COMPUTED-TORQUE BASED CONTROLLER, PARAMETER DETERMINATION METHOD THEREOF AND PERFORMANCE ANALYSIS METHOD THEREOF

• US 20190321972A1
• Filed: 10/23/2018
• Published: 10/24/2019
• Est. Priority Date: 04/19/2018
• Status: Active Grant

• Current Assignee: Korea Advanced Institute of Science and Technology
• Original Assignee: Korea Advanced Institute of Science and Technology
• Inventors: KIM, Jung Hoon, PARK, Jaeyoung
• Granted Patent: US 10,946,516 B2
• Time in Patent Office: Days
• CPC Class Codes: B25J 9/1605 Simulation of manipulator lay-out, design, modelling of manipulator
• CPC Class Codes: B25J 9/163 learning, adaptive, model based, rule based expert control
• CPC Class Codes: B25J 9/1638 compensation for arm bending/inertia, pay load weight/inertia
• CPC Class Codes: G05B 2219/39001 Robot, manipulator control
• CPC Class Codes: G05B 2219/42004 PD proportional derivative
• CPC Class Codes: G05B 2219/42153 Inverse dynamics model idm, computed torque method

Abstract

Provided is a controller of a robot manipulator, a performance analysis method thereof and a parameter determination method thereof. The controller computes an error value of an output value of a control target for a target value through a computational equation and provides a control input value of the control target, and includes an outer loop controller which constitutes closed loop control of the control target, and an inner loop controller which performs feedback linearization to remove nonlinearity of the control target, wherein the computational equation is a linear differential equation designed considering exogenous disturbance acting in the controller and a computational error.

Claims

1. A controller that computes an error value of an output value of a control target for a target value through a computational equation and provides a control input value of the control target, the controller comprising:

an outer loop controller which constitutes closed loop control of the control target, and an inner loop controller which performs feedback linearization to remove nonlinearity of the control target,

wherein a dynamics equation of the control target is represented by the following Equation 1 including an exogenous disturbance torque vector, and

the inner loop controller and the control target form an inner loop system, and a dynamics equation for an trajectory tracking error of the inner loop system is represented by the following Equation 4;

M(q){umlaut over (q)}+C(q,{dot over (q)}){dot over (q)}+G(q)+τ

d=τ

[Equation 1]

where q(t)∈

ⁿ is the output value and corresponds to the joint angle vector, M(q)∈

<sup>n×

n</sup> corresponds to the positive definite matrix corresponding to Inertia, C(q,{dot over (q)}){dot over (q)}∈

ⁿ corresponds to the Coriolis and centrifugal torque vector, G(q)∈

ⁿ corresponds to the gravitational torque vector, τ

_d(t)∈

ⁿ corresponds to the exogenous disturbance torque vector, τ

(t)∈

ⁿ in corresponds to the control input torque vector,

ë

=w+u 

 

[Equation 4]

where w;

=−

M<sup>−

1</sup>(q){tilde over (M)}(q)({umlaut over (q)}_d−

u)−

M<sup>−

1</sup>(q)*{tilde over (C)}(q,{dot over (q)}){dot over (q)}+{tilde over (G)}(q)−

τ

d) is the total exogenous disturbance acting in the inner loop system, and is defined as including both the exogenous disturbance torque vector and the computational error, u is the control output value that is provided to the inner loop system by the outer loop controller.

2. The controller according to claim 1, wherein the inner loop system is represented by a generalized linear model of a continuous-time linear time-invariant system as shown in the following Equation 7,

the outer loop controller performs PD control as shown in the following Equation 8, and

the closed loop system implemented by the controller is represented by the following Equation 9:

3. The controller according to claim 2, wherein when the total exogenous disturbance w has finite energy,

the L_∞

/L₂ induced norm of the closed loop system and the L_∞

norm ∥

x∥

_∞

of the regulated output z have a positive correlation.

4. The controller according to claim 3, wherein the L_∞

/L₂ induced norm of the closed loop system is computed by the following Equation 16;

5. A parameter determination method of a controller that computes an error value of an output value of a control target for a target value through a computational equation and provides a control input value of the control target, the parameter determination method comprising:

computing L_∞

/L₂ induced norm of a control system formed by the controller and the control target through initially set control parameter;

comparing the computed L_∞

/L₂ induced norm with a reference value; and

when the computed L_∞

/L₂ induced norm is larger than the reference value, adjusting the control parameter to reduce the computed L_∞

/L₂ induced norm.

6. The parameter determination method of a controller according to claim 5, wherein the controller forms a closed loop system P_K as shown in the following Equation 9:

7. The parameter determination method of a controller according to claim 6, wherein when the total exogenous disturbance w has finite energy,

the L_∞

/L₂ induced norm of the closed loop system is computed through a performance analysis mathematical expression d_max^1/2(CPC^T) where P is a solution of A_KP+PA_K^T+BB^T=0.

8. The parameter determination method of a controller according to claim 7, wherein the L_∞

/L₂ induced norm of the closed loop system and the L_∞

norm ∥

z∥

_∞

of the regulated output z have a positive correlation.

9. A performance analysis method of a controller that computes an error value of an output value of a control target for a target value through a computational equation and provides a control input value of the control target, the performance analysis method comprising:

the controller forming a closed loop system P_K as shown in the following Equation 9; and

computing L_∞

/L₂ induced norm of the closed loop system through a performance analysis mathematical expression d_max^1/2(CPC^T);