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

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.

Key words： multi-information fusion; contact detection; quadruped robot; probabilistic contact model; unstructured terrain

Nomenclature

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
\dot{(\cdot )}	Derivative quantity
\overline{(\cdot )}	Predicted quantity
\widehat{(\cdot )}	Detection state or corrected quantity
{(\cdot )}_{\mathrm{d}}	Desired quantity
{(\cdot )}_i	Quantity of the ith component
{(\cdot )}_{t/t-1}	Quantity at time t/(t − 1)
{(\cdot )}_{x/y/\mathit{\text{z}}}	Quantity projected on the specified axis
{(\cdot )}^{\mathrm{T}}	Transposed quantity
{}^{\mathrm{B}}(\cdot )	Quantity in the base coordinate
{}^{\mathrm{W}}(\cdot )	Quantity in the world coordinate
a1, a2	Swing trajectory coefficients at the z-axis
ad	Desired linear acceleration
At	State transition matrix
Bt	Control input matrix
c0, c1, c2	Coefficients of the plane equation
c	Inequality constraint matrix
CF	Gaussian random variable based on contact force
Ct	State measurement matrix
dmax, dmin	Upper and lower bounds of the constraint, respectively
dz	Relative distance sensed by the Hall sensor
fz	Force sensed by the thin-pressure sensor
f (fx, fy, fz)	GRFs
fd, fdf	Desired and estimated GRFs, respectively
gd	Gait type
GH	Gaussian random variable for ground height
g	Gravity acceleration
HD	Gaussian random variable based on relative distance
Δh	Step height
I	Identity diagonal matrix
IG	Inertia vector
J	Jacobian matrix
k	Tracking error coefficient
kp, kd	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
Mτ	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) (px, py, pz)	(Desired) Footstep location
{}^{\mathrm{W}}{\mathit{p}}_{\mathrm{c}\mathrm{o}\mathrm{m}}	Position of the center of mass in the world coordinate
{}^{\mathrm{W}}{\mathit{p}}_i, {}^{\mathrm{B}}{\mathit{p}}_i	Foot positions of the ith leg in the world and base coordinates, respectively
{\mathit{p}}_{i,\mathrm{d}}	Desired footstep location of the ith leg
{\mathit{p}}_{i,\mathrm{r}}	Position of the ith leg relative to its shoulder
pr	Position relative to the shoulder
qi,1, qi,2, qi,3	HAA, HFE, and KFE joint positions of the ith leg, respectively
qd, q	Desired and actual joint positions, respectively
{\dot{\mathit{q}}}_{\mathrm{d}},\dot{\mathit{q}}	Desired and actual joint velocities, respectively
Qt	Covariance matrix for δt
r	Vector from the center of mass to the foot position
{}^{\mathrm{W}}{\mathit{R}}_{\mathrm{B}}	Rotation matrix from base to world coordinates
Rt	Covariance matrix for εt
Sd, \hat{S}	Designed and detected contact states, respectively
S	Selection matrix
t	Time
tφ	Time progress
T	Gait cycle
Tp	Probability threshold
Tst	Stance time in a gait cycle
Tsw	Swing time in a gait cycle
∆t	Stance duration
ut (uφ,t, upz,t)	Input matrix
vd, v	Desired and actual locomotion velocities, respectively
WS	Weight for finding the optimal probability threshold
W	Positive definite weight matrix
Wτ	Weight matrix for joint torques
xt (x_{t-1})	System state matrix at time t (t−1)
zt (zτ,t, zf,t, zd,t)	Measurement of the state matrix
α, β	Symbolic variables
δt	Measurement noise
εt	Random process noise
φ (φt)	(Normalized) Phase progress
{\phi }_{t,\mathrm{c}}	Gaussian random variable for the stance phase process
{\phi }_{t,\overline{\mathrm{c}}}	Gaussian random variable for the swing phase process
Δφ	Phase difference
λ	Duty cycle
{\mu }_{\mathrm{c}}, {\mu }_{\overline{\mathrm{c}}}, μH, μτ, μF, μD	Mean for Gaussian distribution of {\phi }_{t,\mathrm{c}}, {\phi }_{t,\overline{\mathrm{c}}}, GH, Mτ, CF, and HD, respectively
{\sigma }_{\mathrm{c}}^2, {\sigma }_{\overline{\mathrm{c}}}^2, {\sigma }_{\mathrm{H}}^2, {\sigma }_{\tau }^2, {\sigma }_{\mathrm{F}}^2, {\sigma }_{\mathrm{D}}^2	Variance for Gaussian distribution of {\phi }_{t,\mathrm{c}}, {\phi }_{t,\overline{\mathrm{c}}}, GH, Mτ, CF, and HD, respectively
τd	Desired joint torque
τM	Joint motor output torque
{\dot{\text{ω}}}_{\mathrm{d}}	Desired angular acceleration

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 52205059 and 52175050) and the Graduate Innovation Special Fund Project of Jiangxi Province, China (Grant No. YC2021-B031).

Conflict of Interest

The authors declare that they have no conflict of interest.

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