Data processing: generic control systems or specific application – Specific application – apparatus or process – Robot control
Reexamination Certificate
1998-04-27
2001-06-26
Beausoleil, Robert (Department: 2181)
Data processing: generic control systems or specific application
Specific application, apparatus or process
Robot control
C700S053000, C700S054000, C901S008000, C901S003000, C901S005000
Reexamination Certificate
active
06253120
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to a position and/or force controlling apparatus using a sliding mode decoupling control, and more particularly to position and/or force controlling apparatus using sliding mode decoupling control which enables robust control responsive to change and a high precision machining of a complicated curved surface and which may suppress the generation of chattering even if elasticity or frictional coefficient of a grind surface of a workpiece to be in contact with a machining device has uncertainty and changes in an unknown manner.
2. Description of the Related Art
Conventionally, a grinding robot as shown in
FIG. 8
is known. An object is pushed against a buff, a grinding stone and a polishing belt driven in the same direction so that grinding is performed by controlling the frictional force and position of the grinding surface. In
FIG. 8
, a grinding device
1
is a buff grinding device, a rotary type grinding device, or the like using a PVA (polyvinyl alcohol) grinding stone or the like. The buff
5
is driven by motors
3
a
and
3
b.
A workpiece or work
7
is gripped by a robot
9
and is pushed in a direction x against the buff
5
by a force f(t) to thereby grind a predetermined surface. The buff
5
is moved in a direction y at a velocity V(t) (which is defined as a tangential directional velocity of the buff
5
at a contact point). In this case, t is the grinding time when the work
7
is pushed against the buff
5
. In this case, control is performed by adjusting a force f
mx
(t) (not shown) in the direction x which force is given to the work
7
by the robot
9
so that the force f(t) has a predetermined level. The control during this period is kept constant even if the grinding device
1
is changed as shown in FIG.
9
.
However, since the conventional control is a simple control which applies the same force f(t) only during the grinding operation even if, for example, the buff
5
is clogged so that the frictional force F(t) (which is the tangential frictional force at a contact point of the outer circumference of the grinding device
1
) between the buff
5
and the work
7
. Thus, there is a concern that grinding may not sufficiently be performed. In the ideal control for this case, it is necessary to increase the force f(t) or to elongate the grinding time t corresponding to the decrement of the frictional force F(t). Namely, the frictional coefficient between the buff
5
and the work
7
is finely changed in accordance with various conditions. Accordingly, control of the force f
mx
(t) in the direction x while supervising the force f(t) in the direction x can not achieve stable grinding work. On the other hand, the essence of the grinding work is under the relation which is equal to the total amount of the energy given from the grinding device
1
(hereinafter referred to as a grinding energy). The reason why it is necessary to enlarge the force f(t) or elongate the grinding time t in the control when the above-described clogging occurs is that it is required to keep the grinding energy constant. Therefore, in order to obtain a stable high quality grinding surface without being influenced by a change in the frictional coefficient, it is ideal to control the grinding energy by the robot
9
.
Also, it is possible to perform the grinding energy control by using a sliding mode control. However, the sliding mode control which has been performed conventionally may be designed only in the case where det(CB)≠0 where the object to be controlled is expressed by formula 1.
{dot over (x)}
(
t
)=
Ax
(
t
)+
Bu
(
t
)+
Bd
(
x,t
),
y
(
t
)=
Cx
(
t
) [formula 1]
For this reason, there is a predetermined restriction for the arrangement of sensors or the like.
It is possible to consider that the elasticity or the frictional coefficient of the grinding surface of the work
7
to be brought into contact with the grinding device
1
has an uncertainty and would be changed in an unknown manner. In such a case, there is a concern that it would be difficult to converge the control quantity to always satisfy the Lyapunov stability condition.
Also, even if the above-described problem is solved, since a method for applying the grinding energy control method using the sliding mode control to a multi-articulated grinding robot is not clarified, it is impossible to grind a complicated curved surface due to the restriction of the degree of freedom for the robot. Furthermore, in the sliding mode control, since the non-linear term appearing in the notion equation is regarded as an extrinsic turbulence and the non-linear control input gain is increased to attain the robustness, there is a concern that the chattering intrinsic to the sliding mode control would be likely to occur.
SUMMARY OF THE INVENTION
In view of the foregoing defects inherent in the prior art, it is an object of the present invention to provide a position and/or force controlling apparatus which makes it possible to perform a robust control which may cope with a change even when an elasticity or a frictional coefficient of the machining surface in which a work is brought into contact with a machining device has uncertainty and changes in an unknown manner, and in which high precision machining of a complicated curved surface is possible and which may suppress generation of chattering.
In order to attain these objects, according to the present invention, a position and/or force controlling apparatus using a sliding mode decoupling control system having decoupling means for decoupling an interacting term existing in the control system on the basis of a regular condition of a decoupling matrix and a sliding mode controlling means for converging a control quantity along a hyperplane which is sought to satisfy the Lyapunov stability condition for the control system decoupled by the decoupling means is characterized in that gain for a non-linear input existing in the control system is set at a value to satisfy the Lyapunov stability condition so that the control quantity converges on the hyperplane in a stable manner even when there is an uncertainty in the C matrix. The C matrix connects state variables with an output of the object to be controlled. It is preferable to set the gain to be greater than a gain when there is no uncertainty in the C matrix.
The interactive term existing in the control system is decoupled on the basis of the regular condition of the decoupling matrix. As a result, the x-direction control and the y-direction control or the position control and the force control or the like may be performed in a separate manner from each other without any interference. Then, a hyperplane obtained to satisfy the Lyapunov stability condition is designed, and the control quantity is converged along the hyperplane. In this case, gain for nonlinear input factor existing in the control system is designed to be greater than a predetermined value for the C matrix without uncertainty, where the magnitude of said gain is large enough to satisfy the Lyapunov stability condition so that the control quantity converges on the hyperplane in a stable manner with satisfaction of the Lyapunov stability condition even when there is uncertainty in the C matrix.
The position and/or force controlling apparatus using the sliding mode decoupling control system according to the present invention is further characterized by comprising a machining device for machining a predetermined surface of a work, and a robot for pressing the work against the machining device or a robot for pressing the machining device against the work fixed at a predetermined position in a space, the control quantity including at least one of a frictional force, in a tangential direction, generated in the machining surface in which the work is in contact with the machining device, and a position in the tangential direction, and the uncertainty of the C matrix depending upon at least one of changes of an elasticity coefficient and a frictional c
Mita Tsutomu
Ohtachi Yoshinobu
Shimada Akira
Adams & Wilks
Beausoleil Robert
Seiko Seiki Kabushiki Kaisha
Vo Tim
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