Landing control method of a lightweight four-legged landing and walking robot

doi:10.1007/s11465-022-0707-1

Front. Mech. Eng.

2022, Vol. 17

Issue (4) : 51 https://doi.org/10.1007/s11465-022-0707-1

RESEARCH ARTICLE

Landing control method of a lightweight four-legged landing and walking robot

Ke YIN¹, Chenkun QI², Yue GAO¹, Qiao SUN², Feng GAO²(

)

¹. School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China
². Key Laboratory of Mechanical System and Vibration, School of Mechanical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

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Abstract

The prober with an immovable lander and a movable rover is commonly used to explore the Moon’s surface. The rover can complete the detection on relatively flat terrain of the lunar surface well, but its detection efficiency on deep craters and mountains is relatively low due to the difficulties of reaching such places. A lightweight four-legged landing and walking robot called “FLLWR” is designed in this study. It can take off and land repeatedly between any two sites wherever on deep craters, mountains or other challenging landforms that are difficult to reach by direct ground movement. The robot integrates the functions of a lander and a rover, including folding, deploying, repetitive landing, and walking. A landing control method via compliance control is proposed to solve the critical problem of impact energy dissipation to realize buffer landing. Repetitive landing experiments on a five-degree-of-freedom lunar gravity testing platform are performed. Under the landing conditions with a vertical velocity of 2.1 m/s and a loading weight of 140 kg, the torque safety margin is 10.3% and 16.7%, and the height safety margin is 36.4% and 50.1% for the cases with or without an additional horizontal disturbance velocity of 0.4 m/s, respectively. The study provides a novel insight into the next-generation lunar exploration equipment.

Keywords landing and walking robot lunar exploration buffer landing compliance control

Corresponding Author(s): Feng GAO

Just Accepted Date: 27 May 2022 Issue Date: 12 December 2022

Cite this article:

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

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-022-0707-1
https://academic.hep.com.cn/fme/EN/Y2022/V17/I4/51

Fig.1 Conceptual sketch of repetitive landing.

Fig.2 Structure of a four-legged landing and walking robot.

Fig.3 Multifunction design during different phase: (a) buffer landing like a cantilever lander and (b) roving like a four-legged robot.

Fig.4 Three active degrees-of-freedom hybrid leg design: (a) leg prototype and (b) leg mechanism. IDU: integrated drive unit, RP: revolute pair, PFBM: parallel five-bar mechanism.

Fig.5 Design of the integrated drive unit: (a) three-dimensional and (b) inner structure.

Fig.6 Hardware structure of motion controller. RTOS: real time operating system.

Fig.7 Coordinate system in motion planning: (a) robot coordinate and (b) leg coordinate.

Fig.8 Landing method framework consisting of three layers: hardware inputs, landing method, and hardware outputs.

Fig.9 State switching method during buffer landing.

Tab.1 Initial tiptoe positions before buffer landing

Fig.10 Trajectory planning of the body and tiptoe of leg 4 during buffer landing.

Fig.11 Compliance planning of stiffness and damping coefficients for thigh and shank joints.

Fig.12 Virtual three-leg supporting algorithm.

Tab.2 Computation time of different algorithms to solve Eq. (29)

Tab.3 Initial conditions of numerical simulation

Fig.13 Results of vertical landing simulation: (a) joint torque in each leg, (b) body angle of roll and pitch, and (c) position and velocity of the body.

Fig.14 Results of parabolic landing simulation: joint torques in (a) legs 1 and 4 and (b) legs 2 and 3; (c) body angle of roll and pitch; and (d) position and velocity of the body.

Fig.15 Components of the 5-DoF-LGSP.

Fig.16 Counterweight system design of the 5-DoF-LGSP.

Fig.17 Keyframe snapshots in the parabolic landing.

Fig.18 Results of vertical landing experiment: joint torques in (a) leg 1, (b) leg 2, (c) leg 3, and (d) leg 4; (e) body angle of roll and pitch; and (f) position and velocity of the body.

Fig.19 Results of parabolic landing experiment: joint torques in (a) leg 1, (b) leg 2, (c) leg 3, and (d) leg 4; (e) body angle of roll and pitch; and (f) position and velocity of the body.

Abbreviations
5-DoF-LGTP	Five-degree-of-freedom lunar gravity testing platform
COM	Center of mass
DoF	Degree-of-freedom
FLLWR	Four-legged landing and walking robot
Geninv	Generalized inverse based on Cholesky factorization
Ginv	Generalized inverse computation method
IDU	Integrated drive unit
IMqrg	Improved generalized inverse computation method based on QR factorization
IMU	Inertial measurement unit
LRV	Lunar roving vehicle
PFBM	Parallel five-bar mechanism
Qrg	Generalized inverse computation method based on QR factorization
RP	Revolute pair
SVD	Singular value decomposition
TPM	Tensor product matrix
VTLSA	Virtual three-leg supporting algorithm
Variables
a₀, a₁	Initial and target acceleration
a_b	Body linear acceleration
B, B₀, B₁, B₂, B₃	Active damping coefficients
B_g	Ground damping coefficient
B_virtual	Virtual damping coefficient
c_i	Coefficient of interpolation trajectory
coe_interp, coe₀, coe₁, coeV₀, coeV₁	Current interpolation coefficient, initial coefficient, target coefficient, initial coefficient velocity, and target coefficient velocity in compliance planning, respectively
d	Active compression distance
E_ps	Elastic potential energy of passive spring
F_i	ith tiptoe force from ground
F_iz, F_iz	Vector and the third component of the ith tiptoe force from ground in the z direction
$F i z k m n$	ith (i = k, m, or n) vertical force in leg k-m-n supporting
F_tip, F_x, F_y, F_z	Tiptoe force vector and its components
F_virtual	Virtual tiptoe force
F_vr	Virtual resultant force in the z direction
g, g	Vector and the third component of gravitational acceleration
g_e	Gravitational acceleration on the Earth
g_m	Gravitational accelerations on the Moon
H	Correction vector
I_b, I_bx, I_by	Body inertia vector and its components
j₀, j₁	Initial and target jerk
J_v (q)	Velocity Jacobian matrix
K, K₀, K₁, K₂	Active stiffness coefficients
k_dz	Derivative gain in the z direction
k_d,θ	Derivative gain of roll and pitch angles
K_g	Ground stiffness coefficient
k_i,z	Integral gain in the z direction
k_i,θ	Integral gain of roll and pitch angles
k_p,z	Proportional gain in the z direction
k_p,θ	Proportional gain of roll and pitch angles
K_ps	Stiffness coefficient of passive spring
K_virtual	Virtual stiffness coefficient
L_l, L_r	Distances from the intersection point of thigh and shank to the left and right fixed points of passive spring, respectively
L_ps, L_ps0	Current and original length of the passive spring, respectively
L_s	Shank length
L_t	Thigh length
m_b	Body mass
m_c1	Counterweight 1 mass
m_c2	Counterweight 2 mass
m_t	System mass of the lander and loads
O_b	Origin of body coordinate frame
O_li	Origin of the ith leg coordinate frame
O_w	Origin of world coordinate frame
$P t i p$ , $P ˙ t i p$	Tiptoe position and velocity, respectively
$b P l i$	Origin position of $Σ l i$ in the body coordinate frame $Σ b$
$l i P t i p$	Tiptoe position in the leg coordinate frame $Σ l i$
$w P b$	Body position in the world coordinate frame $Σ w$
$w P t i p$	Tiptoe position in the world coordinate frame $Σ w$
$q$ , $q ˙$	Generalized coordinate and velocity vector of joints, respectively
$r c o m$ , $r c o m x$ , $r c o m y$	Vector and its components from the COM to the origin O_b
$r i$ , $r i x$ , $r i y$ , $r i z$	Vector and its components from the origin $O b$ to the ith tiptoe
$b R l i$	Rotation transformation matrix from $Σ l i$ to $Σ b$
$w R b$	Rotation transformation matrix from $Σ b$ to $Σ w$
$t$ , $t 0$ , $t 1$ , $t r$ , T	Current time, initial time, end time, duration ratio time, and total duration time, respectively
$T s$ , $T t$	Shank and thigh IDUs torques, respectively
$v 0$ , $v 1$	Initial and target velocity, respectively
$v h$	Horizontal velocity
$v x$	Horizontal velocity in the x direction
$v z$	Vertical velocity
$x b$ , $y b$ , $z b$	Forward, left, and upper direction, respectively
$x l i$ , $y l i$ , $z l i$	Components of tiptoe position in the ith leg coordinate frame, respectively
$x t i p$ , $x t i p 0$ , $x t i p 1$	Current, initial position, and terminated position of tiptoe in the x direction, respectively
$x ˙ t i p$ , $y ˙ t i p$ , $z ˙ t i p$	Current tiptoe velocity in the x, y and z directions, respectively
$y t i p$ , $y t i p 0$ , $y t i p 1$	Current, initial, and terminated positions of tiptoe in the y direction, respectively
$z a b$ , $z ˙ a b$	Actual body position and velocity in the z direction, respectively
$z ¨ b$ , $z ¨ b$	Vector and the third component of body linear acceleration in the z direction, respectively
$z b o d y 0$ , $z b o d y 1$	Body initial and target position in the z direction, respectively
$z i n t e r p$	Real-time body interpolation trajectory
$z r b$ , $z ˙ r b$	Reference body position and velocity in the z direction, respectively
$z t i p$ , $z t i p 0$ , $z t i p 1$	Current, initial, and target positions of the tiptoe in the z direction, respectively
$δ P t i p$	Virtual displacement of tiptoe
$δ q$	Virtual displacement of the generalized coordinate vector $q$
$δ W p s$	Virtual work of passive spring
$θ a j$ , $θ ˙ a j$	Actual joint angle and velocity, respectively
$θ a p$ , $θ ˙ a p$	Actual pitch angle and velocity, respectively
$θ a r$ , $θ ˙ a r$	Actual roll angle and velocity, respectively
$θ r$ , $θ ˙ r$	Rocker arm angle and velocity, respectively
$θ r j$ , $θ ˙ r j$	Reference joint angle and velocity, respectively
$θ r p$ , $θ ˙ r p$	Reference pitch angle and velocity, respectively
$θ r r$ , $θ ˙ r r$	Reference roll angle and velocity, respectively
$θ s$ , $θ ˙ s$	Side angle and velocity, respectively
$θ t$ , $θ ˙ t$	Thigh angle and velocity, respectively
$τ$ , $τ s$ , $τ t$ , $τ r$	Joint torque vector and its components, respectively
$τ a j$ , $τ c j$ , $τ r j$	Actual, command, and reference joint torques, respectively
$τ v i r t u a l$	Virtual joint torque
$τ v r$	Virtual resultant torsions in the $x$ and $y$ directions, respectively
$Σ b$	Body coordinate frame
$Σ i m u$	IMU coordinate frame
$Σ l i$	ith leg coordinate frame
$Σ w$	World coordinate frame
$ω b$	Body angular velocity
$ω ˙ b$ , $ω ˙ b x$ , $ω ˙ b y$	Vector and its components of body angular acceleration, respectively

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