JP5803179B2 - Robot control method and robot control apparatus - Google Patents

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 is.

  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. 15 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. 15 is a 4-axis horizontal articulated robot, and an air chuck is attached as a tool to the hand. In FIG. 15, 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. 15, the tool tip is moved from the current position indicated by the solid line to the target position indicated by the dotted line or broken line, and the work is gripped by the air chuck, which 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 surface of the workpiece (the lower surface in FIG. 15). 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. 15, teaching work is required so that the posture of the robot at the target position (the direction of the tool) is not in a state indicated by a broken line but in a state indicated by a 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 multiple) 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, a first evaluation index based on the movement time required for the hand to move from the current position to the target position is set, and the first evaluation index is optimized to determine the value of the arbitrary variable (variable value determination process). ). 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.

  Now, the first evaluation index is calculated for all possible values of an arbitrary variable (for example, the rotation angle around the Z axis of the tool) at the target position, and expressed as a function of the arbitrary variable (hereinafter referred to as an evaluation function) (graphed) Then, you can see the following. That is, in the evaluation function, the portion of the minimum value (optimum value) of the first evaluation index is the bottom of the valley, and another value that is not the minimum value of the first evaluation index (a value according to the minimum value, Then, the local value) is also the bottom of the valley. The reason for this is as follows.

  Even if the position of the tool tip (each coordinate value) is the same, the robot may have a completely different posture. Therefore, various postures that can be taken by the robot are usually divided into a plurality of forms. For example, in the case of a 4-axis horizontal articulated robot, there are two types of forms (arm forms) with different polarities of the rotation angle of the second axis. That is, the posture of the 4-axis horizontal articulated robot is classified into two types. Further, in the case of a 6-axis vertical articulated robot, two types of configurations (arm configuration) in which the rotation angle of the first axis is 180 degrees different from each other, and two types of configurations (elbow) in which the polarities of the rotation angle of the third axis are different from each other There are two forms (wrist forms) in which the rotation angle of the fourth axis and the fourth axis are different from each other by 180 degrees. That is, it is classified into 8 types in total by the combination of these arm forms, elbow forms, and wrist forms.

  If such a form is the same, the posture of the robot does not change much. However, if the form is different, the posture of the robot is greatly different. The fact that the posture of the robot is greatly different also means that the tendency of the change in the first evaluation index based on the movement time is also greatly different. Therefore, there is a valley of evaluation functions for each robot form. In other words, the evaluation function has a valley portion on both sides of a singular point that is a boundary where the form of the robot changes. For this reason, for example, in the case of a 4-axis horizontal articulated robot, the evaluation function has at least two valleys, and in the case of a 6-axis vertical articulated robot, the evaluation function has at least 8 valleys. It will be.

  In the variable value determination process, if a value corresponding to the local value instead of the minimum value is set as the value of the arbitrary variable at the target position, the effect of shortening the robot operation time as much as possible is slightly reduced. As described above, the robot has a concept of form, and there are valleys of the evaluation function on both sides around the singular point of the boundary where the form changes. That is, the singular point that is the boundary of the form is the boundary of the valley. Therefore, in this means, taking into consideration such points peculiar to the robot, the value corresponding to the local value of the first evaluation index is set as the value of the arbitrary variable of the target position as follows. (Local value avoidance), a value corresponding to the minimum value of the first evaluation index is set (optimization).

  That is, in the variable value determination process, the values of the rotation angles of the respective axes at which the robot takes a predetermined form and the tool tip reaches the target position are acquired for all the forms that the robot can take. Note that the values of the rotation angles of these axes do not have to be values that minimize the first evaluation index, and may be arbitrary values, so that the user can easily prepare them. And any one form among all the forms is set as a calculation object of the calculation which calculates | requires the candidate value of the arbitrary variable in a target position.

  The value of an arbitrary variable (for example, the rotation angle around the Z axis of the tool) is calculated from the value of the rotation angle of each axis acquired for the form set as the calculation target. As the value of the arbitrary variable at the target position, the first evaluation index when the calculated value is set is calculated. Then, the value of the calculated first evaluation index is set as an initial value, and the value of an arbitrary variable (for example, the rotation angle around the Z axis of the tool) when the differential value or minute variation of the first evaluation index becomes zero is obtained. The obtained value is set as a candidate value of an arbitrary variable at the target position. That is, a change in the first evaluation index corresponding to a change in an arbitrary variable is confirmed starting from the value of the first evaluation index corresponding to the calculation target form, and as a result, a value when the first evaluation index does not change is determined. It is set as a candidate value for an arbitrary variable at the target position. In order to realize such a calculation, for example, a steepest descent method, an optimum gradient method, a Newton method, or the like may be used. This candidate value is either one corresponding to the minimum value of the first evaluation index or one corresponding to the local value of the first evaluation index.

  After candidate values are obtained in this way, if there is a form that is not set as a calculation target among all the forms, one of those forms is set as the next calculation target. Each operation for obtaining the candidate value is executed again. On the other hand, if there is no form that is not set as a calculation target among all forms, the value that makes the first evaluation index the smallest among the obtained candidate values is determined as the value of the arbitrary variable at the target position. Is done.

  The value of the arbitrary variable (for example, the rotation angle around the Z axis of the tool) at the target position determined in this way is a value at which the first evaluation index based on the movement time is minimum or a value very close to it. That is, the value of the arbitrary variable at the determined target position is such that the movement time of the tool (robot) when moving from the current position to the target position is as short as possible. Since the above-mentioned control is automatically executed on the robot side, as the work performed by the user during teaching, for example, in the case of a 4-axis horizontal articulated robot, each coordinate value of the tool tip at the target position is designated. In addition, the rotation angle around the Z axis of the tool (hand) need only be specified 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) Based on this value, the tool is moved from the current position toward the target position, thereby reducing the work load on the user (operator) during teaching and shortening 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.

  Further, according to this means, the value of the arbitrary variable is optimized for each robot form in consideration of the fact that the minimum value or the local value (valley of the evaluation function) of the first evaluation index exists for each robot form. Then, among the optimized values of each arbitrary variable, the value that can minimize the first evaluation index is set as the value of the arbitrary variable at the target position. Thereby, it can be surely prevented that a value corresponding to the local value of the first evaluation index is set as the value of the arbitrary variable at the target position. That is, the value of the arbitrary variable at the target position is set so that the effect of shortening the operation time of the robot as much as possible is obtained to the maximum.

  In the variable value determination process, the first evaluation index based on the movement time required when the tip of the tool moves from the current position to the target position is used. Accordingly, for example, a detailed (accurate) moving time considering even the acceleration can be used as the first evaluation index, and an approximate value of the moving time considering only the speed can be used as the first evaluation index. It is. Among these, if the 1st evaluation index is set like the former, the accuracy at the time of determining an arbitrary variable will increase. That is, it is possible to set an arbitrary variable value that can shorten the operation time of the robot more reliably. On the other hand, if the first evaluation index is set as in the latter case, the calculation can be performed relatively easily, so that the calculation time can be shortened.

  According to the means of claim 2 or 4, in the variable value determination process, given the rotation angle of each axis in which the robot takes a predetermined form, the robot takes the predetermined form and places the tool at the target position. The value of the rotation angle of each axis reached by the tip is obtained. That is, when the value of the rotation angle of each axis in which the robot takes a predetermined form is given for each of all forms that the robot can take, the tool tip reaches the target position in any one of those forms. Is set as a calculation target for calculating the rotation angle of each axis. Note that the value of the rotation angle of each axis given above does not have to be a value that minimizes the first evaluation index, and does not have to be a value at which the tool tip reaches the target position. Good.

Then, the tip position of the tool is obtained from the rotation angle value of each axis given for the form set as the calculation target, and the tip position of the tool is set as the calculation target position. Subsequently, regarding variables for determining the tip position and orientation of the tool at the calculation target position, excluding the variables designated as arbitrary variables, and the rotation angle of each axis (each joint) at the calculation target position A Jacobian matrix _Jk is obtained. Further, a second evaluation index Q _k shown in the following formula (1) is set. However, a matrix whose element is the coordinate value of the position error of the tool tip position after the movement with respect to the target position is ε _k , a matrix whose element is the amount of change in the rotation angle of each axis is Δ _k , and the diagonal component is A diagonal matrix that is the square of the reciprocal of the maximum rotation speed of each axis 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 second 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 of the axis is acquired as the value of the rotation angle of each axis where the robot takes the form of the calculation target and the tool tip reaches the target position. 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 of each axis at that time takes the form of the calculation target of the robot. And it is acquired as the value of the rotation angle of each axis at which the tool tip reaches the target position. After the value of the rotation angle of each axis is acquired in this way, until there is no form that is not set as the calculation target, after setting any one of these forms as the next calculation target, Each of the above operations for obtaining the rotation angle of each axis is executed again. As a result, the value of the rotation angle of each axis at which the robot takes a predetermined form and the tool tip reaches the target position is acquired for each of all the forms that the robot can take.

In each calculation described above, a Jacobian matrix is used. The Jacobian matrix represents the ratio between the minute displacement in each axis (each joint) and the minute displacement of the hand position and orientation (posture) associated therewith. While using such a Jacobian matrix and repeating the calculation for minimizing the second evaluation index Q _k including the approximate value of the movement time, the tip position of the tool after movement obtained by the calculation is gradually set to the target. It will approach the position. Therefore, the posture of the robot at the target position based on the finally obtained rotation angle of each axis does not change significantly from the posture of the robot based on the rotation angle of each axis given first. That is, the form of the robot at the target position is the same as the original form. Thus, according to the present means, only the rotation angle of each axis in which the robot takes a predetermined form is given, and the rotation angle of each axis in which the robot takes the predetermined form and the tool tip reaches the target position. Can be obtained. The given value of the rotation angle of each axis may be any value as long as the robot takes a predetermined form. Therefore, regardless of the target position of the tool tip, it is sufficient that one type of value is prepared in advance for each form that the robot can take, and the work burden on the user (operator) is also from this point of view. Can be reduced.

The 1st Embodiment of this invention is shown, The schematic block diagram of a robot system A figure that represents an evaluation index as a function of an arbitrary variable The figure which shows each form of a 4-axis horizontal articulated robot 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. 5 equivalent diagram when the target position is set at any position within the target area The 2nd Embodiment of this invention is shown, and the flowchart corresponded to step S1 of FIG. FIG. 1 equivalent view showing a third embodiment of the present invention The figure which shows the arm form of a 6-axis vertical articulated robot The figure which shows the elbow form of a 6-axis vertical articulated robot The figure which shows the wrist form of a 6-axis vertical articulated robot The 4th Embodiment of this invention is shown, and the flowchart corresponded to step S1 of FIG. A diagram schematically showing a 4-axis horizontal articulated robot Figure 13 equivalent FIG. 5 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) which is the arm tip. 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 sets a first evaluation index based on a movement time required when the tip of the tool moves from the current position to the target position, and optimizes the first evaluation index. The value of the arbitrary variable is determined (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 calculates evaluation indexes for all possible values of the rotation angle Rz (arbitrary variable) of the tool around the Z-axis at the target position, and represents it as a function of the arbitrary variable (hereinafter referred to as an evaluation function) (graph). ). As shown in FIG. 2, the evaluation function has two valleys, and the minimum value (optimum value) portion of the evaluation index is located at the bottom of one valley and is not the minimum value of the evaluation index. The portion of the value (which is a value according to the minimum value, hereinafter referred to as a local value) is located at the bottom of the other valley. The reason why such two valleys exist in the evaluation function is as follows.

  FIG. 3 shows each form of a 4-axis horizontal articulated robot. In FIG. 3, each axis and each link are indicated by a circle and a straight line, respectively, and the illustration of the tool is omitted. Even if the position of the tool tip (X, Y, Z coordinate values) is the same, the robot may have a completely different posture. For this reason, various postures that can be taken by a robot are usually divided into a plurality of forms. For example, the robot 2 (four-axis horizontal articulated robot) of this embodiment is classified into two forms. That is, an arm configuration in which the rotation angle of the second axis J2 is plus (+) (see FIG. 3A) and an arm configuration in which the rotation angle of the second axis J2 is minus (−) (FIG. 3B). Reference). If such a form is the same, the posture of the robot 2 does not change much. However, if the form is different, the posture of the robot 2 is greatly different. The fact that the posture of the robot 2 is greatly different also means that the tendency of change in the evaluation index based on the movement time is greatly different. Therefore, the valley of the evaluation function described above exists for each form of the robot 2. In other words, the evaluation function includes valley portions on both sides of a singular point that is a boundary where the form of the robot 2 switches. For this reason, in the case of the robot 2 of the present embodiment, the evaluation function has at least two valleys.

  In the variable value determination process, if the local value instead of the minimum value is set as the value of the arbitrary variable at the target position, the effect of shortening the operation time of the robot 2 as much as possible is slightly reduced. As described above, the robot has a concept of form, and there are valleys of the evaluation function on both sides around the boundary (singular point) where the form changes. That is, the singular point that is the boundary of the form is the boundary of the valley. Therefore, in the present embodiment, in consideration of such points peculiar to the robot, it is avoided that a value corresponding to the local value of the first evaluation index is set as the value of the arbitrary variable of the target position as follows. However, a value corresponding to the minimum value (optimum value) of the first evaluation index is set (optimization).

  FIG. 4 is a flowchart showing the contents of the variable value determination process. As shown in FIG. 4, when the variable value determination process is started (start), the robot 2 takes a predetermined form and the value of the rotation angle of each axis at which the tool tip reaches the target position is taken by the robot 2. It is acquired for each of all the obtained forms (two arm forms shown in FIG. 3) (step S1). In addition, the value of the rotation angle of each axis shall be prepared in advance by the user. However, the value of the rotation angle of each axis to be prepared does not need to be a value that minimizes the first evaluation index, and may be any value as long as the above conditions are satisfied. Therefore, it is relatively easy for the user to prepare the above value.

  In step S2, any one of all forms is set as a calculation target for calculating a candidate value of the rotation angle Rz (arbitrary variable) around the Z axis of the tool at the target position. In step S3, the value of the rotation angle Rz around the Z axis of the tool is calculated from the value of the rotation angle of each axis acquired for the set calculation target. In step S4, the first evaluation index when the value calculated in step S3 is set as the value of the rotation angle Rz around the Z axis of the tool at the target position is calculated. In step S5, the change of the evaluation index according to the change of the rotation angle Rz is confirmed using the value of the first evaluation index calculated in step S4 as a starting point. As a result, the value of the rotation angle Rz (arbitrary variable) when the first evaluation index does not change is obtained. In order to realize the processing in step S5, the rotation angle Rz about the Z axis of the tool that satisfies the following expression (3) may be obtained using the steepest descent method, the optimum gradient method, the Newton method, or the like. . Here, f (Pc, Pd) represents an evaluation index (evaluation function) when the tool tip is moved from the current position Pc toward the target position Pd.

  In step S6, the value obtained in step S5 is set as a candidate value for the rotation angle Rz around the Z axis of the tool at the target position. This candidate value is a value determined by minimizing the first evaluation index including the approximate value of travel time. Therefore, the movement time when moving the tool tip to the target position in a state in which the robot 2 is in a calculation target form (predetermined form) is a value that is as short as possible. That is, it is either one corresponding to the minimum value of the first evaluation index or one corresponding to the local value of the first evaluation index.

  In step S7, it is determined whether or not there is a form that has not yet been set as a calculation target among all the forms. As a result of the determination, if there is a form that is not set as a calculation target (YES), the process proceeds to step S8. In step S8, any one of the forms not yet set as the calculation target is set as the next calculation target. After the next calculation target is set in this way, the process returns to step S3, and each calculation (steps S3 to S6) for obtaining the next candidate value is executed again. On the other hand, as a result of the determination in step S7, if there is no form that is not set as a calculation target (NO), the process proceeds to step S9. In step S9, the value that makes the first evaluation index the smallest among the obtained candidate values is determined as the value of the rotation angle Rz (arbitrary variable) around the Z axis at the target position, and the process ends (end). ).

  The value of the rotation angle Rz around the Z-axis of the tool at the target position determined in this way is a value at which the first evaluation index including the approximate value of the movement time is minimum or very close to it. . That is, the value of the arbitrary variable at the determined target position is such that the moving time of the tool (robot 2) when moving from the current position to the target position is as short as possible.

  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 present embodiment, the value of the arbitrary variable is optimized for each form of the robot 2 in consideration of the fact that the minimum value or the local value (valley of the evaluation function) of the first evaluation index exists for each form of the robot. Among the optimized values of the arbitrary variable, a value that can make the first evaluation index the smallest is set as the value of the arbitrary variable at the target position. Thereby, it can be surely prevented that a value corresponding to the local value of the first evaluation index is set as the value of the arbitrary variable at the target position. That is, the value of the arbitrary variable at the target position is set so that the effect of shortening the operation time of the robot 2 is maximized.

  In the variable value determination process, the first evaluation index based on the movement time required when the tool tip moves from the current position to the target position is used. Therefore, for example, a detailed (accurate) moving time considering the acceleration of each axis can be used as the first evaluation index, and an approximate value (approximate value) of the moving time considering only the speed of each axis, for example. Can be used as the first evaluation index. That is, the degree of freedom in setting the first evaluation index is high. Among these, if the 1st evaluation index is set like the former, the accuracy at the time of determining an arbitrary variable will increase. That is, it is possible to set the value of an arbitrary variable that can shorten the operation time of the robot 2 more reliably. On the other hand, if the first evaluation index is set as in the latter case, the calculation for obtaining the evaluation index can be performed relatively easily, so that the calculation time can be shortened.

Next, specific effects obtained by the robot system 1 of the present embodiment will be described with reference to FIGS.
FIG. 5 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. 5 is a 4-axis horizontal articulated robot, and an air chuck is attached as a tool to the hand. In FIG. 5, 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. 5A, 5B, and 5C. 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. 5). , (E), and (f)). As a result, the state shown in FIG. 5F 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, a result that the state (direction of the tool) in FIG. 5 (the direction of the tool) is optimal (moving time can be shortened as much as possible) can be easily obtained without going through a repeating 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. 5A) 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. 6 is a diagram corresponding to FIG. 5 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 in the target area Ad shown in FIG. 6A 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. 6 (b), 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 content of the variable value determination process is changed with respect to the first embodiment will be described with reference to FIG.
In this embodiment, given the rotation angle of each axis in which the robot 2 takes a predetermined form, the value of the rotation angle of each axis in which the robot 2 takes the above form and the tool tip reaches the target position is obtained. . That is, in the variable value determination process, the process shown in the flowchart of FIG. 7 is executed instead of step S1 of FIG.

  When the process of FIG. 7 is started (start), the values of the rotation angles of the respective axes in which the robot 2 takes a predetermined form are acquired for each of all forms (two types of arm forms) that the robot 2 can take. (Step T1). In addition, the value of the rotation angle of each axis shall be prepared in advance by the user. However, the value of the rotation angle of each axis to be prepared does not have to be a value that minimizes the first evaluation index, and does not have to be a value at which the tool tip reaches the target position. Any value can be used. Therefore, it is very easy for the user to prepare the above values.

  In step T2, any one of all the forms is set as a calculation target for calculation for obtaining the rotation angle of each axis at which the tool tip reaches the target position. In step T3, the tip position of the tool is obtained from the value of the rotation angle of each axis given for the form set as the calculation target. In step T4, the tip position of the tool obtained in step T3 is set as the calculation target position.

In step T5, 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 (4). 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 T6, a second evaluation index _{Q k} shown in the following equation (5) is set. However, a matrix whose element is the coordinate value of the position error with respect to the target position of the tip position of the tool after movement is ε _k , and a matrix whose element is the change amount of each rotation angle θ1 to θ4 of each axis J1 to J4. _k is a diagonal matrix whose diagonal component is the square of the reciprocal of the maximum rotation speed of each of the axes J1 to J4, and λ is a constant for weighting the position error and the amount of change. Further, ε _k ^T _represents a transposed matrix of ε _k , and Δ _k ^T _represents a transposed matrix of Δ _k . Ε _k and λ are expressed by the following formulas (6) and (7), 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 ... (5)
ε _k = P _d −P _k −J _k · Δ _k (6)

In the above equation (5), 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. Incidentally, if the weight of the approximate value of the position error and the moving time in the second evaluation index Q _k is even, it is possible to omit the constant beta. In step T7, when the second evaluation index Q _k which is set in this manner is minimized, the amount of change delta _k shown in the following equation (8) is calculated.
_{Δ k = (β · λ +} J k T · J k) -1 · J k T (P d -P k) ... (8)

In step T8, as shown in the following equation (9), 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} . 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 (9)

In step T9, as shown in the following formula (10), 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, a 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, and the like is represented as J2P.
P _{k + 1} = J2P (θ _{k + 1} ) (10)

In step T10, the position error of the tool tip position P _{k + 1} after movement obtained by calculation with respect to the target position P _d is obtained. In step T11, it is determined whether or not the position error obtained in step T10 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 T12. In step T12, the tip position P _{k + 1} of the moved tool is set as the next calculation position. After the next calculation position is set in this way, the process returns to step T5, and each calculation (steps T5 to T11) 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 position error is equal to or smaller than the allowable error as a result of the determination in step T11 (YES), the process proceeds to step T13. In step T13, the value of the rotation angle θ _{k + 1} of each of the axes J1 to J4 after the movement shown in the above equation (9) is the value of each axis where the robot 2 takes the form of the calculation target and the tool tip reaches the target position. Obtained as the value of the rotation angle. In step T14, it is determined whether or not there is a form that has not yet been set as a calculation target among all the forms. As a result of the determination, if there is a form that is not set as a calculation target (YES), the process proceeds to step T15. In step T15, any one of the forms not yet set as the calculation target is set as the next calculation target. After the next calculation target is set in this way, the process returns to step T3, and each calculation (steps T3 to T13) for acquiring the rotation angle of each axis is executed again. On the other hand, if the result of determination in step T14 is that there is no form that is not set as a calculation target (NO), the process ends (end). As a result of executing such processing, the values of the rotation angles of the axes at which the robot 2 takes a predetermined form and the tool tip reaches the target position are acquired for all the forms that the robot 2 can take. It will be.

  In each calculation described above, a Jacobian matrix is used. The Jacobian matrix represents the ratio between the minute displacement in each axis (each joint) and the minute displacement of the hand position and orientation (posture) associated therewith. While using such a Jacobian matrix and repeating the calculation to minimize the second evaluation index including the approximate value of the movement time, the tip position of the tool after movement obtained by the calculation gradually becomes the target position. It will approach. Therefore, the posture of the robot 2 at the target position based on the rotation angle of each axis finally obtained does not change greatly from the posture of the robot 2 based on the rotation angle of each axis given first. That is, the form of the robot 2 at the target position is the same as the original form.

  As described above, according to the present embodiment, each axis where the robot 2 takes the predetermined form and the tool tip reaches the target position only by giving the rotation angle of each axis that the robot 2 takes a predetermined form. The value of the rotation angle can be obtained. The given value of the rotation angle of each axis may be any value as long as the robot 2 takes a predetermined form. Therefore, regardless of the target position of the tool tip, it is sufficient that one type of value is prepared in advance for each form that the robot 2 can take. The burden can be reduced.

(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 FIGS.
FIG. 8 is a view corresponding to FIG. 1 in the first embodiment, and the same parts as those in the first embodiment are denoted by the same reference numerals and description thereof is omitted. The robot system 21 of this embodiment shown in FIG. 8 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.

  FIGS. 9 to 11 are diagrams corresponding to FIG. 3 in the first embodiment, and show an arm form, an elbow form, and a wrist form of a 6-axis vertical articulated robot, respectively. FIG. 9A shows a case where the workpiece at the target position is taken from the front, and FIG. 9B shows a case where the workpiece is taken over the back. That is, in FIG. 9A and FIG. 9B, the surface of the portion indicated by the dotted line is switched up and down. As described above, there are two types of arm forms in which the rotation angle of the first axis J21 is different from each other by 180 degrees. FIG. 10A shows a case where the third axis J23 exists above, and FIG. 10B shows a case where the third axis J23 exists below. In addition, the upper and lower sides mentioned here have shown the position of the Z-axis direction. As described above, there are two types of elbow forms having different polarities of the rotation angle of the third axis J23. In FIG. 11A and FIG. 11B, the surface of the portion indicated by the dotted line is switched up and down. As described above, there are two types of wrist forms in which the rotation angle of the fourth axis J24 is different from each other by 180 degrees.

  In the case of the robot 22 (6-axis vertical articulated robot) of the present embodiment, there are two types of arm form, elbow form and wrist form, respectively, and therefore, they are classified into 8 forms in total by their combination. For this reason, in the case of the robot 22 of this embodiment, the evaluation function has at least eight valleys. Also in the configuration of this embodiment, the controller 3 can execute the same arbitrary variable setting process and variable value determination process as those of 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.

  However, when any two of the variables for determining the direction of the tool are designated as arbitrary variables, the following formulas (11) to (13) are substituted for the formula (3) in the process of step S5 in FIG. ) The value of an arbitrary variable that satisfies one of the conditions may be obtained. Expression (11) shows a conditional expression when the rotation angles Rx and Ry around the X and Y axes are designated as arbitrary variables, and Expression (12) shows the rotation angles Ry and Rz around the Y and Z axes as arbitrary variables. The conditional expression when specified is shown, and the expression (13) shows the conditional expression when the rotation angles Rx and Rz around the X and Z axes are specified as arbitrary variables.

In the configuration of this embodiment, the Jacobian matrix J _k obtained at step T5 of FIG. 7, may be changed based on the change of the number of axes. The Jacobian matrix J _k is expressed by the following equation (14) 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, for example. 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 in the first embodiment and the second embodiment can be obtained.

(Fourth embodiment)
Hereinafter, a fourth embodiment in which the content of the variable value determination process is changed with respect to the first embodiment will be described with reference to FIGS.
In this embodiment, given the target position (X, Y, Z axis coordinate values) of the tool tip, the robot 2 takes a predetermined form and the value of the rotation angle of each axis at which the tool tip reaches the target position. However, it is calculated | required about each of all the forms (two arm forms shown in FIG. 3) which the robot 2 can take. That is, in the variable value determination process, the process shown in the flowchart of FIG. 12 is executed instead of step S1 of FIG. 13 and 14 schematically show the posture of the robot 2 (the rotation angle of each axis) according to the target position of the set tool tip. 13 and 14, the base 5 and the flange 9 (hands) of the robot 2 are indicated by circles, and the other arms and the like are not shown.

  When the processing of FIG. 12 is started (start), it is determined whether or not the length obtained by adding the tool length to the tool tip distance is longer than the link length of the robot 2 (step U1). The tool tip distance is a distance from the base 5 of the robot 2 to the target position of the tool tip. The tool length is an offset length of the tool attached to the hand (flange 9) (see FIGS. 13 and 14). That is, the tool length corresponds to the radius of a circle drawn by a dotted line in FIGS. Further, the link length corresponds to the radius of a circle drawn by a one-dot chain line in FIGS. Note that the length (distance) in the present embodiment corresponds to the length (distance) on the XY plane.

  If the result of determination in step U1 is that the tool tip distance + tool length is longer than the link length (YES), the process proceeds to step U2. The hand position cannot be moved farther than the link length of the robot 2. Accordingly, in this case, it is determined in step U2 that the movement is impossible, and the process ends (END).

On the other hand, if the result of determination in step U1 is that the link length is longer than the tool tip distance + tool length (NO), the process proceeds to step U3. In this case, it is possible to move the hand so that the tool tip reaches the target position. However, if the hand position is too close to the base 5, the hand and the base 5 may collide. Therefore, a target value (target distance) for the distance from the base 5 to the hand (flange 9) is determined as in the following equation (21).
Distance that may collide with base <target distance <link length (21)

The target distance shown in the above equation (21) corresponds to the radius of a circle drawn by a solid line in FIGS. In step U3, it is determined whether or not the condition of the following equation (22) is satisfied. That is, as in the state of FIG. 13A, the dotted line and the solid line circle intersect with each other, and the target position of the tool tip is between the outside of the solid line circle and the inside of the dashed line circle. It is determined whether or not
Tool tip distance-Tool length ≤ Target distance ≤ Tool tip distance (22)

When the condition of the above expression (22) is not satisfied (“NO” in step U3), the process proceeds to step U4. In Step U4, it is determined whether or not the condition of the following equation (23) is satisfied. That is, as in the state of FIG. 13B, it is determined whether or not the condition that the dotted line and the solid line circle intersect each other and the target position of the tool tip is inside the solid line circle is satisfied. .
Tool tip distance + tool length ≧ target distance ≧ tool tip distance (23)

  When the condition of the above expression (22) or the condition of the above expression (23) is satisfied (“YES” in step U3 or U4), the process proceeds to step U5. In step U5, the position of the hand that satisfies the condition that the distance (hand distance) from the base 5 to the hand (flange 9) matches the target distance and the distance from the hand to the tool tip matches the tool length is derived. The That is, in FIG. 13, the position of the flange 9 positioned at two points where the dotted and solid circles intersect (the point indicated by the white circle and the black circle in FIG. 13) is derived as a candidate value. The In step U6, the two hand positions (candidate values) derived in step U5 that have the maximum inner product with the direction vector (1, 0) pointing to the front are selected. That is, among the candidate values, a value closer to the front of the robot 2 (a point indicated by a white circle in FIG. 13) is selected.

  On the other hand, if neither the condition of the above expression (22) nor the condition of the above expression (23) is satisfied (“NO” in both steps U3 and U4), the process proceeds to step U7. That is, as shown in FIGS. 14A and 14B, when the dotted and solid circles do not intersect each other, the process proceeds to step U7. In this case, it is impossible to set the position of the hand so that the distance from the base 5 to the hand (flange 9) matches the target distance. In step U7, it is determined whether or not the tool tip distance is greater than or equal to the target distance. That is, the target position of the tool tip is located outside the solid circle (the state shown in FIG. 14A), or the target position of the tool tip is located inside the solid circle (see FIG. 14B). ) State). As a result, when it is determined that the tool tip distance is greater than or equal to the target distance (YES), that is, when the tool tip state is as shown in FIG. 14A, the process proceeds to step U8.

In step U8, the position of the hand is derived based on the following equation (24). That is, the position (the position of the flange 9 in FIG. 14A) that is on the dotted circle and has the shortest distance from the solid circle is derived as the hand position. However, the tool tip position is the X and Y axis coordinate values of the tool tip. That is, in the following equation (24), the hand position (X, Y axis coordinate value) is obtained by multiplying the ratio obtained from the distance (tool tip distance and tool length) by the tool tip position (X, Y axis coordinate value). Calculated.
Hand position = ((tool tip distance-tool length) ÷ tool tip distance) x tool tip position
... (24)

On the other hand, as a result of the determination in step U7, if it is determined that the tool tip distance is less than the target distance (NO), that is, if it is determined as shown in FIG. 14B, the process proceeds to step U9. In step U9, the position of the hand is derived based on the following equation (25). That is, the position (the position of the flange 9 in FIG. 14B) that is on the dotted circle and has the shortest distance from the solid circle is derived as the hand position. For the following formula (25), the hand position (X and Y axis coordinate values) is calculated based on the same idea as the formula (24).
Hand position = ((tool tip distance + tool length) ÷ tool tip distance) x tool tip position
... (25)

In step U10, the rotation angle of each axis for realizing the hand position selected in step U6 or the hand position derived in steps U8 and U9 is obtained for each of all the forms (two arm forms), Processing ends (END). As a result of executing such processing, the values of the rotation angles of the axes at which the robot 2 takes a predetermined form and the tool tip reaches the target position are acquired for all the forms that the robot 2 can take. .

  As described above, according to the present embodiment, the robot 2 that is a 4-axis horizontal articulated robot takes a predetermined form only at the target position (each axis coordinate value) of the tool tip and takes the target position. The value of the rotation angle of each axis reached by the tool tip can be obtained for each of all forms (two arm forms) that the robot 2 can take. Therefore, the effect that the work burden of the user (operator) is further reduced 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 drawing, 2 and 22 are robots, 3 is a controller (robot control device, arbitrary variable setting processing means, variable value determination processing means), 9 and 31 are flanges (hands), and J1 to J4 and J21 to J26 are axes. Show.

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,
A variable that sets a first evaluation index based on a moving time required for the tip of the tool to move from the current position to the target position, optimizes the first evaluation index, and determines a value of an arbitrary variable at the target position The value determination process,
Including
The variable value determination process includes:
In accordance with a form in which the posture of the robot is previously divided into a plurality based on the rotation angle of each axis, the value of the rotation angle of each axis at which the robot takes a predetermined form and the tip of the tool reaches the target position, A first step of acquiring for each of all possible forms of the robot;
A second step of setting any one of all the forms as a calculation target of a calculation for obtaining a candidate value of an arbitrary variable at the target position;
A third step of calculating the value of the arbitrary variable from the value of the rotation angle of each axis acquired for the calculation target;
A fourth step of calculating the first evaluation index when the calculated value is set as the value of the arbitrary variable at the target position;
Using the calculated value of the first evaluation index as an initial value, the value of the arbitrary variable when the differential value or minute variation of the first evaluation index becomes zero is obtained, and the obtained value is arbitrarily set at the target position. A fifth step as a variable candidate value;
Including
After execution of the fifth step, when there is a form that is not set as the calculation target, after setting any one of the forms as the next calculation target, the third to fifth steps are performed. Run again,
After execution of the fifth step, when there is no form that is not set as the calculation target, a value that makes the first evaluation index the smallest among the candidate values is determined as a value of an arbitrary variable at the target position And a robot control method. The first step of the variable value determination process is:
When the value of the rotation angle of each axis that the robot takes a predetermined form is given for each of all the forms that the robot can take, any one of those forms is placed at the target position of the tool. A sixth step of setting as a calculation target for calculation for obtaining the rotation angle of each axis to which the tip reaches;
A seventh step of obtaining the tip position of the tool from the value of the rotation angle of each axis given for the calculation object;
An eighth step of setting the obtained tip position of the tool as a calculation target position;
A ninth step of obtaining a Jacobian matrix J _k relating 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; ,
Ε _k is a matrix whose element is the coordinate value of the position error of the tool tip position relative to the target position after movement, Δ _k is a matrix whose element is the amount of change in the rotation angle of each axis, and each diagonal component is A diagonal matrix that is the square of the reciprocal of the maximum rotational speed of the axis is λ, a matrix having the coordinate value of the target position as an element is P _d, and a matrix having the coordinate value of the calculation target position as an element is P _k A tenth step of calculating a change amount Δ _k shown in the following equation (2) by minimizing a second evaluation index Q _k shown in the following equation (1):
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)
An eleventh 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 Δk to the rotation angle of each axis at the calculation target position;
A twelfth 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 a predetermined allowable error or less;
Including
As a result of the determination in the twelfth step, when the position error exceeds the allowable error, the calculated tip position of the moved tool is set as the next calculation target position, and then the ninth to twelfth steps are performed. Run again,
If the position error is equal to or smaller than the allowable error as a result of the determination in the twelfth step, the value of the rotation angle of each axis _obtained by adding the calculated change Δk to the rotation angle of each axis at the calculation target position Is acquired as the value of the rotation angle of each axis where the robot takes the form of the calculation target and the tip of the tool reaches the target position,
After acquiring the value of the rotation angle of each axis, until there is no form that is not set as the calculation target, after setting any one of these forms as the next calculation target, 7. The robot control method according to claim 1, wherein the seventh to twelfth steps are executed again. 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,
A variable that sets a first evaluation index based on a moving time required for the tip of the tool to move from the current position to the target position, optimizes the first evaluation index, and determines a value of an arbitrary variable at the target position A value determination processing means;
With
The variable value determination processing means includes:
In accordance with a form in which the posture of the robot is previously divided into a plurality based on the rotation angle of each axis, the value of the rotation angle of each axis at which the robot takes a predetermined form and the tip of the tool reaches the target position, Acquire for each of all possible forms that the robot can take,
Any one of the above forms is set as a calculation target of a calculation for obtaining a candidate value of an arbitrary variable at the target position,
The value of the arbitrary variable is calculated from the value of the rotation angle of each axis acquired for the calculation target,
As the value of the arbitrary variable at the target position, the first evaluation index when the calculated value is set is calculated,
Using the calculated value of the first evaluation index as an initial value, the value of the arbitrary variable when the differential value or minute variation of the first evaluation index becomes zero is obtained, and the obtained value is arbitrarily set at the target position. Variable candidate values,
After obtaining the candidate value of the arbitrary variable, when there is a form that is not set as the calculation target, after setting any one of these forms as the next calculation target, the candidate of the arbitrary variable Re-execute each of the above operations to obtain a value,
After obtaining the candidate value of the arbitrary variable, if there is no form that is not set as the calculation target, the value that makes the first evaluation index the smallest among the candidate values is determined as the value of the arbitrary variable at the target position. A control device for a robot, characterized in that the value is determined as a value. The variable value determination processing means includes:
When the value of the rotation angle of each axis that the robot takes a predetermined form is given for each of all the forms that the robot can take, any one of those forms is placed at the target position of the tool. Set as the calculation target of calculation to obtain the rotation angle of each axis that the tip reaches,
Obtain the tip position of the tool from the value of the rotation angle of each axis given for the calculation object,
Set the calculated tool tip position as the position to be calculated,
Obtaining a Jacobian matrix J _k relating to a variable excluding the arbitrary variable among variables for determining a tip position and an orientation of the tool at the calculation target position and a rotation angle of each axis at the calculation target position;
Ε _k is a matrix whose element is the coordinate value of the position error of the tool tip position relative to the target position after movement, Δ _k is a matrix whose element is the amount of change in the rotation angle of each axis, and each diagonal component is A diagonal matrix that is the square of the reciprocal of the maximum rotational speed of the axis is λ, a matrix having the coordinate value of the target position as an element is P _d, and a matrix having the coordinate value of the calculation target position as an element is P _k Then, by minimizing the second evaluation index Q _k shown in the following formula (1), a change amount Δ _k shown in the following formula (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 Δk to the rotation angle of each axis at the calculation target position, the tip position of the tool after movement 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 robot calculates the rotation angle value of each axis _obtained by adding the calculated change Δk to the rotation angle of each axis at the calculation target position. Obtaining the value of the rotation angle of each axis that takes the form and the tip of the tool reaches the target position;
After obtaining the value of the rotation angle of each axis, until there is no form that is not set as the calculation target, after setting any one of those forms as the next calculation target, The robot control apparatus according to claim 3, wherein each of the operations for acquiring the rotation angle is executed again.

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