Contact detection with multi-information fusion for quadruped robot locomotion under unstructured terrain

doi:10.1007/s11465-023-0760-4

Front. Mech. Eng.

2023, Vol. 18

Issue (3) : 44 https://doi.org/10.1007/s11465-023-0760-4

RESEARCH ARTICLE

Contact detection with multi-information fusion for quadruped robot locomotion under unstructured terrain

Yangyang HAN¹, Zhenyu LU¹(

), Guoping LIU¹, Huaizhi ZONG², Feifei ZHONG¹, Shengyun ZHOU¹, Zekang CHEN¹

¹. School of Advanced Manufacturing, Nanchang University, Nanchang 330031, China
². State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China

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Abstract

Reliable foot-to-ground contact state detection is crucial for the locomotion control of quadruped robots in unstructured environments. To improve the reliability and accuracy of contact detection for quadruped robots, a detection approach based on the probabilistic contact model with multi-information fusion is presented to detect the actual contact states of robotic feet with the ground. Moreover, a relevant control strategy to address unexpected early and delayed contacts is planned. The approach combines the internal state information of the robot with the measurements from external sensors mounted on the legs and feet of the prototype. The overall contact states are obtained by the classification of the model-based predicted probabilities. The control strategy for unexpected foot-to-ground contacts can correct the control actions of each leg of the robot to traverse cluttered environments by changing the contact state. The probabilistic model parameters are determined by testing on the single-leg experimental platform. The experiments are conducted on the experimental prototype, and results validate the contact detection and control strategy for unexpected contacts in unstructured terrains during walking and trotting. Compared with the body orientation under the time-based control method regardless of terrain, the root mean square errors of roll, pitch, and yaw respectively decreased by 60.07%, 54.73%, and 64.50% during walking and 73.40%, 61.49%, and 61.48% during trotting.

Keywords multi-information fusion contact detection quadruped robot probabilistic contact model unstructured terrain

Corresponding Author(s): Zhenyu LU

Just Accepted Date: 16 June 2023 Issue Date: 26 September 2023

Cite this article:

Yangyang HAN,Zhenyu LU,Guoping LIU, et al. Contact detection with multi-information fusion for quadruped robot locomotion under unstructured terrain[J]. Front. Mech. Eng., 2023, 18(3): 44.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-023-0760-4
https://academic.hep.com.cn/fme/EN/Y2023/V18/I3/44

Fig.1 Robot models: (a) simplified model and coordinate systems, (b) experimental prototype, and (c) leg–foot structure and single-leg experimental platform.

Fig.2 Mount diagram of the Hall sensor and thin-film pressure sensor: (a) front view of mounting and (b) back view of mounting.

Fig.3 Contact detection process diagram based on the Kalman filter.

Fig.4 Gait pattern: (a) gait sequence for walk gait, (b) phase relation for walk gait, (c) gait sequence for trot gait, and (d) phase relation for trot gait.

Fig.5 Phase progress, desired state, and corresponding contact probability: (a) phase progress during walking, (b) phase progress during trotting, (c) contact probability and desired state during walking, and (d) contact probability and desired state during trotting. The solid and dashed lines indicate the desired state and the contact probability, respectively, in Figs. 5(c) and 5(d).

Fig.6 Foot height and corresponding contact probability: (a) foot height during walking, (b) contact probability during walking, (c) foot height during trotting, and (d) contact probability during trotting.

Fig.7 Joint torque and corresponding contact probability: (a) in walking (λ = 0.75) and (b) in trotting (λ = 0.5). Each plot from top to bottom indicates the output joint torque, the overall joint torque, and the associated contact probability. Solid, dashed, and dotted lines are the joint torques of the hip abduction/adduction (HAA), hip flexion/extension (HFE), and knee flexion/extension (KFE), respectively.

Fig.8 Fitting curves, measurement values, and corresponding contact probability based on the press sensor: (a) relation curve between the output voltage and the pressure sensed by the thin-film pressure sensor and (b) measurement values and corresponding contact probability.

Fig.9 Fitting curves, measurement values, and corresponding contact probability based on the Hall sensor: (a) relation curve between the output voltage and the relative distance from the magnet to the Hall sensor and (b) measurement values and corresponding contact probability.

Fig.10 Classification and determination of contact state in the contact detection.

Fig.11 Block diagram of control strategy to address unexpected early or delayed contact.

Parameter	Mean	Variance	Units
$φ t, c ～ N (μ c, σ c 2)$	$μ c$ = 1	$σ c 2$ = 0.05²	?
$φ t, c ˉ ～ N (μ c ˉ, σ c ˉ 2)$	$μ c ˉ$ = 0	$σ c ˉ 2$ = 0.05²	?
$G H ～ N (μ H, σ H 2)$	$μ H$ = 0.035	$σ H 2$ = 0.025²	m
$M τ ～ N (μ τ, σ τ 2)$	$μ τ$ = 3.5	$σ τ 2$ = 1.5²	N?m
$C F ～ N (μ F, σ F 2)$	$μ F$ = 25	$σ F 2$ = 15²	N
$H D ～ N (μ D, σ D 2)$	$μ D$ = 0.008	$σ D 2$ = 0.005²	m

Tab.1 Probability model parameters

Tab.2 Parameters of robot physical and controller

Fig.12 Experimental snapshots on the prototype in unstructured terrains: locomotions in (a) walk gait and (b) trot gait.

Fig.13 Experimental results of contact detection in unstructured terrain: contact detection results during (a) walking and (b) trotting. The first three plots indicate the contact probability based on joint torque, contact force, and relative distance. The bottom plot indicates the overall contact probability. Solid, dashed, dotted, and chain-dotted lines represent the contact probability, detected contact state, desired contact state, and probability threshold, respectively.

Fig.14 Control strategy for unexpected contact: (a) during walking and (b) during trotting. The solid and dashed lines represent the planned values and the corrected values, respectively.

Fig.15 Orientation of the body in the experiment under unstructured terrain: Euler angles during (a) walking and (b) trotting. The solid and dotted lines indicate the Euler angles under the control strategy with contact detection (WCD) and without contact detection (WOCD), respectively.

Fig.16 Orientation errors and variations in experiments: boxplots of the body orientation during (a) walking and (b) trotting; (c) bar plots of the root mean square error (RMSE) for walk and trot gaits.

Abbreviations
ANN	Artificial neural network
DOF	Degree of freedom
GRF	Ground reaction force
HAA	Hip abduction/adduction
HFE	Hip flexion/extension
KFE	Knee flexion/extension
LF	Left front
LH	Left hind
PD	Proportional-derivative
RF	Right front
RH	Right hind
RMSE	Root mean square error
VCM	Voltage conversion module
WCD	Control strategy with contact detection
WOCD	Control strategy without contact detection
Variables
$(?) ˙$	Derivative quantity
$(?) ˉ$	Predicted quantity
$(?)^$	Detection state or corrected quantity
$(?) d$	Desired quantity
$(?) i$	Quantity of the ith component
$(?) t / t ? 1$	Quantity at time t/(t ? 1)
$(?) x / y / z$	Quantity projected on the specified axis
$(?) T$	Transposed quantity
$B (?)$	Quantity in the base coordinate
$W (?)$	Quantity in the world coordinate
a₁, a₂	Swing trajectory coefficients at the z-axis
a_d	Desired linear acceleration
A_t	State transition matrix
B_t	Control input matrix
c₀, c₁, c₂	Coefficients of the plane equation
c	Inequality constraint matrix
C_F	Gaussian random variable based on contact force
C_t	State measurement matrix
d_max, d_min	Upper and lower bounds of the constraint, respectively
d_z	Relative distance sensed by the Hall sensor
f_z	Force sensed by the thin-pressure sensor
f (f_x, f_y, f_z)	GRFs
f_d, f_df	Desired and estimated GRFs, respectively
g_d	Gait type
G_H	Gaussian random variable for ground height
g	Gravity acceleration
H_D	Gaussian random variable based on relative distance
Δh	Step height
I	Identity diagonal matrix
I_G	Inertia vector
J	Jacobian matrix
k	Tracking error coefficient
k_p, k_d	Proportionality and derivative gain matrices, respectively
l	Number of inequality constraints
L₁, L₂, L₃, L₄, L₅	Physical robot parameters
m	Total mass of the robot
M_τ	Gaussian random variable based on joint motor output torque
n	Number of stance legs
N	Number of robotic legs used
P(C)	Contact probability
p_(d) (p_x, p_y, p_z)	(Desired) Footstep location
$W p c o m$	Position of the center of mass in the world coordinate
$W p i$ , $B p i$	Foot positions of the ith leg in the world and base coordinates, respectively
$p i, d$	Desired footstep location of the ith leg
$p i, r$	Position of the ith leg relative to its shoulder
p_r	Position relative to the shoulder
q_i,1, q_i,2, q_i,3	HAA, HFE, and KFE joint positions of the ith leg, respectively
q_d, q	Desired and actual joint positions, respectively
$q ˙ d, q ˙$	Desired and actual joint velocities, respectively
Q_t	Covariance matrix for δ_t
r	Vector from the center of mass to the foot position
$W R B$	Rotation matrix from base to world coordinates
R_t	Covariance matrix for ε_t
S_d, $S^$	Designed and detected contact states, respectively
S	Selection matrix
t	Time
t_φ	Time progress
T	Gait cycle
T_p	Probability threshold
T_st	Stance time in a gait cycle
T_sw	Swing time in a gait cycle
?t	Stance duration
u_t (u_φ,t, u_pz,t)	Input matrix
v_d, v	Desired and actual locomotion velocities, respectively
W_S	Weight for finding the optimal probability threshold
W	Positive definite weight matrix
W_τ	Weight matrix for joint torques
x_t ( $x t ? 1$ )	System state matrix at time t (t?1)
z_t (z_τ,t, z_f,t, z_d,t)	Measurement of the state matrix
α, β	Symbolic variables
δ_t	Measurement noise
ε_t	Random process noise
φ (φ_t)	(Normalized) Phase progress
$φ t, c$	Gaussian random variable for the stance phase process
$φ t, c ˉ$	Gaussian random variable for the swing phase process
Δφ	Phase difference
λ	Duty cycle
$μ c$ , $μ c ˉ$ , μ_H, μ_τ, μ_F, μ_D	Mean for Gaussian distribution of $φ t, c$ , $φ t, c ˉ$ , G_H, M_τ, C_F, and H_D, respectively
$σ c 2$ , $σ c ˉ 2$ , $σ H 2$ , $σ τ 2$ , $σ F 2$ , $σ D 2$	Variance for Gaussian distribution of $φ t, c$ , $φ t, c ˉ$ , G_H, M_τ, C_F, and H_D, respectively
τ_d	Desired joint torque
τ_M	Joint motor output torque
$ω ˙ d$	Desired angular acceleration

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