Contact detection with multiinformation fusion for quadruped robot locomotion under unstructured terrain
Yangyang HAN, Zhenyu LU, Guoping LIU, Huaizhi ZONG, Feifei ZHONG, Shengyun ZHOU, Zekang CHEN
Contact detection with multiinformation fusion for quadruped robot locomotion under unstructured terrain
Reliable foottoground 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 multiinformation 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 modelbased predicted probabilities. The control strategy for unexpected foottoground 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 singleleg 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 timebased 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.
multiinformation fusion / contact detection / quadruped robot / probabilistic contact model / unstructured terrain
[1] 
He J , Gao F . Mechanism, actuation, perception, and control of highly dynamic multilegged robots: a review. Chinese Journal of Mechanical Engineering, 2020, 33(1): 79
CrossRef
Google scholar

[2] 
Li X , Zhang S Y , Zhou H T , Feng H B , Fu Y L . Locomotion adaption for hydraulic humanoid wheellegged robots over rough terrains. International Journal of Humanoid Robotics, 2021, 18(1): 2150001
CrossRef
Google scholar

[3] 
Chai H , Rong X W , Tang X P , Li Y B . Gaitbased quadruped robot planar hopping control with energy planning. International Journal of Advanced Robotic Systems, 2016, 13(1): 20
CrossRef
Google scholar

[4] 
Zhao Y , Gao F , Sun Q , Yin Y P . Terrain classification and adaptive locomotion for a hexapod robot Qingzhui. Frontiers of Mechanical Engineering, 2021, 16(2): 271–284
CrossRef
Google scholar

[5] 
Hammoud B , Khadiv M , Righetti L . Impedance optimization for uncertain contact interactions through risk sensitive optimal control. IEEE Robotics and Automation Letters, 2021, 6(3): 4766–4773
CrossRef
Google scholar

[6] 
Jin Y B , Liu X W , Shao Y C , Wang H T , Yang W . Highspeed quadrupedal locomotion by imitationrelaxation reinforcement learning. Nature Machine Intelligence, 2022, 4(12): 1198–1208
CrossRef
Google scholar

[7] 
AnanthanarayananAFoongSKimS. A compact two DOF magnetoelastomeric force sensor for a running quadruped. In: Proceedings of 2012 IEEE International Conference on Robotics and Automation (ICRA). Saint Paul: IEEE, 2012, 1398–1403

[8] 
Chuah M Y , Kim S . Enabling force sensing during ground locomotion: a bioinspired, multiaxis, composite force sensor using discrete pressure mapping. IEEE Sensors Journal, 2014, 14(5): 1693–1703
CrossRef
Google scholar

[9] 
KäslinRKolvenbachHPaezLLikaKHutterM. Towards a passive adaptive planar foot with ground orientation and contact force sensing for legged robots. In: Proceedings of 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Madrid: IEEE, 2018, 2707–2714

[10] 
LiX QWangY BWangWYiJ Q. Footground contact force during quadruped locomotion using CPG control. In: Proceedings of 2018 the 37th Chinese Control Conference (CCC). Wuhan: IEEE, 2018, 5233–5238

[11] 
RuppertFBadriSpröwitzA. FootTile: a rugged foot sensor for force and center of pressure sensing in soft terrain. In: Proceedings of 2020 IEEE International Conference on Robotics and Automation (ICRA). Paris: IEEE, 2020, 4810–4816

[12] 
Xu Y T , Wang Z Y , Hao W J , Zhao W Y , Lin W E , Jin B C , Ding N . A flexible multimodal sole sensor for legged robot sensing complex ground information during locomotion. Sensors, 2021, 21(16): 5359
CrossRef
Google scholar

[13] 
Weerakkodi MudaligeN DNazarovaEBabataevIKopanevPFedoseevACabreraM ATsetserukouD. DogTouch: CNNbased recognition of surface textures by quadruped robot with high density tactile sensors. In: Proceedings of 2022 IEEE the 95th Vehicular Technology Conference (VTC2022Spring). Helsinki: IEEE, 2022, 1–5

[14] 
Buchanan R , Bednarek J , Camurri M , Nowicki M R , Walas K , Fallon M . Navigating by touch: haptic Monte Carlo localization via geometric sensing and terrain classification. Autonomous Robots, 2021, 45(6): 843–857
CrossRef
Google scholar

[15] 
Ba K X , Song Y H , Shi Y P , Wang C Y , Ma G L , Wang Y , Yu B , Yuan L P . A novel onedimensional force sensor calibration method to improve the contact force solution accuracy for legged robot. Mechanism and Machine Theory, 2022, 169: 104685
CrossRef
Google scholar

[16] 
Park H W , Ramezani A , Grizzle J W . A finitestate machine for accommodating unexpected large groundheight variations in bipedal robot walking. IEEE Transactions on Robotics, 2013, 29(2): 331–345
CrossRef
Google scholar

[17] 
HwangboJBellicosoC DFankhauserPHutterM. Probabilistic foot contact estimation by fusing information from dynamics and differential/forward kinematics. In: Proceedings of 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Daejeon: IEEE, 2016, 3872–3878

[18] 
Wensing P M , Wang A , Seok S , Otten D , Lang J , Kim S . Proprioceptive actuator design in the MIT Cheetah: impact mitigation and highbandwidth physical interaction for dynamic legged robots. IEEE Transactions on Robotics, 2017, 33(3): 509–522
CrossRef
Google scholar

[19] 
Camurri M , Fallon M , Bazeille S , Radulescu A , Barasuol V , Caldwell D G , Semini C . Probabilistic contact estimation and impact detection for state estimation of quadruped robots. IEEE Robotics and Automation Letters, 2017, 2(2): 1023–1030
CrossRef
Google scholar

[20] 
BledtGWensingP MIngersollSKimS. Contact model fusion for eventbased locomotion in unstructured terrains. In: Proceedings of 2018 IEEE International Conference on Robotics and Automation (ICRA). Brisbane: IEEE, 2018, 4399–4406

[21] 
Cong Z , Honglei A , Wu C Y , Lang L , Wei Q , Hongxu M . Contact force estimation method of leggedrobot and its application in impedance control. IEEE Access: Practical Innovations, Open Solutions, 2020, 8: 161175–161187
CrossRef
Google scholar

[22] 
Chatzinikolaidis I , You Y W , Li Z B . Contactimplicit trajectory optimization using an analytically solvable contact model for locomotion on variable ground. IEEE Robotics and Automation Letters, 2020, 5(4): 6357–6364
CrossRef
Google scholar

[23] 
WolfslagW JMcGreavyCXinG YTiseoCVijayakumarSLiZ B. Optimisation of bodyground contact for augmenting the wholebody locomanipulation of quadruped robots. In: Proceedings of 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Las Vegas: IEEE, 2020, 3694–3701

[24] 
LiX SShenY GLuoCXuQ WChenX LLiC. A probabilistic models fusion based contact detection for quadruped robot. In: Proceedings of 2021 IEEE International Conference on Mechatronics and Automation (ICMA). Takamatsu: IEEE, 2021, 703–708

[25] 
Liu Q Y , Yuan B , Wang Y . Online learning for foot contact detection of legged robot based on data stream clustering. Frontiers in Bioengineering and Biotechnology, 2022, 9: 771415
CrossRef
Google scholar

[26] 
Han Y Y , Liu G P , Lu Z Y , Zong H Z , Zhang J H , Zhong F F , Gao L Y . A stability locomotioncontrol strategy for quadruped robots with centerofmass dynamic planning. Journal of Zhejiang University−Science A, 2023, 24(6): 516–530
CrossRef
Google scholar

[27] 
ThrunSBurgardWFoxD. Probabilistic Robotics. Cambridge: MIT Press, 2005, 39–43

[28] 
Park H W , Wensing P M , Kim S . Highspeed bounding with the MIT Cheetah 2: control design and experiments. International Journal of Robotics Research, 2017, 36(2): 167–192
CrossRef
Google scholar

[29] 
RaibertM H. Legged Robots That Balance. Cambridge: MIT Press, 1986

[30] 
Di CarloJWensingP MKatzBBledtGKimS. Dynamic locomotion in the MIT Cheetah 3 through convex modelpredictive control. In: Proceedings of 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS). Madrid: IEEE, 2018, 7440–7447

[31] 
Focchi M , del Prete A , Havoutis I , Featherstone R , Caldwell D G , Semini C . Highslope terrain locomotion for torquecontrolled quadruped robots. Autonomous Robots, 2017, 41(1): 259–272
CrossRef
Google scholar

[32] 
BoaventuraTSeminiCBuchliJFrigerioMFocchiMCaldwellD G. Dynamic torque control of a hydraulic quadruped robot. In: Proceedings of 2012 IEEE International Conference on Robotics and Automation (ICRA). Saint Paul: IEEE, 2012, 1889–1894

[33] 
CebeOTiseoCXinG YLinH CSmithJMistryM. Online dynamic trajectory optimization and control for a quadruped robot. In: Proceedings of 2021 IEEE International Conference on Robotics and Automation (ICRA). Xi’an: IEEE, 2021, 12773–12779

[34] 
Lin P C , Komsuoglu H , Koditschek D E . A leg configuration measurement system for fullbody pose estimates in a hexapod robot. IEEE Transactions on Robotics, 2005, 21(3): 411–422
CrossRef
Google scholar

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  Proportionalderivative 
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 
$\phantom{\rule{thickmathspace}{0ex}}\phantom{\rule{thickmathspace}{0ex}}\phantom{\rule{thickmathspace}{0ex}}\overline{(\cdot )}$  Predicted quantity 
$\hat{(\cdot )}$  Detection state or corrected quantity 
${(\cdot )}_{\mathrm{d}}$  Desired quantity 
${(\cdot )}_{i}$  Quantity of the ith component 
${(\cdot )}_{t/t1}$  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 
a_{1}, a_{2}  Swing trajectory coefficients at the zaxis 
a_{d}  Desired linear acceleration 
A_{t}  State transition matrix 
B_{t}  Control input matrix 
c_{0}, c_{1}, c_{2}  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 thinpressure 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 
L_{1}, L_{2}, L_{3}, L_{4}, L_{5}  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 
${}^{}\mathrm{W}{\mathit{p}}_{\mathrm{c}\mathrm{o}\mathrm{m}}$  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 
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 
${\dot{\mathit{q}}}_{\mathrm{d}},\dot{\mathit{q}}$  Desired and actual joint velocities, respectively 
Q_{t}  Covariance matrix for δ_{t} 
r  Vector from the center of mass to the foot position 
${}^{}\mathrm{W}{\mathit{R}}_{\mathrm{B}}$  Rotation matrix from base to world coordinates 
R_{t}  Covariance matrix for ε_{t} 
S_{d}, $\hat{S}$  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} (${x}_{t1}$)  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 
${\phi}_{t,\mathrm{c}}$  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 
$\phantom{\rule{thinmathspace}{0ex}}{\mu}_{\mathrm{c}}$, ${\mu}_{\overline{\mathrm{c}}}$, μ_{H}, μ_{τ}, μ_{F}, μ_{D}  Mean for Gaussian distribution of ${\phi}_{t,\mathrm{c}}$, ${\phi}_{t,\overline{\mathrm{c}}}$, G_{H}, M_{τ}, C_{F}, and H_{D}, 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 ${\phi}_{t,\mathrm{c}}$, ${\phi}_{t,\overline{\mathrm{c}}}$, G_{H}, M_{τ}, C_{F}, and H_{D}, respectively 
τ_{d}  Desired joint torque 
τ_{M}  Joint motor output torque 
${\dot{\text{\omega}}}_{\mathrm{d}}$  Desired angular acceleration 
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