JP3215841B2 - Articulated polishing robot using sliding mode decoupling control - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a multi-joint polishing robot using sliding mode non-interference control, and more particularly to a multi-joint polishing robot capable of applying sliding mode non-interference control to achieve high-precision polishing of complicated curved surfaces. The present invention relates to a multi-joint polishing robot using sliding mode non-interference control, which makes possible and reduces chattering.

[0002]

2. Description of the Related Art Conventionally, there is known a polishing system in which a work 1 to be processed is gripped by a robot 1 and pressed against a rotary polishing apparatus 5 (not shown). With respect to such a polishing system, it is possible to control the position of the work 3 and the tangential force, that is, the frictional force acting on the polishing surface, by using sliding mode non-interference control (1997 Patent Application No. 124933). . Here, the sliding mode non-interference control will be described. First, the control target is
Describe as follows.

[0003]

(Equation 1) Where A (n × n), B (n × m), C (m × n), d
(X, t) is a nonlinear disturbance with a known magnitude, and Equation 2 holds, and Equation 3 holds without det (CB) ≠ 0.

[0004]

(Equation 2)

(Equation 3) Here, c _i means the i-th row of the C matrix. As is well known, if Equation 4 is regular, it is possible to make the control system non-interfering.

[0005]

(Equation 4) Next, the coefficient matrix number 5 is defined using the C matrix and the differentiable target value r (t), and a hyperplane σ (t) is designed.

[0006]

(Equation 5) At this time, Equation 6 holds.

[0007]

(Equation 6)

(Equation 7)

(Equation 8)

(Equation 9) At this time, the following equations 10 and 11 are used as control inputs,
The candidate of the Lyapunov function for each row is V _i (t) = σ _i
Equation (12) is obtained assuming that ² (t) / 2 ≧ 0. _Ki (x,
If t) is selected as in Equation 14, V _i (t) becomes a Lyapunov function, and σ _i ^(k) → 0, k ≧ 0 is obtained.

[0008]

(Equation 10)

[Equation 11]

(Equation 12)

(Equation 13)

[Equation 14] Further, a necessary and sufficient condition for stabilizing the equivalent linear system when V _i (t) = σ _i ² (t) / 2 ≧ 0 is that the invariant zero of Equation 15 is stable. h _i (s)
= 0 (i = 1,..., M) are all stable polynomials,
This is equivalent to the fact that the invariant zero of (C, A, B) is stable.

[0009]

(Equation 15)

(Equation 16)

[Equation 17]

(Equation 18) However, in the case of Equation 19, since there is no zero, h _i (s) = 0
(I = 1,..., M) may be selected as a stable polynomial.

[0010]

[Equation 19] Next, the correspondence to the uncertainty of the C matrix will be described. It is assumed that the C matrix has the uncertainty represented by Expression 20, but the output y can be directly observed.

[0011]

(Equation 20) Although the σ value of the number 9 of hyperplanes is accurately obtained, the _expression 21 of the control input number 10 must use the _expression 22 or 23 corresponding to C _0i . Then, since V becomes a Lyapunov function,
The K _i (x, t) of 4 needs to be modified to Equation 24.

[0012]

(Equation 21)

(Equation 22)

(Equation 23)

(Equation 24) As described above, the uncertainty of the elastic coefficient and the friction coefficient of the polished surface, which are elements of the C matrix, is set to be larger than the predetermined value when there is no uncertainty, so that the control amount can be stably superimposed. It is possible to converge on a plane.

[0013]

However, in the conventional control system, the work 3 in the work coordinate system of the robot 1 is not used.
The invention is not limited to the invention of the control method of the position and the frictional force, and the control method for realizing using the multi-joint polishing robot, that is, the control method when the control input is the joint torque in the joint coordinate system has not been invented. However, practical applications have been naturally limited to some manipulators such as orthogonal robots.
The orthogonal type manipulator has a disadvantage that complicated curved surfaces cannot be polished due to restrictions on the number of degrees of freedom. In addition, in the conventional control system, the term that is a function of the joint angle is regarded as a disturbance using the sliding mode non-interference control, and robustness is achieved by increasing the nonlinear input gain. Had the drawback of easily occurring.

SUMMARY OF THE INVENTION The present invention has been made in view of the above-mentioned conventional problems. By applying sliding mode non-interference control to an articulated polishing robot, highly accurate polishing of a complicated curved surface is enabled, and chattering is prevented. An object of the present invention is to provide an articulated polishing robot using sliding mode non-interference control with reduced occurrence.

[0015]

SUMMARY OF THE INVENTION Accordingly, the present invention provides a multi-joint polishing robot for controlling a position and a frictional force, wherein a motion equation in a joint coordinate system of the multi-joint polishing robot is converted from a joint coordinate system using a Jacobian. The error between the control target, which is previously controlled and designed based on the equation of motion in the working coordinate system of the multi-joint polishing robot converted to the working coordinate system, the target value of the force on the working coordinate system, and the detected value of the force on the working coordinate system. Sliding mode non-interference control means for compensating for non-linearity peculiar to an articulated polishing robot based on an error between a target value of a position and a detected value of a position ; Parameter variation
A joint torque calculating means for calculating each joint torque of the multi-joint polishing robot based on an addition signal to which inverse dynamics is added; and a joint driving means for driving each joint based on each joint torque calculated by the joint torque calculating means. Configured.
The present invention is applied to an articulated polishing robot that controls the position and frictional force of a control target. The equation of motion in the joint coordinate system of the multi-joint polishing robot is converted from the joint coordinate system to the work coordinate system using Jacobian. That is, a motion equation in the work coordinate system of the multi-joint polishing robot is obtained. Then, the control target is controlled and designed in advance based on the equation of motion. In the sliding mode non-interference control means, based on the error between the target value of the force on the work coordinate system and the detected value of the force and the error between the target value of the position on the work coordinate system and the detected value of the position, the articulated polishing robot Compensate for inherent nonlinearities. The joint torque calculation means calculates each joint torque of the multi-joint polishing robot based on the control input signal obtained by the sliding mode non-interference control means. The joint driving means drives each joint based on the calculated joint torque. As a result, multi-joints polishing robot it is possible to apply the sliding mode decoupling control means, high precision polishing of a complex curved surface which could not have none for the number of degrees of freedom constraint is orthogonal manipulator capable ing. Articulated polishing
In the equation of motion specific to the robot, the function term of the joint angle
For known parameter variations such as
Consider the mix. Where the known parameter variation is
More specifically, for example, viscous friction, centrifugal force, Coriolis force
And the torque generated by at least one of gravity
It is. Then, Suraidi ring mode decoupling control non
Linear inputs, for example, have as much error as these unknown variations.
I just compensated. This allows for sliding
Chatter of an articulated polishing robot using mode non-interference control
The occurrence of rings can be reduced.

[0016]

[0017]

Embodiments of the present invention will be described below with reference to the drawings. FIG. 1 shows an embodiment of the present invention. In FIG. 1, a multi-joint polishing robot 10 presses a work 3 against a grindstone 9 (a polishing belt or a buff may be used in place of the grindstone 9) in which a vertical two-joint manipulator 7 operates in the same direction, and provides the work on a polishing surface. The polishing operation is performed by controlling the position and the frictional force of the work 3 in the working coordinate system.

Next, the operation will be described with reference to FIG. The vertical two-joint manipulator 7 presses the workpiece 3 against a grindstone 9 (hatched portion) operating in the _Yop direction to polish. Articulated polishing robot 10, the position P and the frictional force F _y of the work 3 is controlled so as to match the target value in the working coordinate system sigma _op.
The friction force F _y is the first axis 11 of the vertical two-joint manipulator 7.
And by controlling the torque of the second shaft 13 and adjusting the pressing force. Although the multi-joint polishing robot 10 has been described with two joints, the application of the present invention is not limited to two joints.

Next, a method of converting the equation of motion from the joint coordinate system to the working coordinate system using the Jacobian will be described. Mass m of first link 15 of articulated polishing robot 10
_1, the mass m ₂ of the second link 17, the length l ₁ from the first axis 11 to the second shaft 13, the length l ₂ of the second shaft 13 to the polishing surface, the first link 15 from the first shaft 11 the length r ₁ to the center of gravity, to the second shaft 13 and the length r ₂ up to the center of gravity of the second link 17. Also, multi-articular polishing robot 10 the base coordinate system sigma _B, a task coordinate system and sigma _OP, sigma in sigma _{OP B}
The origin coordinate values of _{(X A, Y A),} Σ OP about the Z axis of the sigma
The rotation angle of the _B and theta _A. Also, the friction force of the work 3 is represented by F _y
And The equation of motion in the joint coordinate system of the n-axis manipulator is given by Equation 25.

[0020]

(Equation 25) Here, M (q) (n × n) is an inertia matrix, q (n × 1) is a joint angle, Equation 26 is viscous friction, centrifugal force, Coriolis force, torque generated by gravity, J _r (q) (nx n) is a Jacobian linking the working coordinate system and the joint coordinate system, and F (n ×
1) represents the force received from the polished surface, and τ (n × 1) represents the input torque of the joint.

[0021]

(Equation 26) On the other hand, the position of the work 3 in the work coordinate system is defined as p (n ×
Assuming that 1), p is a function of the joint angle q and is expressed by Expression 27.

[0022]

[Equation 27] By differentiating both sides of Expression 27, Expression 29 is established in Expression 28.

[0023]

[Equation 28]

(Equation 29) However, the number is set to 30.

[0024]

[Equation 30] By differentiating both sides of Equation 29, Equation 31 is obtained.

[0025]

(Equation 31) Obtaining a motion equation number 32 in the working coordinate system by multiplying from the left by substituting the number 31 to number 25 ^{_{(J r (q) T)}} -1.

[0026]

(Equation 32) However, Equations 33 and 34 are provided.

[0027]

[Equation 33]

(Equation 34) Next, an external force is defined as follows, and a control system is designed. First, the following assumptions are made. Of the force F (n × 1), the normal force on the polished surface is generated by elasticity, and the tangential friction force is obtained by multiplying the normal force by the friction coefficient. When the coefficient matrix K (n × n) is defined, the force F (n × 1) is expressed as shown in Expression 35 in consideration of the nominal value and the fluctuation.

[0028]

(Equation 35) At this time, the element of K (n × n) is not arbitrary, has a structure corresponding to the physical property, and relates to the controllability as described later. In addition, the moment of inertia M _x , the nonlinear force h
_{x is} also given by Equations 36 and 3 in consideration of the nominal value and fluctuation.
7 can be defined.

[0029]

[Equation 36]

(37) Then, the equation of motion can be expressed as shown in Equation 38.

[0030]

(38) However, it is Equation 39.

[0031]

[Equation 39] Here, the state quantity is defined as shown in Expression 40.

[0032]

(Equation 40) Equation 41 is defined as a linearization input.

[0033]

[Equation 41] Then, the state equation of Formula 42 is obtained.

[0034]

(Equation 42) Next, the observation y (l × n) consists of the tangential position and the tangential frictional force, but it is assumed that the components of the output are not dependent on each other. This assumption is derived from the above-mentioned assumption.

[0035]

[Equation 43] Here, y ₁ is a force observation component vector, y ₂ is a position observation component vector, and S ₁ and S ₂ are selection matrices that are selected according to the application so that the elements of y have a non-dependent relationship with each other. Note that the switching gain is expressed as in Equation 44.

[0036]

[Equation 44] However, it is Equation 45.

[0037]

[Equation 45] Here, ΔM, Δh, and ΔK are unknown variations of M, h, and K. The joint input torque τ (t) of the manipulator 7 is expressed by the following equation (46).

[0038]

[Equation 46] However, it is Equation 47.

[0039]

[Equation 47] FIG. 2 shows a control system block diagram. In the sliding mode decoupling control unit 21, inputs the target value F _r of the target value P _r and the frictional force of tangential positions. Then, these target values are compared with the detected tangential position P and the detected frictional force F, and the error is obtained. Then, a calculation based on the sliding mode non-interference control is performed, and a control input signal u is output. The inverse dynamics of the nonlinear force h _x0 is added to the control input signal u. This addition signal is converted into a joint torque by the Jacobian and input to the vertical two-joint manipulator 7.

FIG. 3 shows the friction coefficient α. = 0.5, elastic modulus k. = 1000 (N / m), α. , K. , M _X0 show a simulation result when the variation is 10%.
Solid line is friction force F _y , dotted line is target value F _ry , broken line is work 3
_Is the position P _{y in} the Y direction and the target value P _ry = 0. From this example, it can be seen that F _y and P _y follow the target values, and a hybrid control system that is robust against parameter variations is realized.

As described above, by converting the equation of motion of the manipulator 7 from the joint coordinate system to the working coordinate system using the Jacobian, the sliding mode non-interference control is applied to the position / friction force control of the multi-joint polishing robot. This enables highly accurate position / friction force control of the multi-degree-of-freedom polishing robot. In addition, for a known parameter fluctuation such as a function term of a joint angle in the equation of motion peculiar to the manipulator 7, the inverse dynamics is considered, and the nonlinear input of the sliding mode non-interference control only compensates for the unknown parameter fluctuation. did. Therefore, occurrence of chattering peculiar to the sliding mode control can be reduced.

[0042]

As described above, according to the present invention, the sliding mode non-interference control means is applied to the articulated polishing robot by converting the motion equation of the manipulator from the joint coordinate system to the work coordinate system. This has enabled high-precision polishing of complicated curved surfaces that could not be achieved with the orthogonal manipulator due to the restriction of the number of degrees of freedom.
Then, the nonlinear input to the sliding mode non-interference control
The force is controlled by using only unknown parameter variations.
Articulated polishing robot using riding mode decoupling control
It is possible to reduce the occurrence of chattering
Was.

[0043]

[0044]

[Brief description of the drawings]

FIG. 1 is a configuration diagram of an embodiment of the present invention.

FIG. 2 is a control system block diagram.

FIG. 3 Simulation results

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Robot 3 Work 7 Vertical two-joint manipulator 9 Grinding stone 10 Multi-joint polishing robot 11 First axis 13 Second axis 15 First link 17 Second link 21 Sliding mode non-interference control unit

──────────────────────────────────────────────────続 き Continuation of the front page (56) References JP-A-9-103945 (JP, A) JP-A-7-121209 (JP, A) JP-A-63-47058 (JP, A) JP-A-5-105 88749 (JP, A) JP-A-2-297612 (JP, A) (58) Fields investigated (Int. Cl. ⁷ , DB name) B25J 13/00 B25J 9/16 B24B 27/00 G05B 13/00 G05D 3/12 305

Claims (1)

(57) [Claims] An articulated polishing robot for controlling a position and a frictional force, wherein a motion equation in an articulated coordinate system of the articulated polishing robot is converted from an articulated coordinate system to a working coordinate system using a Jacobian. The error between the control target pre-designed based on the equation of motion in the work coordinate system, the target value of the force on the work coordinate system and the detected value of the force, and the difference between the target value of the position on the work coordinate system and the detected value of the position a sliding mode decoupling control means for compensating articulated polishing robot inherent nonlinearity based on an error, already to the control input signal obtained by said sliding mode decoupling control means
Joint torque calculating means for calculating each joint torque of the multi-joint polishing robot based on an addition signal obtained by adding the inverse dynamics of the known parameter fluctuation, and each joint based on each joint torque calculated by the joint torque calculating means. A multi-joint polishing robot using sliding mode decoupling control, characterized by comprising a joint driving means for driving the robot.