JP2012196715A - Method and device of controlling robot - Google Patents

Abstract

PROBLEM TO BE SOLVED: To reduce the workload of a user for setting a value of a variable for determining the direction of a tool at a target position and furthermore to reduce the movement time of a robot.SOLUTION: When a user sets a rotational angle of the tool around a predetermined axis as an optional variable, a controller sets the rotational angle around the predetermined axis as the optional variable settable to an optional value by the controller side. The controller sets an evaluation index which is based on the movement time required when a leading end of the tool moves from the present position to the target position and a positional error of the leading end of the tool after movement in relation to the target position, and determines the value of the optional variable by optimizing the evaluation index. Since each of the above processing is executed by the controller, the direction of the tool at the target position is automatically determined to a direction for minimizing the movement time of the robot.

Description

  The present invention relates to a robot control method and a robot control device for moving a tip of a tool attached to a hand of a robot having a plurality of axes from a current position toward a target position.

  The purpose of introducing robots in factories and the like is to improve production efficiency, that is, to shorten production tact time. In order to shorten the production tact time, it is necessary to shorten the operation time in each work performed by the robot. Therefore, teaching (teaching) is performed by an operator so that the operation time of the robot is as short as possible. That is, in the present situation, the work for shortening the operation time of the robot greatly depends on the individual ability of the worker in charge of teaching.

  In teaching performed to move the tip of the tool attached to the hand of the robot from the current position toward the target position, the value of each variable for determining the tip position and orientation of the tool at the target position is determined by the operator. All are specified. Each of the above variables is a rotation angle around a predetermined axis of the tool (hand) in addition to each coordinate value of the tool tip (for example, a rotation angle around the fourth axis in the case of a 4-axis horizontal articulated robot) That's it.

  Now, depending on the type of tool attached to the hand of the robot and the work content, there are cases where the work can be achieved regardless of the direction of the tool (= the direction of the hand). For example, when an air chuck is used as a tool in a 4-axis horizontal articulated robot, the workpiece can be gripped regardless of the direction of the tool (the direction around the fourth axis). As described above, the specific direction of the tool at the position where the workpiece can be gripped (target position) may be any direction.

  FIG. 7 schematically shows an aspect of the robot when the tool tip is moved from the current position toward the target position. The robot shown in FIG. 7 is a 4-axis horizontal articulated robot, and an air chuck is attached as a tool to the hand. In FIG. 7, each axis (each joint) and each link are indicated by a circle and a straight line, respectively, and the tip of the tool is indicated by an arrow. In FIG. 7, the tool tip is moved from the current position indicated by the solid line to the target position indicated by the dotted line or the broken line, and the work is gripped by the air chuck that is a tool.

  When the robot is in a state indicated by a broken line, the tip of the tool is oriented to face the front of the workpiece (the lower surface in FIG. 7). On the other hand, when the robot is in a state indicated by a dotted line, the tool tip is inclined with respect to the front surface of the workpiece. In each of these states, the rotation angles of the respective axes (joints) are different from each other. That is, the posture of the robot changes according to the direction of the tool. Therefore, in each of the above states, the movement times from the current position are different from each other. Specifically, the movement time from the current position to the target position is shorter when the posture of the robot at the target position is the state indicated by the broken line than when the posture is indicated by the dotted line. The reason is that the amount of movement (rotation amount) of the first axis that takes the longest movement time is smaller in the dotted line state than in the broken line state.

  Even in the teaching in the case where the orientation of the tool (hand) at the target position is not questioned, the values of variables for determining the tip position and orientation of the tool at the target position are all designated by the operator. In other words, the posture of the robot at the target position (the rotation angle of each axis) is determined by the operator. However, as described above, in the case where the direction of the tool at the target position is unquestioned, there are many postures of the robot where the tip position of the tool is the same target position. The worker needs to select and determine the optimum posture from the many postures. That is, the operator needs to set the value of a variable for determining the direction of the tool at the target position so that the operation time of the robot is as short as possible. In the case of FIG. 7, teaching work is required so that the posture of the robot (the direction of the tool) at the target position is not the state indicated by the broken line but the state indicated by the dotted line.

  In this way, in cases where the orientation of the tool at the target position is unquestioned, the task of finding the robot posture (rotation angle of each axis) at the target position where the operation time is the shortest from among the many robot postures that exist It is very difficult, and even a skilled worker often requires a lot of time for the work, and the work load is very large.

  By the way, as a prior art for shortening the cycle time of the operation | work using a robot, the technique described in patent document 1 is mentioned, for example. The technique described in Patent Document 1 does not perform position control for a predetermined direction or rotation direction, but instead performs control based on force or torque value.

JP-A-5-23982

  However, the technique described in Patent Document 1 is based on the premise that position information, force, and torque value information are given by the user so that the target position can be calculated correctly. For this reason, it is considered necessary to obtain the posture of the robot at the target position. That is, the technique described in Patent Document 1 requires the same work load only by using a different method from the conventional technique, and it is considered that the work load on the user is unlikely to be reduced. It cannot be said that it is a means.

  The present invention has been made in view of the above circumstances, and its object is to reduce the work load on the user when setting the value of a variable for determining the direction of the tool at the target position, while moving the robot. It is an object of the present invention to provide a robot control method and a robot control apparatus capable of shortening the length of the robot.

  According to the means of claim 1 or 3, in the control for moving the tip of the tool attached to the hand of the robot having a plurality of axes from the current position toward the target position, an arbitrary variable setting process, a variable A value determination process is executed. In general teaching work, the values of the variables for determining the tip position and orientation of the tool are all specified by the user. Note that the values of each variable are the coordinate values (X-axis coordinates, Y-axis coordinates, and Z-axis coordinates) of the tool tip and the rotation angle (for example, four-axis horizontal multiples) around a predetermined axis of the tool (hand). In the case of an articulated robot, this is the value of the rotation angle around the fourth axis (Z axis). However, depending on the type of tool attached to the hand and the work content, the work may be able to be achieved regardless of the orientation of the tool (= the orientation of the hand). For example, when an air chuck is used as a tool in a 4-axis horizontal articulated robot, the workpiece can be gripped regardless of the direction of the tool (the direction around the fourth axis). In this case, it can be said that the orientation of the tool at the target position may be any orientation. Conventionally, even in such a case, the user has specified a variable (for example, a rotation angle around the Z axis) for determining the direction of the tool.

  On the other hand, according to the present means, one or two variables designated by the user among variables for determining the direction of the tool are set as arbitrary variables that can be set to arbitrary values (arbitrary variables Setting process). Then, an evaluation index is set based on the movement time required for the tool tip to move from the current position to the target position and the position error of the tool tip position after movement relative to the target position, and the evaluation index is optimized. Thus, the value of the arbitrary variable is determined (variable value determination processing). For example, when an air chuck is attached to the tip of a 4-axis horizontal articulated robot, if the rotation angle around the Z axis of the tool (hand) is specified as an arbitrary variable, the tool around the Z axis of the tool at the target position The rotation angle is automatically determined to a value that minimizes the movement time of the tool.

That is, in the variable value determination process, the current position is set as a calculation target position, and variables for determining the tip position and orientation of the tool at the calculation target position (X, Y, Z axis coordinate values and rotation around the Z axis) The Jacobian matrix J _k relating to the variable excluding the rotation angle around the Z axis designated as an arbitrary variable and the rotation angle of each axis (joint) at the calculation target position is obtained. In addition, an evaluation index Q _k shown in the following formula (1) is set. However, ε _k is a matrix whose element is the coordinate value of the position error, Δ _k is a matrix whose element is the amount of change in the rotation angle of each axis, and the diagonal component is the square of the reciprocal of the maximum rotation speed of each axis. A diagonal matrix is λ. Note that ε _k ^T is a transposed matrix of ε _k , and Δ _k ^T is a transposed matrix of Δ _k .
^{_{Q k = ε k T · ε}} k + Δ k T · λ · Δ k ... (1)

In the above equation (1), the first term on the right side is the sum of squares of the position error. The second term on the right-hand side is the sum of squares of the change amount (movement amount) of the rotation angle of each axis multiplied by the diagonal matrix λ, and corresponds to the maximum rotation speed of each axis with respect to the square sum of movement time. Given weights. That is, it corresponds to an approximate value of travel time. By minimizing the evaluation index Q _k set in this way, a change amount Δ _k shown in the following equation (2) is calculated. However, the matrix that the coordinate values of the target position and element and P _d, the matrix of the coordinate values of the calculation target position and element is set to P _k. J _k ^T is a transposed matrix of J _k .
^{_{Δ k = (λ + J k}} T · J k) -1 · J k T (P d -P k) ... (2)

By performing forward conversion on the rotation angle of each axis _obtained by adding the calculated change amount Δk to the rotation angle of each axis at the calculation target position, that is, the rotation angle of each axis after movement, a tool after movement is obtained. The tip position of is calculated. Then, a position error with respect to the target position of the calculated tool tip position is obtained, and it is determined whether or not the position error is equal to or less than a predetermined allowable error. That is, it is determined whether or not the tip position of the moved tool obtained by the calculation is sufficiently close to the target position. As a result, if the position error exceeds the allowable error, the above calculation for obtaining the tool tip position after the next movement is performed again after setting the calculated tool tip position as the next calculation target position. Executed.

On the other hand, if the position error is equal to or less than the allowable error as a result of the above determination, the rotation angle of each axis (each moved position) _obtained by adding the calculated change Δk to the rotation angle of each axis at the calculation target position. The value of the rotation angle around the Z axis at the target position is determined based on the rotation angle of the shaft. That is, when it is determined that the tip position of the tool after movement obtained by the above calculation is sufficiently close to the target position, the value of the rotation angle (arbitrary variable) around the Z axis at that time is the value at the target position. It is set as the value of the rotation angle (arbitrary variable) around the Z axis. Since the set value of the rotation angle around the Z axis is set by minimizing the evaluation index Q _k including the approximate value of the moving time, the moving time of the tool (robot) is as much as possible. The value becomes shorter.

  Since the above-mentioned control is automatically executed on the robot side, the user performs the teaching operation by specifying each coordinate value of the tool tip at the target position and setting the rotation angle of the tool (hand) around the Z axis. Just specify it as an arbitrary variable. Then, in addition to the X, Y and Z axis coordinate values of the tool tip at the specified target position, the rotation angle of the tool around the Z axis at the target position automatically determined as described above (arbitrary variable) By moving the tip of the tool from the current position toward the target position based on the value of the robot, it is possible to reduce the work load on the user (operator) during teaching and shorten the movement time of the robot. .

  Here, the case of a 4-axis horizontal articulated robot has been described as an example. However, for example, the case of a 6-axis vertical articulated robot is as follows. That is, if any one or two of variables for determining the direction of the tool (respective rotation angles around the X, Y, and Z axes) are designated as arbitrary variables, the tool at the target position The rotation angle of the (hand) around a specific axis is automatically determined to a value that minimizes the movement time of the robot. As a result, the same effects as those of the above-described 4-axis horizontal articulated robot can be obtained. That is, according to this means, the above-mentioned operation and effects can be obtained for all robots having a plurality of axes.

In this means, an optimization calculation using a Jacobian matrix is performed using a quadratic evaluation index Q _k including an approximate value of travel time. Therefore, it is possible to perform an arithmetic process for determining the value of an arbitrary variable at a relatively high speed. By the way, the Jacobian matrix represents a ratio between a minute displacement in each axis (each joint) and a minute displacement of the hand position and orientation (posture) associated therewith. In this means, as a result of repeating the calculation using such a Jacobian matrix, the tip position of the moved tool obtained by the calculation gradually approaches the target position. Therefore, the posture (form) of the target position of the robot based on the value of the arbitrary variable determined by the variable value determination process does not change significantly with respect to the posture at the current position. A small change in posture means that the amount of movement of each axis (joint) is small. From this, it is clear that the effect of shortening the movement time of the robot can be obtained.

  In the means according to claim 1 or 3, when it is determined that the tip position of the moved tool obtained by the calculation using the Jacobian matrix is sufficiently close to the target position, the value of the arbitrary variable at that time is set. This was set as an arbitrary variable at the target position. However, since the Jacobian matrix has the above-described characteristics, even the tip position of the tool after the final movement by the above calculation slightly deviates from the target position. Therefore, it cannot be said that the value of the determined arbitrary variable can surely minimize the moving time of the robot. Thus, there is room for improvement in the value of the arbitrary variable determined by the means described in claim 1 or 3.

  According to the means described in claim 2 or 4, a variable value changing process for changing the value of the arbitrary variable determined by the means described in claim 1 or 3 is executed. The variable value change process sets the evaluation index based on the movement distance of each axis that indicates the amount of change in the rotation angle of each axis with the rotation angle of each axis at the current position as a reference, and does not change the tip position of the tool. Under the condition, the evaluation index is optimized, and the value of the determined arbitrary variable is changed. For example, in the case of the 4-axis horizontal articulated robot described above, the rotation angle (arbitrary variable) around the Z axis of the tool is excluded from the variables for determining the tip position and orientation of the tool at the target position. After the value of the variable is fixed, an operation for minimizing the evaluation index based on the movement distance of each axis is repeatedly executed. As a result, the rotation angle of the tool around the Z axis at the target position is changed to a value that further shortens the movement time.

Specifically, in the variable value changing process, the target position (X, Y, Z-axis coordinate values) of the tool tip specified by the user and the rotation angle around the Z-axis of the tool at the determined target position (arbitrary) Variable) value (tool direction) is set as the calculation target position. As described above, the calculation target position in this means includes not only the respective axis coordinate values of the tool tip but also the direction of the tool. Then, among the variables for determining the calculation target position, a Jacobian matrix J _k relating to a variable excluding the rotation angle around the Z axis, which is an arbitrary variable, and the rotation angle of each axis at the calculation target position is obtained. . In addition, an evaluation index Q _k shown in the following equation (3) is set. However, in this means, a matrix whose elements are the movement distances of the respective axes is ε _k . Note that ε _k ^T is a transposed matrix of ε _k .
Q _k = ε _k ^T · λ · ε _k (3)

The evaluation index Q _k shown in the above equation (3) is obtained by multiplying the sum of squares of the movement distances of each axis by the diagonal matrix λ, and weighting according to the maximum rotation speed of each axis with respect to the sum of squares of the movement times. Is given. That is, it corresponds to an approximate value of travel time. By minimizing the evaluation index Q _k set in this way while satisfying the constraint condition that the tip position of the tool is not changed (J _k · Δ _k = 0), the change amount Δ shown in the following equation (4) _k is calculated. However, a matrix having the rotation angle of each axis at the calculation target position as an element is θ _k , and a matrix having the rotation angle of each axis at the current position as an element is θ _c .
^{_{Δ k = {λ -1 · J}} k T · (J k · λ -1 · J k T) -1 · J k -I} (θ k -θ c)
... (4)

By performing forward conversion on the rotation angle (rotation angle of each axis after movement) of each axis _obtained by adding the calculated change amount Δk to the rotation angle of each axis at the calculation target position, the tool after movement Is calculated. Then, the tendency of the change in the evaluation index Q _k is determined. As a result, if the evaluation index Q _k is above the decline predetermined inclination, it considered there is room for further minimizing the metric Q _k. In that case, after setting the target position and the calculated tool direction as the next calculation target position, the above-described respective calculations for determining the direction of the tool after the next movement are executed again.

On the other hand, the result of the determination, if the evaluation index Q _k is decreasing below a predetermined slope, or, if there is no change, is believed to be less susceptible to further minimize the evaluation index Q _k. In that case, based on the rotation angle (rotation angle of each axis after movement) of each axis _obtained by adding the calculated change amount Δk to the rotation angle of each axis at the calculation target position, the tool at the target position is determined. The value of the rotation angle around the Z axis is changed. Since the value of the rotation angle around the Z-axis of the changed tool is a value determined by minimizing the evaluation index Q _k including the approximate value of the movement time, the movement time of the tool (robot) The value is such that is as short as possible. Further, the above calculation is performed after fixing the values of variables excluding the rotation angle (arbitrary variable) around the Z axis of the tool among variables for determining the tip position and orientation of the tool at the target position. Yes. That is, the rotation angle around the Z-axis of the tool that requires the moving time as short as possible with the position of the tool tip fixed at the target position is required. Therefore, the effect that the movement time of the robot can be further shortened can be obtained.

The 1st Embodiment of this invention is shown, The schematic block diagram of a robot system Flow chart showing the contents of variable value decision processing A diagram schematically showing the robot mode at the current position and target position FIG. 3 equivalent view when the target position is set at any position within the target area The flowchart which shows the 2nd Embodiment of this invention and shows the content of the variable value change process FIG. 1 equivalent view showing a third embodiment of the present invention 3 equivalent diagram showing the prior art

(First embodiment)
Hereinafter, a first embodiment of the present invention will be described with reference to FIGS.
FIG. 1 shows a system configuration of a general industrial robot. A robot system 1 shown in FIG. 1 includes a robot 2, a controller 3 that controls the robot 2, and a teaching pendant 4 connected to the controller 3.

  The robot 2 is configured as, for example, a 4-axis horizontal articulated robot. The robot 2 includes a base 5 fixed to the installation surface, a first arm 6 connected to the base 5 so as to be rotatable about a first axis J1 having an axis in the Z-axis (vertical axis) direction, A second arm 7 that is rotatably connected around a second axis J2 having an axis center in the Z-axis direction on the tip of the first arm 6 and can be moved up and down to the tip of the second arm 7 And a shaft 8 that is rotatably provided. The axis when moving the shaft 8 up and down is the third axis J3, and the axis when rotating the shaft 8 is the fourth axis J4. A flange 9 is positioned and attached to the tip (lower end) of the shaft 8 so as to be detachable.

  The base 5, the first arm 6, the second arm 7, the shaft 8 and the flange 9 function as an arm of the robot 2. Although not shown in the drawing, a tool such as an air chuck is attached to the flange 9 (corresponding to the hand) that is the tip of the arm. A plurality of axes (J1 to J4) provided in the robot 2 are driven by motors (not shown) provided corresponding to the respective axes. In the vicinity of each motor, a position detector (not shown) for detecting the rotation angle (rotation position) of each rotation shaft is provided.

  In general, an industrial robot operates according to a predetermined operation program created by performing teaching or the like in advance. The controller 3 (corresponding to a control device for the robot) performs feedback control of the motor drive based on the operation program and controls the operation of the arm of the robot 2.

  The teaching pendant 4 is, for example, a size that can be operated by being carried by a user or carried by a hand, and is formed in, for example, a thin, substantially rectangular box shape. The teaching pendant 4 is provided with various key switches, and the user performs various input operations using these key switches. The teaching pendant 4 is connected to the controller 3 via a cable, and performs high-speed data transfer with the controller 3 via a communication interface. An operation input by operating a key switch Information such as signals is transmitted from the teaching pendant 4 to the controller 3.

  In general, when a teaching operation is performed in which the tip of a tool attached to the flange 9 that is the hand of the robot 2 is moved from the current position toward the target position, the posture of the robot 2 at the target position is set to any type. Whether to do so is determined by the user. That is, in such teaching work, variables for determining the target position of the tool tip (X-axis coordinate value, Y-axis coordinate value and Z-axis coordinate value of the tool tip) and the tool (hand) at the target position All variables for determining the direction (the rotation angle of the tool around the Z axis) are specified by the user. However, depending on the type (shape) of the tool attached to the flange 9 and the content of work using the tool, the direction of the tool can be made unquestioned. For example, when an air chuck is used as a tool, the workpiece can be gripped regardless of the orientation of the tool around the Z axis (fourth axis J4).

  In the robot system 1 of the present embodiment, in the case where the orientation of the tool can be made unquestioned, the user only has to specify the values of the X, Y, and Z axis coordinates indicating the target position of the tool tip. The value of the rotation angle Rz around the Z axis of the tool at the target position need not be specified. Instead, the user specifies the rotation angle Rz about the Z axis of the tool as an arbitrary variable. Receiving this, the controller 3 sets the rotation angle Rz as an arbitrary variable that can be set to an arbitrary value on the controller 3 side (arbitrary variable setting process). Although details will be described later, the controller 3 calculates an evaluation index based on the movement time required for the tool tip to move from the current position to the target position and the position error of the tool tip position after the movement with respect to the target position. The value of an arbitrary variable is determined by setting and optimizing the evaluation index (variable value determination process). Thus, the controller 3 functions as an arbitrary variable setting processing unit and a variable value determination processing unit. In the present embodiment, the controller 3 executes the processes described above, so that the direction of the tool at the target position is determined such that the movement time of the robot 2 is as short as possible.

FIG. 2 is a flowchart showing the contents of variable value determination processing. As shown in FIG. 2, when the variable value determination process is started (start), the current position is set as the calculation target position (step S1). In step S2, a variable excluding the rotation angle Rz designated as an arbitrary variable from among variables (X, Y, Z-axis coordinate values and rotation angle Rz) for determining the tip position and orientation of the tool at the calculation target position. And the Jacobian matrix J _k related to the rotation angle of each axis (joint) at the calculation target position. The Jacobian matrix J _k is expressed as the following equation (5). However, the X, Y, and Z axis coordinate values are X _k , Y _k , and Z _k , respectively, and the rotation angles of the first axis J1 to the fourth axis J4 are θ1 _{k to} θ4 _k .

In step S3, the evaluation index _{Q k} shown in the following equation (6) is set. However, the matrix that the coordinate values of the position error between element and epsilon _k, a matrix with variation elements of each rotation angle θ1~θ4 of each axis J1~J4 and delta _k, diagonal components each axis J1 A diagonal matrix that is the square of the reciprocal of the maximum rotational speed of each of J4 is λ, and a constant for weighting the position error and the amount of change is β. Further, ε _k ^T _represents a transposed matrix of ε _k , and Δ _k ^T _represents a transposed matrix of Δ _k . Note that ε _k and λ are expressed by the following equations (7) and (8), respectively. However, a matrix having the X, Y, Z axis coordinate values of the target position as elements is P _d , a matrix having the X, Y, Z axis coordinate values of the calculation target position as elements is P _k, and the first axes J1 to J1 The maximum rotation speed for each of the fourth axes J4 is set to V1 _{max to} V4 _max .
^{_{Q k = ε k T · ε}} k + β · Δ k T · λ · Δ k ... (6)
ε _k = P _d −P _k −J _k · Δ _k (7)

In the above equation (6), the first term on the right side is the sum of squares of the position error. The second term on the right side is obtained by multiplying the sum of squares of the change amounts (movement amounts) of the rotation angles of the axes J1 to J4 by the diagonal matrix λ, and corresponds to an approximate value (approximate value) of the movement time. The constant β is proportional to the movable range and operation speed of each joint of the robot 2. Therefore, the constant β may be set as appropriate for each model of the robot 2. Note that if uniform weighting approximate value of the position error and the moving time in the evaluation index Q _k, it is possible to omit the constant beta. In step S4, by the set evaluation index Q _k thus is minimized, the amount of change delta _k shown in the following equation (9) is calculated. However, J _k ^T _represents a transposed matrix of J _k .
_{Δ k = (β · λ +} J k T · J k) -1 · J k T (P d -P k) ... (9)

In step S5, as shown in the following equation (10), the rotation angle of each axis after movement is obtained. However, a matrix having the rotation angles of the axes J1 to J4 after movement as elements is θ _{k + 1} , and a matrix having the rotation angles of the axes J1 to J4 at the calculation target position as elements is θ _k . The constant γ is a constant for adjusting the convergence speed to the target position. In the present embodiment, the value of the constant γ is set to 1. However, when the convergence speed to the target position is increased, the constant γ may be increased, and when the convergence speed is decreased, the constant γ The value of can be reduced.
θ _{k + 1} = θ _k + γ · Δ _k (10)

In step S6, as shown in the following equation (11), the tip position of the moved tool is obtained. That is, by performing forward conversion on the matrix θ _{k + 1} having the rotation angle of each axis after movement as an element, a matrix P _{k + 1} having the X, Y, and Z-axis coordinate values of the tool tip position after movement as elements is obtained. It is done. However, the function for obtaining the tool tip position from the rotation angle of each axis in consideration of the offset length of the tool, the link length of each arm, etc. is represented as J2P.
P _{k + 1} = J2P (θ _{k + 1} ) (11)

In step S7, the position error after the movement determined by operation of the tool tip position P _{k + 1} of the relative target position P _d is calculated. In step S8, it is determined whether or not the position error obtained in step S7 is equal to or smaller than a predetermined allowable error. That is, it is determined whether or not the tip position P _{k + 1} of the moved tool obtained by the calculation is sufficiently close to the target position P _d . As a result, when the position error exceeds the allowable error (NO), the process proceeds to step S9. In step S9, the tool tip position P _{k + 1} after the movement is set as the next calculation position. After the next calculation position is set in this way, the process returns to step S2, and each calculation (steps S2 to S8) for determining the tip position of the tool after the next movement is executed again. The allowable error may be set as appropriate based on the accuracy of position control in the robot 2, for example.

On the other hand, if the result of determination in step S8 is that the position error is less than or equal to the allowable error (YES), the process proceeds to step S10. In step S10, the value of the rotation angle Rz around the Z axis at the target position is determined based on the rotation angle θ _{k + 1} of each of the axes J1 to J4 after the movement shown in the above equation (10), and the process ends ( End). That is, when it is determined that the tip position of the tool after the movement obtained by the above calculation is sufficiently close to the target position, the value of the rotation angle Rz around the Z axis at that time is the value around the Z axis at the target position. Is set as the value of the rotation angle Rz. Since the set rotation angle Rz about the Z axis is set by minimizing the evaluation index Q _k including the approximate value of the moving time, the moving time of the tool (robot 2) is as much as possible. The value is shorter.

  Since the above-described control is automatically executed by the controller 3, the work performed by the user during teaching is to specify each coordinate value of the tool tip at the target position as described above, and to rotate the tool around the Z axis. It is only necessary to specify Rz as an arbitrary variable. Then, the controller 3 rotates the tool around the Z-axis at the target position automatically determined by the above-described processes in addition to the X, Y, and Z-axis coordinate values of the tool tip at the specified target position. Based on the value of the angle Rz (tool direction), the tool tip can be moved from the current position toward the target position. As a result, the burden on the user (operator) during teaching is reduced, and the movement time of the robot 2 is shortened.

  In the variable value determination process, an optimization calculation using a Jacobian matrix is performed using a secondary-form evaluation index including an approximate value of travel time. For this reason, various arithmetic processes in the variable value determination process can be performed at a relatively high speed. By the way, the Jacobian matrix represents the ratio between the minute displacement in each axis (joint) and the minute displacement of the hand position and orientation (posture of the robot 2) associated therewith. In this embodiment, as a result of repeating the calculation using such a Jacobian matrix, the tip position of the tool after movement obtained by the calculation gradually approaches the target position. Therefore, the posture at the target position of the robot 2 determined based on the value of the arbitrary variable determined by the variable value determination process does not change significantly with respect to the posture at the current position. A small change in posture means that the amount of movement of each joint is also small. Also from such a thing, according to this embodiment, it turns out that the effect that the movement time of the robot 2 is shortened is acquired.

Next, specific effects obtained by the robot system 1 of the present embodiment will be described with reference to FIGS.
FIG. 3 schematically shows an aspect of the robot when the tool tip is moved from the current position Pc toward the target position Pd. The robot shown in FIG. 3 is a 4-axis horizontal articulated robot, and an air chuck is attached as a tool to the hand. In FIG. 3, each axis and each link are indicated by a circle and a straight line, respectively, and the tool tip is indicated by an arrow. In addition, the state of the robot at the current position is indicated by a dotted line, and the state of the robot at the target position is indicated by a solid line. Here, it is assumed that the tool tip is moved from the current position Pc to the target position Pd and the work is gripped by an air chuck that is a tool.

  The teaching work in the above case is performed as follows according to the conventional method. That is, the worker in charge of teaching first considers the states (postures) shown in FIGS. 3A, 3B, and 3C. That is, the worker roughly changes the direction of the tool and estimates which direction is likely to be good. As a result, when it is determined that the state of (c) looks good, the direction of the tool is gradually changed from the state of (c) based on the state of (c) ((d) of FIG. 3). , (E), and (f)). As a result, the state shown in FIG. 3F is determined to be optimal (movement time is shortened). Here, in order to simplify the description, the number of states examined by the operator is reduced, and the optimum state can be found with a small number of repeated operations. In practice, more states may be considered or the number of repetitions may increase.

  On the other hand, according to the robot system 1 of the present embodiment, the direction of the tool at the target position Pd is automatically determined by the controller 3 so that the movement time of the robot 2 is as short as possible. Therefore, the result of the state (tool direction) in FIG. 3 (optimized) (optimized movement time can be shortened as much as possible) can be easily obtained without going through an iterative process as in the conventional method.

  Thus, according to the conventional method, the state (posture) of the robot at the target position is changed little by little based on the experience and guess of the worker in charge of teaching. Then, as a result of repeating the operation several times (for example, five times), for example, the robot operation time is longer than the robot posture (FIG. 3A) in which the tool orientations at the current position and the target position are the same. It has become possible to obtain a tool orientation that is shorter (for example, an improvement of about 25%). On the other hand, according to the robot system 1 of the present embodiment, the same effect as that obtained by the conventional method can be obtained regardless of the experience of the worker in charge of teaching. Further, at that time, the operator does not need to specifically examine the posture of the robot at the target position, so that the work load is greatly reduced.

  FIG. 4 is a view corresponding to FIG. 3 when the tool tip is moved from the current position Pc toward an arbitrary target position in the target area Ad. In this case, the position to be moved within the target area Ad shown in FIG. 4A is given from an external device such as a camera during actual work, and the worker cannot know at the time of teaching. And In such a case, the optimum direction of the tool changes depending on the position in the target area Ad where the target position is set. Therefore, in the conventional method, as shown in FIG. 4B, the target area Ad is divided into a plurality of small areas, and the optimum tool orientation is taught for each of the small areas. It was. Also, depending on how the target area Ad is divided, whether or not the optimum tool orientation can be obtained changes, and therefore there is a part that depends greatly on the individual ability of the worker in charge of teaching.

  On the other hand, according to the robot system 1 of the present embodiment, even in a case where a target position is given from an external device such as a camera for the first time during actual work, the controller 3 The optimum tool orientation at the target position is automatically determined. For this reason, it is possible to save the time-consuming work of dividing the target area Ad into small areas and teaching for each small area as in the conventional method.

(Second Embodiment)
Hereinafter, a second embodiment in which the control content of the controller 3 is changed with respect to the first embodiment will be described with reference to FIG.
In the first embodiment, when it is determined that the tip position of the moved tool obtained by calculation using the Jacobian matrix is sufficiently close to the target position, an arbitrary variable at that time (around the Z axis of the tool) The value of the rotation angle Rz) was set as the value of an arbitrary variable at the target position. However, since the Jacobian matrix has the characteristics as described in the first embodiment, even the tip position of the tool after the final movement by the above calculation slightly deviates from the target position. . Therefore, it cannot be said that the determined value of the arbitrary variable can surely minimize the movement time of the robot 2. Thus, there is room for improvement in the value of the arbitrary variable determined by the variable value determination process.

  The controller 3 of the present embodiment executes an arbitrary variable change process for changing the value of the rotation angle Rz (arbitrary variable) of the tool at the determined target position after the execution of the arbitrary variable value determination process shown in FIG. That is, the controller 3 of this embodiment also functions as variable value change processing means. The variable value change process sets the evaluation index based on the movement distance of each axis that indicates the amount of change in the rotation angle of each axis with the rotation angle of each axis at the current position as a reference, and does not change the tip position of the tool. Under the condition, the evaluation index is optimized, and the value of the determined arbitrary variable is changed. That is, among the variables for determining the tip position and orientation of the tool at the target position, the values of the variables (X and YZ axis coordinate values) excluding the rotation angle Rz around the Z axis of the tool are fixed. An operation for minimizing the evaluation index based on the axis movement distance is repeatedly executed. As a result, the rotation angle Rz around the Z axis of the tool at the target position is changed to a value that further shortens the movement time.

FIG. 5 is a flowchart showing the contents of the arbitrary variable changing process. As shown in FIG. 5, when the arbitrary variable changing process is started (start), step T1 is executed. In step T1, the target position (X, Y, Z axis coordinate values) of the tool tip designated by the user is set as the calculation target position. Further, the rotation angle Rz (tool direction) of the tool around the Z axis at the calculation target position is set to a value determined by the variable value determination process. As described above, the calculation target position in the variable value changing process includes not only each axis coordinate value at the tip of the tool but also the direction of the tool. In step T2, among the variables for determining the calculation target position (including the direction of the tool), a variable excluding the rotation angle Rz around the Z axis, which is an arbitrary variable, and the rotation angle of each axis at the calculation target position And the Jacobian matrix J _k for. The Jacobian matrix J _k is expressed as the above equation (5).

In step T3, the evaluation index _{Q k} shown in the following equation (12) is set. However, here, a matrix having the movement distance of each axis as an element is ε _k . Ε _k ^T _represents a transposed matrix of ε _k .
Q _k = ε _k ^T · λ · ε _k (12)

The evaluation index Q _k shown in the above equation (12) is obtained by multiplying the sum of squares of the movement distances of each axis by a diagonal matrix λ, and weighting according to the maximum rotation speed of each axis with respect to the square sum of the movement times. Is given. That is, it corresponds to an approximate value (approximate value) of travel time. In step T4, the evaluation index Q _k set in this way is minimized while satisfying the constraint condition g _k shown in the following equation (13), thereby calculating the change amount Δ _k shown in the following equation (14). Is done. However, and a matrix with the rotation angle of each axis J1~J4 element at the current position and theta _c. As a method of the above calculation, for example, Lagrange's undetermined multiplier method or the like can be used.
J _k · Δ _k = 0 (13)
^{_{Δ k = {λ -1 · J}} k T · (J k · λ -1 · J k T) -1 · J k -I} (θ k -θ c)
... (14)

In step T5, similarly to step S5 in the first embodiment, the rotation angle of each axis after movement shown in the above equation (10) is obtained. In step T6, as shown in the following equation (15), the tip position and orientation of the moved tool are obtained. That is, by performing forward conversion on the rotation angle θ _{k + 1} of each axis after movement, a matrix P whose elements are the X, Y, Z axis coordinate values of the tool tip position after movement and the rotation angle Rz around the Z axis. _{k + 1} is determined.
P _{k + 1} = J2P (θ _{k + 1} ) (15)

In steps T7 and T8, how is the value of the evaluation index Q _k optimized by the current optimization calculation (steps T3 and T4) determined from the evaluation index Q _k−1 optimized by the previous optimization calculation? It is judged whether it has changed. That is, steps T7 and T8 are for judging the tendency of change in the evaluation index. Therefore, when the process proceeds to step T7 for the first time after the variable value changing process is executed, the process skips steps T7 and T8 and proceeds to step T9. In step T7 is performed after the first time, the value of this metric Q _k is whether decreased from the value of the evaluation index Q _k-1 of the previous time is determined.

  As a result, when it is determined that the number has decreased ("YES" in step T7), the process proceeds to step T8. In step T8, it is determined whether or not the reduction amount of the evaluation index is equal to or greater than a predetermined threshold value. That is, in step T8, it is determined whether or not the evaluation index has a decreasing tendency equal to or greater than a predetermined inclination. As a result, when it is determined that the amount of decrease in the evaluation index is equal to or greater than a predetermined threshold value, that is, the evaluation index is in a decreasing tendency equal to or greater than a predetermined slope (“YES” in step T8), the process proceeds to step T9. In such a case, it is considered that there is much room for further minimizing the evaluation index.

  In step T9, the calculation target position is reset as follows. That is, in step T9, the X, Y, and Z axis coordinate values of the tool tip remain at the target position, and the direction of the moved tool calculated in step T6 is set as the direction of the tool at the next calculation target position. The After the next calculation target position is set in this way, the process returns to step T2, and each calculation (steps T2 to T8) for determining the direction of the tool after the next movement is executed again.

On the other hand, when it is determined in step T7 that the evaluation index has not decreased (NO), or in step T8, the amount of decrease in the evaluation index is less than a predetermined threshold, that is, the evaluation index is predetermined. If it is determined that there is a decreasing tendency less than the inclination of (NO), the process proceeds to step T10. In these cases, there is little room for further minimizing the evaluation index. If it is determined in step T7 that the evaluation index has not decreased, it is considered that the evaluation index has not changed. This is because the calculation for minimizing the evaluation index is performed here, and it is almost impossible to increase the evaluation index. Therefore, if the evaluation index has not decreased, that is, the evaluation index has not changed. In step T10, the value of the rotation angle Rz around the Z axis at the target position is changed based on the rotation angle θ _{k + 1} of each of the axes J1 to J4 after the movement shown in the above equation (10), and the process ends ( End).

The value of the rotation angle Rz around the Z axis of the tool in the changed target position in step T10, since the evaluation index Q _k the estimated value is included in the travel time is a value determined by minimizing, tool The value is such that the movement time of (robot 2) is as short as possible. Further, in each of the above operations (steps T2 to T8), among the variables for determining the tip position and orientation of the tool at the target position, the values of variables excluding the rotation angle Rz (arbitrary variable) around the Z axis of the tool are It is done on a fixed basis. That is, the value (tool direction) of the rotation angle Rz around the Z-axis of the tool that minimizes the movement time with the position of the tool tip fixed at the target position is obtained. Therefore, according to this embodiment, the effect that the movement time of the robot 2 can be further shortened is acquired.

  Now, as the threshold value is reduced, the accuracy of optimization (minimization) of the evaluation index increases, and the effect of shortening the movement time of the robot 2 increases. However, if the threshold is made too small, the optimization operation will take a great deal of time. The threshold value may be set to an appropriate value in consideration of such a trade-off relationship. However, no matter how small the threshold is, the effect of shortening the movement time is limited by the output resolution of the command value for moving the robot 2. Therefore, for example, setting the value according to the output resolution of the command value in the controller 3 is one idea. For example, if the output resolution is 8 ms, setting it to one-tenth of 0.8 ms, etc., the calculation time required for optimization will not increase unnecessarily, and the effect of shortening the travel time can be sufficiently obtained. It is done.

(Third embodiment)
Hereinafter, a third embodiment in which the target robot type is changed with respect to each of the above embodiments will be described with reference to FIG.
FIG. 6 is a view corresponding to FIG. 1 in the first embodiment, and the same parts as those of the above-described embodiments are denoted by the same reference numerals and description thereof is omitted. The robot system 21 of this embodiment shown in FIG. 6 differs from the robot system 1 of the first embodiment shown in FIG. 1 in that a robot 22 is provided instead of the robot 2.

  The robot 22 is configured as, for example, a 6-axis vertical articulated robot. In other words, the shoulder portion 26 is coupled to the base 25 so as to be rotatable in the horizontal direction via a first axis J21 having an axis in the Z-axis direction. A lower end portion of a lower arm 27 extending upward is connected to the shoulder portion 26 via a second axis J22 having an axis in the Y-axis direction so as to be rotatable in the vertical direction. A first upper arm 28 is connected to the distal end portion of the lower arm 27 via a third axis J23 having an axis in the Y-axis direction so as to be rotatable in the vertical direction. A second upper arm 29 is connected to the distal end portion of the first upper arm 28 via a fourth axis J24 having an axis in the X-axis direction so as to be able to rotate. A wrist 30 is connected to the tip of the second upper arm 29 via a fifth axis J25 having an axis in the Y-axis direction so as to be rotatable in the vertical direction. A flange 31 is connected to the wrist 30 via a sixth axis J26 having an axis in the X-axis direction so as to be able to rotate.

  The base 25, the shoulder portion 26, the lower arm 27, the first upper arm 28, the second upper arm 29, the wrist 30 and the flange 31 function as an arm of the robot 22. Although not shown, a tool such as an air chuck is attached to the flange 31 (corresponding to the hand) that is the tip of the arm. The plurality of axes (J21 to J26) provided in the robot 22 are driven by motors (not shown) provided corresponding to the respective axes, similarly to the robot 2 of the first embodiment. Further, in the vicinity of each motor, a position detector (not shown) for detecting the rotational position of each rotating shaft is provided.

  Also in the configuration of the present embodiment, the controller 3 can execute the arbitrary variable setting process, the variable value determining process, and the arbitrary variable changing process similar to those in the above embodiments. For example, if any one or two of the variables for determining the direction of the tool (the rotation angles Rx, Ry, Rz around the X, Y, and Z axes) are designated as arbitrary variables, The designated variable is set as an arbitrary variable (arbitrary variable setting process). Then, the controller 3 performs variable value determination processing (and variable value change processing).

In the present embodiment, the Jacobian matrix J _k obtained at step T2 in step S2 and 5 of Figure 2, may be changed based on the change of the number of axes. The Jacobian matrix J _k is expressed by the following equation (16), for example, when the rotation angle Rx around the X axis and the rotation angle Ry around the Y axis of the tool are set as arbitrary variables. However, the rotation angles of the first axis J21 to the sixth axis J26 are θ1 _{k to} θ6 _k, and the rotation angle around the Z axis of the tool is Rz _k .

  Thereby, the value of the arbitrary variable (tool direction) at the target position is automatically determined to a value that minimizes the movement time of the robot 22. As a result, also in the configuration of the present embodiment, the same operations and effects as those of the above embodiments can be obtained.

(Other embodiments)
The present invention is not limited to the embodiments described above and illustrated in the drawings, and the following modifications or expansions are possible.
In each of the above embodiments, the example in which the present invention is applied to the 4-axis horizontal articulated robot 2 or the 6-axis vertical articulated robot 22 has been described. However, the present invention is a robot having a plurality of axes. Applicable in general.

  In the drawings, 2 and 22 are robots, 3 is a controller (robot control device, arbitrary variable setting processing means, variable value determination processing means, variable value change processing means), 9 and 31 are flanges (hands), J1 to J4, J21 to J26 indicate axes.

Claims (4)

A method for controlling a robot when moving the tip of a tool attached to the hand of a robot having a plurality of axes from a current position toward a target position,
Arbitrary variable setting processing for setting one or two variables designated by the user as arbitrary variables that can be set to arbitrary values among the variables for determining the orientation of the tool after movement,
An evaluation index is set based on a movement time required for the tool tip to move from the current position to the target position and a position error of the tool tip position after the movement with respect to the target position, and the evaluation index is optimized. Variable value determination processing for determining an arbitrary variable value at the target position,
Including
The variable value determination process includes:
A first step of setting the current position as a calculation target position;
A second step of obtaining a Jacobian matrix J _k relating to a variable excluding the arbitrary variable among variables for determining a tool tip position and orientation at the calculation target position and a rotation angle of each axis at the calculation target position;
The matrix having the coordinate value of the position error as an element is ε _k , the matrix having the change amount of the rotation angle of each axis as an element is Δ _k , and the diagonal component is the square of the reciprocal of the maximum rotation speed of each axis. Assume that the diagonal matrix is λ, the matrix having the coordinate value of the target position as an element is P _d , and the matrix having the coordinate value of the calculation target position as an element is P _k , the evaluation index Q shown in the following equation (1) a third step of calculating a change amount Δ _k shown in the following equation (2) by minimizing _k ;
^{_{Q k = ε k T · ε}} k + Δ k T · λ · Δ k ... (1)
^{_{Δ k = (λ + J k}} T · J k) -1 · J k T (P d -P k) ... (2)
A fourth step of calculating the tip position of the moved tool by performing forward conversion on the rotation angle of each axis _obtained by adding the calculated change amount Δk to the rotation angle of each axis at the calculation target position;
A fifth step of determining a position error of the calculated tool tip position with respect to the target position and determining whether the position error is equal to or less than a predetermined allowable error;
Including
When the position error exceeds the allowable error as a result of the determination in the fifth step, the calculated tip position of the moved tool is set as the next calculation target position, and then the second to fifth steps are performed. Run again,
As a result of the determination in the fifth step, when the position error is equal to or less than the allowable error, based on the rotation angle of each axis _obtained by adding the calculated change amount Δk to the rotation angle of each axis at the calculation target position. And determining a value of the arbitrary variable for determining the direction of the tool at the target position. An evaluation index is set based on the movement distance of each axis indicating the amount of change in the rotation angle of each axis with respect to the rotation angle of each axis at the current position, and under the constraint that the tip position of the tool is not changed, A variable value changing process for optimizing the evaluation index and changing the value of the determined arbitrary variable,
The variable value changing process is:
A sixth step of setting a direction of a tool determined based on the target position and the determined value of the arbitrary variable as a calculation target position;
A seventh step of obtaining a Jacobian matrix J _k relating to a variable excluding the arbitrary variable among variables for determining the calculation target position and a rotation angle of each axis at the calculation target position;
A matrix having the movement distance of each axis as an element is ε _k , a matrix having a rotation angle of each axis at the calculation target position as an element is θ _k, and a matrix having a rotation angle of each axis at the current position as an element. An eighth step of calculating a change amount Δ _k shown in the following equation (4) by minimizing an evaluation index Q _k shown in the following equation (3) as θ _c while satisfying the constraint condition;
Q _k = ε _k ^T · λ · ε _k (3)
^{_{Δ k = {λ -1 · J}} k T · (J k · λ -1 · J k T) -1 · J k -I} (θ k -θ c)
... (4)
A ninth step of calculating the direction of the tool after movement by performing forward conversion on the rotation angle of each axis _obtained by adding the calculated change amount Δk to the rotation angle of each axis at the calculation target position;
A tenth step of determining a tendency of change in the evaluation index Q _k ;
Including
As a result of the determination in the tenth step, when the evaluation index Q _k tends to decrease more than a predetermined inclination, the target position and the calculated direction of the moved tool are set as the next calculation target position. , Execute the seventh to tenth steps again,
As a result of the determination in the tenth step, when the evaluation index Q _k tends to decrease below a predetermined inclination or when the evaluation index Q _k does not change, the rotation angle of each axis at the calculation target position is based on the rotation angle of each axis plus the variation delta _k computed, robot according to claim 1, characterized in that to change the value of the arbitrary variables for determining the orientation of the tool at the target position Control method. A control device for a robot that moves a tip of a tool attached to a hand of a robot having a plurality of axes from a current position toward a target position,
Of the variables for determining the orientation of the tool after movement, one or two variables designated by the user are set as arbitrary variables that can be set to arbitrary values, arbitrary variable setting processing means,
An evaluation index is set based on a movement time required for the tool tip to move from the current position to the target position and a position error of the tool tip position after the movement with respect to the target position, and the evaluation index is optimized. Variable value determination processing means for determining the value of an arbitrary variable at the target position;
With
The variable value determination processing means includes:
Set the current position as a calculation target position,
Obtaining a Jacobian matrix J _k related to a variable excluding the arbitrary variable among variables for determining the tip position and orientation of the tool at the calculation target position, and a rotation angle of each axis at the calculation target position;
The matrix having the coordinate value of the position error as an element is ε _k , the matrix having the change amount of the rotation angle of each axis as an element is Δ _k , and the diagonal component is the square of the reciprocal of the maximum rotation speed of each axis. Assume that the diagonal matrix is λ, the matrix having the coordinate value of the target position as an element is P _d , and the matrix having the coordinate value of the calculation target position as an element is P _k , the evaluation index Q shown in the following equation (1) By minimizing _k , the change amount Δ _k shown in the following equation (2) is calculated,
^{_{Q k = ε k T · ε}} k + Δ k T · λ · Δ k ... (1)
^{_{Δ k = (λ + J k}} T · J k) -1 · J k T (P d -P k) ... (2)
By performing forward conversion on the rotation angle of each axis _obtained by adding the calculated change amount Δk to the rotation angle of each axis at the calculation target position, the tip position of the moved tool is calculated,
Obtaining a position error of the calculated tool tip position relative to the target position, and determining whether the position error is a predetermined allowable error or less;
When the position error exceeds the allowable error, the calculated tool tip position is set as the next calculation target position, and then each calculation for obtaining the tool tip position after the next movement is performed. Run again,
When the position error is equal to or less than the allowable error, the orientation of the tool at the target position based on the rotation angle of each axis _obtained by adding the calculated change amount Δk to the rotation angle of each axis at the calculation target position. A control apparatus for a robot, wherein a value of the arbitrary variable for determining the value is determined. An evaluation index is set based on the movement distance of each axis indicating the amount of change in the rotation angle of each axis with respect to the rotation angle of each axis at the current position, and under the constraint that the tip position of the tool is not changed, Variable value change processing means for optimizing the evaluation index and changing the value of the determined arbitrary variable,
The variable value change processing means includes:
The direction of the tool determined based on the target position and the value of the determined arbitrary variable is set as a calculation target position,
Obtaining a Jacobian matrix J _k related to a variable excluding the arbitrary variable among variables for determining the calculation target position and a rotation angle of each axis at the calculation target position;
A matrix having the movement distance of each axis as an element is ε _k , a matrix having a rotation angle of each axis at the calculation target position as an element is θ _k, and a matrix having a rotation angle of each axis at the current position as an element. As θ _c , the evaluation index Q _k shown in the following formula (3) is minimized while satisfying the constraint condition, thereby calculating the change amount Δ _k shown in the following formula (4),
Q _k = ε _k ^T · λ · ε _k (3)
^{_{Δ k = {λ -1 · J}} k T · (J k · λ -1 · J k T) -1 · J k -I} (θ k -θ c)
... (4)
By performing forward conversion on the rotation angle of each axis _obtained by adding the calculated change amount Δk to the rotation angle of each axis at the calculation target position, the direction of the tool after movement is calculated,
Determining a tendency of change in the evaluation index Q _k ;
When the evaluation index Q _k tends to decrease beyond a predetermined inclination, the target position and the calculated tool direction after movement are set as the next calculation target position, and then the tool direction after the next movement is set. Re-execute each of the operations for obtaining
When the evaluation index Q _k is in a decreasing tendency less than a predetermined inclination or when the evaluation index Q _k is not changed, the calculated change amount Δ _k is added to the rotation angle of each axis at the calculation target position. 4. The robot control apparatus according to claim 3, wherein a value of the arbitrary variable for determining a direction of the tool at the target position is changed based on a rotation angle of each axis.

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