US 11,772,264 B2 · Neural network adaptive tracking control method for joint robots

Abstract

The present disclosure discloses a neural network adaptive tracking control method for joint robots, which proposes two schemes: robust adaptive control and neural adaptive control, comprising the following steps: 1) establishing a joint robot system model; 2) establishing a state space expression and an error definition when taking into consideration both the drive failure and actuator saturation of the joint robot system; 3) designing a PID controller and updating algorithms of the joint robot system; and 4) using the designed PID controller and updating algorithms to realize the control of the trajectory motion of the joint robot. The present disclosure may solve the following technical problems at the same time: the drive saturation and coupling effect in the joint system, processing parameter uncertainty and non-parametric uncertainty, execution failure handling during the system operation, compensation for non-vanishing interference, and the like.

A neural network adaptive tracking control method for joint robots, comprising:

1) Establishing a joint robot system model:
Dq(q){umlaut over (q)}+Cq(q,{dot over (q)}){dot over (q)}+Gq(q)+τ({dot over (q)},t)=ua
in the model mentioned above, q represents a position vector of the joint robot, {dot over (q)} represents a velocity vector of the joint robot, {umlaut over (q)} represents an acceleration vector of a joint robot action, ua represents a control input of the joint robot system, the system parameter Dq(q) represents an inertia matrix of the joint robot system, the system parameter Cq(q, {dot over (q)}) represents a centrifugal matrix of the joint robot system, the system parameter Gq(q) represents a universal gravitation matrix of the joint robot system, and the system parameter τ({dot over (q)}, t) represents uncertainty and interference factors of the joint robot system;
2) establishing a state space expression and an error definition when taking into consideration both a drive failure and actuator saturation of the joint robot system:
ua(t)=ρ(t)[Γ(0)+L(ξ)ν+ε(ν)]+ε(t)=ρ(t)L(ξ)ν+[ρ(t)Γ(0)+ρ(t)ε(ν)+ε(t)]
e=x1−q*
ë={umlaut over (x)}1−{umlaut over (q)}*=Dq−1(q)ρ(t)L(ξ)ν+Dq−1(q)[ρ(t)Γ(0)+ρ(t)ε(ν)+ε(t)]+F(⋅)+Q(x1,t)−{umlaut over (q)}*
in the above formulas, ua(t) represents a system control input signal considering both drive failure and actuator saturation, Γ(0)+L(τ)ν+ε(ν) represents a control signal in a case of actuator saturation, wherein ν represents an actual controller design quantity of the system, Γ(0)+L(ξ)ν represents a smooth function proposed according to a mean value theorem of ν, Γ(0) is a bounded matrix, L(ξ) is a non-negative positive definite matrix, ε(ν) is a bounded approximate error and represents an uncertain factor of a controller;
ρ(t) represents a health coefficient of a driver, ε(t) represents an interference factor of the driver;
e(or e(⋅)) represents a dynamic error of the system (e(⋅) is written as e for simplification in subsequent derivation), ë represents the second derivative of the dynamic error, wherein x1=q represents a motion trajectory of the joint robot, {umlaut over (x)}1 represents an acceleration of the joint robot motion, q* represents a given joint tracking trajectory;
{umlaut over (q)}* represents an acceleration of the given joint tracking, F(⋅)=−Dq−1(q) (Cq(q){dot over (q)}+Gq(q), and Q(x1, t)=−Dq−1(q)τ({dot over (q)}, t);
3) designing a proportion integration differentiation (PID) controller and updating algorithms of the joint robot system:
the PID controller ν is expressed as
v
=
-
(
k
D
⁢
0
+
Δ
⁢
k
D
(
t
)
)
⁢
(
2
⁢
γ
⁢
e
(
·
)
+
γ
2
⁢
∫
0
t
e
⁡
(
·
)
⁢
d
⁢
τ
+
de
⁡
(
·
)
dt
)
wherein γ is a predetermined parameter, and kD0 is a constant;
wherein the updating algorithms consist of two algorithms as follows:
(1) algorithm based on a robust adaptive control:
the robust adaptive algorithm is designed for automatically updating the controller parameters at an updating rate of:
Δ
⁢
k
D
(
t
)
=
c
^
⁢
φ
0
2
(
·
)
⁢
{
c
^
.
=
-
σ
0
⁢
c
^
+
σ
1
⁢
φ
0
2
(
·
)
⁢

E

2
c
^
(
0
)
≥
0
wherein, σ0 and σ1 are positive constants;
{
c
-
max
⁢
{
a
1
,
1
2
⁢
γ
d
}
φ
0
(
·
)
=
φ
1
(
·
)
+

q
.

⁢

E

⁢

,
wherein ĉ is an estimated value of c;
a1=max {γdaf, γdγ2, 2γdγ,γdx2}, φ1(⋅)=φf(⋅)+∥e∥+∥ė∥+1, wherein afφf(⋅) is a product of a constant af and a scalar function φf (⋅), representing the upper bound of the system uncertainty factor Dq−1(q)[ρ(t)Γ(0)+ρ(t)ε(ν)+ε(t)]+F(⋅)+Q(x1, t)−{umlaut over (q)}*, x2 is the upper bound of an second derivative {umlaut over (q)}* of a given joint motion trajectory, γd is the upper bound of an system parameter Dq(q), and it is set that
E
=
2
⁢
γ
⁢
e
(
·
)
+
γ
2
⁢
∫
0
t
e
⁡
(
·
)
⁢
d
⁢
τ
+
de
⁡
(
·
)
dt
;
(2) algorithm based on a neural adaptive control:
the neural adaptive algorithm is designed for automatically updating the controller parameters at an updating rate of:
{
b
^
.
=
-
σ
0
⁢
b
^
+
σ
1
⁢
φ
2
(
·
)
⁢

E

2
b
^
(
0
)
≥
0
⁢
Δ
⁢
k
D
(
t
)
=
b
^
⁢
φ
2
(
·
)
wherein:
θ0 and θ1 are positive constants;
Ψ(⋅)=∥S(⋅)∥+1, wherein S(⋅) is a primary function of a neural network;
b=max{∥WT∥, m}, wherein {circumflex over (b)} is an estimated value of b, WT is an ideal unknown weight, and m is the upper limit of an reconstruction error ∥η(⋅)∥ of the model;
E
=
2
⁢
γ
⁢
e
(
·
)
+
γ
2
⁢
∫
0
t
e
⁡
(
·
)
⁢
d
⁢
τ
+
de
⁡
(
·
)
dt
;
4) controlling trajectory motion of the joint robot by using the PID controller and the updating algorithms designed in step 3) for the joint robot system.

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Neural network adaptive tracking control method for joint robots

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Neural network adaptive tracking control method for joint robots

Life of this patent

Abstract

Claims1