Controller for robot and inverse transforming method for robot

An inverse transform processing method, applied to a robot provided with a vertical 6-axis articulated arm having an offset arm, the offset arm being provided with a fifth axis, linking a fourth axis and a sixth axis with each other, and having a link length d5, the fourth axis having a shaft center and the sixth axis having a shaft center, both of the shaft centers being parallel with each other, the arm having a head portion designated as a control point, a position and an orientation targeted to the control point being processed by an inverse transform in order to calculate an angle of each of the axes, the method comprising:

• a step configured to provisionally decide an angle of a sixth angle;
• a step configured to calculate a direction of the offset arm based on the provisionally decided angle of the sixth axis;
• a step configured to calculate a provisional target position which is subtracted from a target position of the sixth axis by the link length d5;
• a step configured to apply an inverse transform process to the provisional target position in a state where the link length d5 is set to 0;
• and
• a step configured to repeat the processes starting from the provisional decision until a difference between an angle of the sixth axis, which is obtained by estimating a result from the inverse transform process based on an estimation function, and the provisionally decided angle of the sixth axis becomes equal to or less than a predetermined value.

A controller, applied to a robot provided with a vertical 6-axis articulated arm having an offset arm, the offset arm being provided with a fifth axis, linking a fourth axis and a sixth axis with each other, and having a link length d5, the fourth axis having a shaft center and the sixth axis having a shaft center, both of the shaft centers being parallel with each other, the arm having a head portion designated as a control point, a position and an orientation targeted to the control point being processed by an inverse transform in order to calculate an angle of each of the axes, the controller comprising:

• a position provisional deciding unit configured to provisionally decide a position P6′ of the sixth axis and provisionally decide a position P5′ of the fifth axis based on the provisionally decided position P6′;
• a motion range determining unit configured to determine whether or not the provisionally decided positions P5′ and P6′ are within a motion range defined based on link parameters of the robot;
• an inverse transform processing unit configured to perform an inverse transform process of a homogeneous transformation matrix based on the positions P5′ and P6′ in a case where the provisionally decided positions P5′ and P6′ are within the motion range, the inverse transform process being performed under a condition that the link length d5=0;
• a forward transform processing unit configured to perform a forward transform process based on angles of the respective axes obtained by the inverse transform process;
• an evaluation value calculating unit configured to calculate a position matrix pE of a difference between a target position of the control point and a position resulting from the forward transform process, and calculate a rotation matrix RE by multiplying a rotation matrix corresponding to the target position, by an inverse matrix of the rotation matrix resulting from the forward transform process;
• and
• a calculation repeating unit configured to repeatedly calculate processes starting from the inverse transform process, based on a homogeneous transformation matrix in which the position matrix pE and the rotation matrix RE are reflected, when the position matrix pE has a norm exceeding a threshold thereof or the rotation matrix RE has an angle exceeding a threshold thereof.

An inverse transform processing method, applied to a robot provided with a vertical 6-axis articulated arm having an offset arm, the offset arm being provided with a fifth axis, linking a fourth axis and a sixth axis with each other, and having a link length d5, the fourth axis having a shaft center and the sixth axis having a shaft center, both of the shaft centers being parallel with each other, the arm having a head portion designated as a control point, a position and an orientation targeted to the control point being processed by an inverse transform in order to calculate an angle of each of the axes, the method comprising:

• a step configured to provisionally decide a position P6′ of the sixth axis and provisionally decide a position P5′ of the fifth axis based on the provisionally decided position P6′;
• a step configured to determine whether or not the provisionally decided positions P5′ and P6′ are within a motion range defined based on link parameters of the robot;
• a step configured to perform an inverse transform process of a homogeneous transformation matrix based on the positions P5′ and P6′ in a case where the provisionally decided positions P5′ and P6′ are within the motion range, the inverse transform process being performed under a condition of the link length d5=0;
• a step configured to perform a forward transform process based on angles of the respective axes obtained by the inverse transform process;
• a step configured to calculate a position matrix pE of a difference between a target position of the control point and a position resulting from the forward transform process, and calculate a rotation matrix RE by multiplying a rotation matrix corresponding to the target position, by an inverse matrix of the rotation matrix resulting from the forward transform process;
• and
• a step configured to repeatedly calculate processes starting from the inverse transform process, based on a homogeneous transformation matrix in which the position matrix pE and the rotation matrix RE are reflected, when the position matrix pE has a norm exceeding a threshold thereof or the rotation matrix RE has an angle exceeding a threshold thereof.

A controller, applied to a robot provided with a vertical 6-axis articulated arm having an offset arm, the offset arm being provided with a fifth axis, linking a fourth axis and a sixth axis with each other, and having a link length d5, the fourth axis having a shaft center and the sixth axis having a shaft center, both of the shaft centers being parallel with each other, the arm having a head portion designated as a control point, a position and an orientation targeted to the control point being processed by an inverse transform in order to calculate an angle of each of the axes, the controller comprising:

• a position provisional deciding unit configured to provisionally decide a position P6′ of the sixth axis and provisionally decide a position P5′ of the fifth axis based on the provisionally decided position P6′;
• a motion range determining unit configured to determine whether or not the provisionally decided positions P5′ and P6′ are within a motion range defined based on link parameters of the robot;
• an inverse transform processing unit configured to perform an inverse transform process of a homogeneous transformation matrix based on the positions P5′ and P6′ in a case where the provisionally decided positions P5′ and P6′ are within the motion range, the inverse transform process being performed under a condition of the link length d5=0;
• a forward transform processing unit configured to perform a forward transform process based on angles of the respective axes obtained by the inverse transform process;
• an evaluation value calculating unit configured to calculate a position matrix pE of a difference between a target position of the control point and a position resulting from the forward transform process, and calculate a rotation matrix RE by multiplying a rotation matrix corresponding to the target position, by an inverse matrix of the rotation matrix resulting from the forward transform process;
• and
• a calculation repeating unit configured to:
• calculate a rotation axis vector qE of the rotation matrix RE when the position matrix pE has a norm ∥pE∥ exceeding a threshold thereof or the rotation matrix RE provides an angle ∥RE∥ exceeding a threshold thereof,
• calculate a rotation vector rE defined as a product between the angle ∥RE∥ and a unit rotation axis vector qE/∥qE∥, and
• update the angles of the respective axes based on results obtained by multiplying a position matrix PE defined by the position matrix pE and the rotation vector rE, by an inverse matrix of the Jacobian matrix obtained from the angels of the respective axes calculated by the inverse transform process, processes starting from the forward transform process being repeated.

An inverse transform processing method, applied to a robot provided with a vertical 6-axis articulated arm having an offset arm, the offset arm being provided with a fifth axis, linking a fourth axis and a sixth axis with each other, and having a link length d5, the fourth axis having a shaft center and the sixth axis having a shaft center, both of the shaft centers being parallel with each other, the arm having a head portion designated as a control point, a position and an orientation targeted to the control point being processed by an inverse transform in order to calculate an angle of each of the axes, the method comprising:

• a step configured to provisionally decide a position P6′ of the sixth axis and provisionally decide a position P5′ of the fifth axis based on the provisionally decided position P6′;
• a step configured to determine whether or not the provisionally decided positions P5′ and P6′ are within a motion range defined based on link parameters of the robot;
• a step configured to perform an inverse transform process of a homogeneous transformation matrix based on the positions P5′ and P6′ in a case where the provisionally decided positions P5′ and P6′ are within the motion range, the inverse transform process being performed under a condition of the link length d5=0;
• a step configured to perform a forward transform process based on angles of the respective axes obtained by the inverse transform process;
• a step configured to calculate a position matrix pE of a difference between a target position of the control point and a position resulting from the forward transform process, and calculate a rotation matrix RE by multiplying a rotation matrix corresponding to the target position, by an inverse matrix of the rotation matrix resulting from the forward transform process;
• and
• a step configured to:
• calculate a rotation axis vector qE of the rotation matrix RE when the position matrix pE has a norm ∥pE∥ exceeding a threshold thereof or the rotation matrix RE provides an angle ∥RE∥ exceeding a threshold thereof,
• calculate a rotation vector rE defined as a product between the angle ∥RE∥ and a unit rotation axis vector qE/∥qE∥, and
• update the angles of the respective axes based on results obtained by multiplying a position matrix PE defined by the position matrix pE and the rotation vector rE, by an inverse matrix of the Jacobian matrix obtained from the angels of the respective axes calculated by the inverse transform process, processes starting from the forward transform process being repeated.