Compliance motion control of the hydraulic dual-arm manipulator with adaptive mass estimation of unknown object

doi:10.1007/s11465-023-0773-z

Frontiers of Mechanical Engineering

2024, Vol. 19

Issue (1): 7 https://doi.org/10.1007/s11465-023-0773-z

本期目录

Compliance motion control of the hydraulic dual-arm manipulator with adaptive mass estimation of unknown object

Bolin SUN¹, Min CHENG¹, Ruqi DING²(

), Bing XU³

¹. State Key Laboratory of Mechanical Transmissions, Chongqing University, Chongqing 400044, China
². Key Laboratory of Conveyance and Equipment (Ministry of Education), East China Jiaotong University, Nanchang 330013, China
³. State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, Hangzhou 310027, China

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Abstract：

Given the limited operating ability of a single robotic arm, dual-arm collaborative operations have become increasingly prominent. Compared with the electrically driven dual-arm manipulator, due to the unknown heavy load, difficulty in measuring contact forces, and control complexity during the closed-chain object transportation task, the hydraulic dual-arm manipulator (HDM) faces more difficulty in accurately tracking the desired motion trajectory, which may cause object deformation or even breakage. To overcome this problem, a compliance motion control method is proposed in this paper for the HDM. The mass parameter of the unknown object is obtained by using an adaptive method based on velocity error. Due to the difficulty in obtaining the actual internal force of the object, the pressure signal from the pressure sensor of the hydraulic system is used to estimate the contact force at the end-effector (EE) of two hydraulic manipulators (HMs). Further, the estimated contact force is used to calculate the actual internal force on the object. Then, a compliance motion controller is designed for HDM closed-chain collaboration. The position and internal force errors of the object are reduced by the feedback of the position, velocity, and internal force errors of the object to achieve the effect of the compliance motion of the HDM, i.e., to reduce the motion error and internal force of the object. The required velocity and force at the EE of the two HMs, including the position and internal force errors of the object, are inputted into separate position controllers. In addition, the position controllers of the two individual HMs are designed to enable precise motion control by using the virtual decomposition control method. Finally, comparative experiments are carried out on a hydraulic dual-arm test bench. The proposed method is validated by the experimental results, which demonstrate improved object position accuracy and reduced internal force.

Key words： hydraulic dual-arm manipulator compliance motion control unknown object adaptive mass estimation nonlinear control

收稿日期: 2023-06-18 出版日期: 2024-01-10

Corresponding Author(s): Ruqi DING

引用本文:

. [J]. Frontiers of Mechanical Engineering, 2024, 19(1): 7.
Bolin SUN, Min CHENG, Ruqi DING, Bing XU. Compliance motion control of the hydraulic dual-arm manipulator with adaptive mass estimation of unknown object. Front. Mech. Eng., 2024, 19(1): 7.

链接本文:

https://academic.hep.com.cn/fme/CN/10.1007/s11465-023-0773-z
https://academic.hep.com.cn/fme/CN/Y2024/V19/I1/7

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Tab.3

Parameter	Symbol	Value	From Eq.
Position error gain	k_p	2	(7)
Orientation error gain	k_o	0	(7)
Velocity vector gain matrix	$K O$	diag(20,20,20,20,20,20)	(9)
Adaptive gain	$ρ O$	40 × [1 1 1 1 1 1 1 1 1 1 1 1 1]^T	(11)
Adaptive lower bound	$θ O ?$	[50 ?2 ?2 ?10 0 0 0 ?1 ?1 ?2 0 0 0]^T	(11)
Adaptive upper bound	$θ O +$	[100 2 2 10 1 1 2 1 1 2 10 10 10]^T	(11)
Adaptive initial value	$θ^i O$	[60 0 0 0 0 0 0 0 0 0 2.7 2.7 1.3]^T	(11)
Internal force error gain matrix	K_in	diag(60,60,60,60,60,60) × 10^?6	(38)
Internal force filtering matrix	C_in	diag(20,20,20,20,20,20)	(39) and (40)
Cylinder velocity error gain	k_v	12 × 10^?3	(42) and (44)
Cylinder force error gain	k_f	10 × 10^?8	(42) and (44)

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Abbreviations
AIFE	Average internal force error
APE	Average position error
CMC	Compliance motion control
DH	Denavit–Hartenberg
DOF	Degree-of-freedom
EDCM	Electrically driven cooperative manipulator
EE	End-effector
FK	Forward kinematics
HDM	Hydraulic dual-arm manipulator
HM	Hydraulic manipulator
IK	Inverse kinematics
LC	Linear cylinder
MIFE	Maximum internal force error
MPE	Maximum position error
PC	Position control
SC	Swing cylinder
VDC	Virtual decomposition controller
Variables
c_p1, c_p2, c_n1, c_n2	Flow coefficients of the valve
C_i	Coriolis and centrifugal matrix of the ith HM
C_in	Filter cut-off frequency matrix
$C O$	Coriolis and centrifugal matrix of the object
D	Displacement of the SC
$e O$	Position/orientation error feedback term of the object
$in e ave$ , $in e max$	Average and maximum internal force errors, respectively
$in e k$	Internal force error at the kth sampling point
$p e ave$ , $p e max$	Average and maximum position errors, respectively
$p e k$	Position error at the kth sampling point
f_cr	Required output force of the hydraulic cylinder
f_f	Friction force of the hydraulic cylinder obtained from the identification
f_pij	jth element of F_pi
f_pr	Required driven force
$f ˙ pr$	Derivative of the required driven force
$T 1 F$ , $T 2 F$	Force vectors in frames {T₁} and {T₂}, respectively
$O F ∗$	Net force vector of the object
F_ci	Estimated contact force vector of the ith HM
F_fi	Friction force vector of the hydraulic cylinder
F_i	External force vector applied to the ith EE
$T 1 F pc$ , $T 2 F pc$	Desired external force vectors in frames {T₁} and {T₂} of PC, respectively
$O F pc ∗$	Desired net force of the object in PC
F_pi	Output force vector calculated from the pressure of the cylinder
$T 1 F r$ , $T 2 F r$	Required force vectors in frames {T₁} and {T₂}, respectively
$O F r ∗$	Required net force vector of the object
G_i	Gravity vector of the ith HM
$G O$	Gravity vector of the object
i	Serial number of the HM
I₆	Sixth-order identity matrix
j	Serial number of the joint (or actuator)
J_hij	jth element of J_hi
J_hi	Mapping matrix that converts the output force vector of the cylinder into the joint torque vector
J_i	Jacobian matrix of the ith HM
k	Sampling moment
k_f	Force error gain of the cylinder
k_o	Orientation error gain of the object
k_p	Position error gain of the object
k_v	Velocity error gain of the cylinder
K_in	Internal force gain matrix
$K O$	Velocity error gain matrix
l₁, l₂	Lengths of two links for the closed chain
M_i	Inertial matrix of the ith HM
$M O$	Inertial matrix of the object
p_a, p_b	Pressure of the two chambers of the cylinder
p_r	Tank pressure
p_s	System pressure
q	Joint angle
$q ˙$	Actual joint velocity
q_i	Initial joint angle
q_p	Pendulum angle of the SC
$q ˙ r$	Required joint velocity or angular velocity of the SC
$q i$ , $q ˙ i$ , $q ¨ i$	Joint angle, velocity, and acceleration vectors of the ith HM, respectively
$O R W$	Rotation matrix from frame {O} to {W}
$s O γ$	γth element of $s O$
$s O$	Auxiliary vector for the object adaptive parameter update
S_a, S_b	Areas of the cap-side and rod-side of the LC, respectively
t	Time
t₀	Initialization time of the HDM system
T	Running period of the trajectory
u_fr	Relevant term of the valve control signal
u_v	Control signal of the valve,
$E i U O$	Velocity transformation matrix from frame {O} to {E_i}
$W U O i$	Velocity transformation matrix from frame {O_i} to {W}
$O U T 1$ , $O U T 2$	Velocity transformation matrix from frames {T₁} and {T₂} to {W}, respectively
$O U W$	Velocity transformation matrix from frame {W} to {O}
$O v$	Actual linear velocity vector of frame {O} expressed in frame {O}
$O V$	Actual velocity vector of the object
$T 1 V$ , $T 2 V$	Velocity vectors of frames {T₁} and {T₂}, respectively
$O V d$	Desired velocity vector of the object
$O i V E i$	Velocity vector from frame {E_i} to {O_i}
$O V pc$	Desired velocity of the object of PC
$W V O$	Velocity vector from frame {O} to {W}
$O V r$	Required velocity vector of the object
$T 1 V pc$ , $T 2 V pc$	Desired velocity vectors of frames {T₁} and {T₂} in PC, respectively
$T 1 V r$ , $T 2 V r$	Required velocity vectors of frames {T₁} and {T₂}, respectively
x_ip	Initial length of the cylinder
x_p	Displacement of the cylinder
$x ˙ p$	Actual cylinder velocity
$x pl$ , $x ˙ pl$	Actual displacement and velocity of the LC, respectively
$x ˙ plr$	Required velocity of the LC
$x ps$ , $x ˙ ps$	Actual displacement and velocity of the SC, respectively
$x ˙ psr$	Required velocity of the SC
x_s	Stroke of the LC
x	Actual position vector from frame {O} to {W}
$x ˙$	Actual linear velocity vector from frame {O} to {W}
x_d	Desired position vector from frame {O} to {W}
$x ˙ d$	Desired linear velocity vector from frame {O} to {W}
X	Coordinate value of the trajectory on the x-axis
$X O$	Initial x-axis coordinate value of the object
Y_i	Regression matrix of the ith HM
$Y O$	Regression matrix of the object
$Y O r$	Required regression matrix of the object
Z	Coordinate value of the trajectory on the z-axis
$Z O$	Initial z-axis coordinate value of the object
α₁, α₂	Two load distribution factors
$β$	Oil effective bulk modulus
$γ$	Sequence number of the element of the parameter vector
$η$ , $η d$	Actual and desired internal force vectors, respectively
$η ~$ , $η ~ d$	Filtered actual and desired internal force vectors, respectively
$η ~ ˙$ , $η ~ ˙ d$	Derivative of the filtered actual and desired internal force vectors, respectively
$θ O γ ?$ , $θ O γ +$	Adaptive lower bound and upper bounds of element $θ^O γ$ , respectively
$θ^O γ$	γth element of the parameter vector $θ^O$
$θ i$	Inertial parameter vector of the ith HM
$θ^i O$	Adaptive initial value parameter vector of the object
$θ O$	Inertial parameter vector of the object
$θ^O$	Adaptive estimate of $θ O$
$θ O ?$ , $θ O +$	Adaptive lower bound and upper bound vectors, respectively
$μ O$	Part of a quaternion representing the orientation error of the object
$ζ$	Adaptive function
$ρ O γ$	Adaptive gain
$ρ O$	Adaptive gain vector
$ω$	Actual angular velocity vector of the object from frame {O} to {W}
$O ω$	Actual angular velocity vector of the object
$ω d$	Desired angular velocity vector of the object from frame {O} to {W}
$Ω ld$	Load distribution matrix
$Ω m$	Internal force mapping matrix
κ	Adaptive switching function

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