14 is driven by a motor 24 incorporated in the third arm 13 to rotate in the horizontal plane. The distal end portion of the hand 14 is branched into a fork shape such that the workpiece 50 can be placed thereon.

As described above, the robot 1 is a horizontal articulated robot, and the arms 11 to 13 and the hand 14 are respectively driven by the motors 21 to 24 to rotate in the horizontal plane. Therefore, in order to describe the operation of the robot 1, XY coordinates are set in the horizontal plane. The X-axis direction is the direction serving as a reference of the operation of the robot 1, and the Y-axis direction is orthogonal to the X-axis direction. In the illustrated example, the X-axis direction is the longitudinal direction of the elongated rectangular work area 5, and coincides with the direction in which the stages arranged on the wall surface surrounding the work area 5 are arranged. Further, a position of the rotation center of the first arm 11 with respect to the base 10 is defined as a joint point J0, a position of the rotation center of the second arm 12 with respect to the first arm 11 is defined as a joint point J1, the position of the rotation center of the third arm 13 with respect to the second arm 12 is defined as s a joint point J2, and a position of the rotation center of the hand 14 with respect to the third arm 13 is defined as a joint point J3. The length between the joint points J0 and J1 is defined as an effective length L1 of the first arm 11, the length between the joint points J1 and J2 is defined as an effective length L2 of the second arm 12, the length between the joint points J2 and J3 is defined as an effective length L3 of the third arm 13, and the length between the joint point J3 and the distal end of the hand 14 is defined as an effective length L4 of the hand 14. In the example illustrated herein, the effective length L1 of the first arm 11 is equal to the effective length L2 of the second arm 12.

As illustrated in FIG. 2, a robot control device 30 that controls the robot 1 is connected to the robot 1, and a pendant 32 can be connected to the robot control device 30 via a cable 31 in order to perform teaching of the robot 1. The robot control device 30 can drive and control the motors 21 to 24 and the elevating and lowering motor (not illustrated) on the basis of a command input from the outside or a command by teaching using the pendant 32.

FIGS. 3A to 3F are diagrams each illustrating the posture of the robot in the XY coordinate system. A control method based on at least an embodiment of the present invention will be described with reference to FIGS. 3A to 3F. The joint point J0 (that is, the rotation center of the first arm 11 with respect to the base 10) is defined as the origin of the XY coordinate system. FIG. 3A is a plan view illustrating an origin position of the robot 1. In the robot 1, the origin position which is a posture serving as a reference of operation of the robot 1 is determined. At the origin position, the arms 11 to 13 and the hand 14 are folded, and the folded arms and hand extend in the Y-axis direction. Therefore, the joint point J2 overlaps with the joint point J0 which is the origin of the XY coordinate system, XY coordinate values of the joint point J1 are (0, −L1), and XY coordinate values of the joint point J3 are (0, −L3). The joint point J1 is hidden by the third arm 13 and therefore is not illustrated in the figure.

FIG. 3B illustrates a state in which the arms 11 to 13 and the hand 14 are opened in order to access the stage. The rotation angle of the first arm 11 from the origin posture around the joint point J0 is denoted by TH1. That is, the angle TH1 is a joint angle formed by the Y-axis and the first arm 11. Similarly, a joint angle formed by the first arm 11 and the second arm 12 around the joint point J1 is denoted by TH2, a joint angle formed by the second arm 12 and the third arm 13 around the joint point J2 is denoted by TH3, and a joint angle formed by the third arm 13 and the hand 14 around the joint point J3 is denoted by S. At the origin position, the angles TH1 to TH3 and S are all 0. Herein, the orientation of the hand 14 in the XY coordinate system is generally controlled to coincide with the access direction (i.e., the direction in which loading and unloading are performed) with respect to the stage to be accessed by the hand 14. Therefore, when the robot 1 is moved in the work area 5 in order to transport the workpiece 50, the XY coordinate values of the position of the joint point J3 serve as a control target, and the position of the joint point J3 at the time of completion of the movement serves as a target position. In FIG. 3B, the angle formed by the third arm 13 and the hand 14 is defined as the angle S of the hand 14, but the angle S is represented by joint coordinates.

In the robot 1, the motors 21 to 23 drive the arms 11 to 13, respectively, so that the position of the joint point J3, that is, the XY coordinate values can be changed. However, while the XY coordinate values are two dimensional values, the joint angles TH1 to TH3 can be independently changed by the motors 21 to 23, respectively, and therefore the robot 1 has only one redundant freedom degree. Assuming that the position of the joint point J3 is given as the target position, there are innumerable postures of the arms 11 to 13 for realizing the target position. Depending on the posture to which each of the arms 11 to 13 moves, a large difference may occur in the movement time, or the arms 11 to 13 or the hand 14 may interfere with surrounding objects during the movement. When a target position is given and an optimum posture at that time is obtained without a constraint condition, a large amount of calculation is required. Therefore, in this embodiment, in order to prevent the amount of calculation for control from increasing due to a redundant degree of freedom when the robot 1 is moved with the position of the joint point J3 as the target position, as virtual travel axis P which is a straight line passing through the origin is considered, and a condition that the joint point J2 which is a connection point of the second arm 12 and the third arm 13 is on the virtual travel axis P is added, and the movement of the robot 1 is controlled. The angle formed by the virtual travel axis P with respect to the X axis which is the reference direction of the robot 1 is defined as the virtual travel axis angle TW. When the positions of the virtual travel axis P and the joint point J3 are given, in other words, when the positions of the virtual travel axis angle TW and the joint point J3 are given, the postures of the arms 11 to 13 of the robot 1 are uniquely determined except for a difference between a left-handed system and a right-handed system described below. That is, the position of the joint point J3 as the target position in the XY coordinate system and the virtual travel axis angle TW at the end of the movement are given, so that the movement of the robot 1 can be controlled in one way. The robot described in Patent Document 1 corresponds to a case where the virtual travel axis P always coincides with the X axis which is the reference direction in the robot 1 according to this embodiment.

FIG. 3C and FIG. 3D are diagrams illustrating the difference between the left-handed system and the right-handed system. FIG. 3C illustrates the left-handed system and FIG. 3D illustrates the right-handed system, assuming that the positions (X, Y) of the joint points J3 are the same. The reason why the left-handed system and the right-handed system are generated is that there are generally two points at which a circle having the joint point J3 as its center and the effective length L3 of the third arm 13 as its radius intersects with the virtual travel axis P. When a perpendicular line is drawn from the joint point J3 to the virtual travel axis P and the angle H formed by this perpendicular line and the third arm 13 around the joint point J3 is measured from the perpendicular line side, in a case of H<0 (i.e., in a case where the joint point J2 is on the right side with respect to the perpendicular line), the robot is the left-handed system, and conversely, in a case where the joint point is H≥0, the robot is the right-handed system. The orientation of the hand 14 in the XY coordinate system is determined by the access direction with respect to the stage regardless of the orientation of the third arm 13, and therefore the angle formed by the positive direction of the X-axis and the hand 14 around the joint point J3 is defined as the angle S of the hand 14 in FIG. 3C and FIG. 3D. Such an angle S is represented by an orthogonal coordinate system.

FIG. 3E illustrates a posture in which the first arm 11 and the second arm 12 in the posture illustrated in FIG. 3C are arranged at symmetrical positions with respect to the virtual travel axis P. Even in the posture illustrated in FIG. 3E, the joint point J2 is on the virtual travel axis P, but it is different whether the joint point J1 is on the right side or on the left side with respect to the virtual travel axis P when viewed from the origin toward the joint point J3. Such a difference is not classified into the difference between the left-hand system and the right-hand system, but is treated as a difference caused by the fact that the virtual travel axis angle TW formed by the X-axis direction and the virtual travel axis P is different from that illustrated in FIG. 3C by 180°. In order to express such a difference, the virtual travel axis angle TW is defined within a range of −180°<TW≤180°. Similarly, FIG. 3F illustrates a posture in which the first arm 11 and the second arm 12 are arranged at symmetrical positions with respect to the virtual travel axis P in the posture illustrated in FIG. 3D, and FIG. 3D and FIG. 3F are treated as if the virtual travel axis angle TW is different by 180°.

Consequently, in this embodiment, when the robot 1 is moved from the position before the movement to the target position, the position (X, Y) of the joint point J3 is used as the position of the robot 1, the virtual travel axis angle TW before the movement and the virtual travel axis angle TW after the movement are designated, and the motors 21 to 24 of the respective axes of the robot 1 are controlled. The virtual travel axis angle TW before the movement and the virtual travel axis angle TW after the end of the movement are generally different, and when the virtual travel axis angle TW is different before and after the movement, the virtual travel axis angle TW changes during the movement. The virtual travel axis angle TW itself after the movement needs to be set to an optimum value, but in the robot 1, the target position of the movement is sequentially determined by teaching, and every time the target position is determined by teaching, the optimum virtual travel axis angle TW corresponding to the target position can be determined. Once the target position and the optimum virtual travel axis angle TW are determined, the robot control device 30 thereafter controls the movement of the robot 1 on the basis of the target position and the optimum virtual travel axis angle TW, and the robot 1 transports the workpiece 50. Now, a method for determining the angle TW will be described.

In a case where the robot 1 is moved by the PTP operation, when the position before the movement, the target position (X, Y), and the virtual travel axis angles TW before the movement and after the movement are given, the rotation amount (movement amount) required for each of the motors 21 to 24 is calculated. Assuming that the motors 21 to 24 of respective axes start rotating at the same time and stop rotating at the same time, time required for movement can also be calculated from the allowable maximum velocity for each axis. The positions (X, Y) before and after the movement and the virtual travel axis angle TW before the movement are input, and the calculation of the movement time is repeated while the virtual travel axis angle TW after the movement is changed little by little, so that the virtual travel axis angle TW after the movement that minimizes the movement time can be obtained as the optimum condition. An algorithm for determining whether or not the arms 11 to 13 and the hand 14 interfere with another object in the PTP operation is also known, and therefore when the movement time is repeatedly obtained while the virtual travel axis angle TW after the movement is changed, it is determined whether or not the arms 11 to 13 and the hand 14 interfere with another object and whether or not the arms 11 to 13 and the hand 14 deviate from the changeable range of the joint angle determined for each axis. When it is determined that there is interference or deviation from the angle range, the virtual travel axis angle TW is excluded from the optimum condition. When a series of transport operation is actually performed by the robot 1, the origin position illustrated in FIG. 3A is given as an initial position, and the robot 1 is sequentially moved from this initial position. The joint point J0 and the joint point J2 overlap with each other at the origin position, and therefore the virtual travel axis P cannot be uniquely determined. However, in the case of the origin position, the virtual travel axis angle TW is defined as 0°. Then, when moving from the origin position to a position other than the origin position, the optimum virtual travel axis angle TW can be determined including whether the system is a right-handed system or a left-handed system. Thereafter, the position and the virtual travel axis angle TW before the movement are known, and therefore when the position of the next movement destination, that is, the next target position is given, the optimum virtual travel axis angle TW after the movement can be obtained. When the virtual travel axis angle TW after the movement is prepared as a function QTWOPT for obtaining the optimum condition by the above repetitive calculation and the function QTWOPT is implemented in the robot control device