the body stabilizer
τ_vi	Torque generated by the virtual compliance control

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[1]	Ke YIN, Chenkun QI, Yue GAO, Qiao SUN, Feng GAO. Landing control method of a lightweight four-legged landing and walking robot[J]. Front. Mech. Eng., 2022, 17(4): 51-.

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