Method and apparatus for calibrating position and attitude of arm tip of robot

A method of positionally calibrating a tip of an arm of a manipulated type of robot by using a computer, the arm tip being defined as a tip of a tool held by the arm, comprising steps of:

• calculating with the computer, at a plurality of positions at which the arm tip is moved, n pieces of errors (Δφ:
• Δφ1, Δφ1, Δφ2, . . . , Δφn, wherein n is a natural number larger than a value obtained by dividing the number of unknown parameters by 6), respectively, each of the errors being an error between a position of the arm tip measured by a measurement device and a position commanded by control at each of the plurality of positions;
• calculating an inter-error difference (Δεy (1≦y≦n−1)) between a given reference error (Δφm (1≦m≦n)) arbitrarily selected from the n-piece errors (Δφ) and other errors (Δφx (x≦n, except for m)) left other than the given reference error (Δφm) among the n-piece errors;
• and
• making a parameter, which is a basis for calculating the inter-error differences (Δεy), converge until a sum of absolute values of the respective inter-error differences (Δεy) becomes equal to or less than a given threshold (ε0(ε0>0)),
• wherein the converging step further includes steps of:
• calculating a Jacobian determinant (J) for parameter matrices (q, θ), wherein (q) is a matrix of the parameters and θ is a matrix of angles of respective axes of the arm,
• calculating an error matrix (Δq) of the parameter matrix q based on a product of an inter-error difference (Δεy) and a simulated inverse matrix of the Jacobian determinant (J),
• updating the parameter matrix (q) by adding the error matrix (Δq) to the parameter matrix (q), and
• re-calculating the position of the arm tip depending on the updated parameter matrix (q), so that the parameter matrix (q) is made to converge so as to calibrate the position of the arm tip,
• wherein the given reference error (Δφm) is composed of a plurality of reference errors which are set at a plurality of positions among the positions (n),
• the inter-error differences (Δεy), the Jacobian dominant J, and the error matrix (Dq) are calculated as for each of the plurality of reference errors, and
• the parameter which is a basis for calculating each of the inter-error differences (Δεy) is made to converge until a sum of absolute values of the respective inter-error differences (Δεy) at the difference reference errors (Δφm) becomes equal to or less than a given threshold (ε1(ε1>0)),
• wherein the position of the arm tip includes a spatial position and an attitude of the arm tip, and
• the plurality of positions (n) includes a plurality of spatial positions and attitudes (n).

An apparatus for calibrating of a position of a tip of an arm of a manipulated type of robot, the arm tip being defined as a tip of a tool held by the arm, comprising:

• an arm control unit that controls the arm to move to a plurality of positions (n);
• an error calculating unit that calculates, at the plurality of positions, n-piece errors (Δφ:
• Δφ1, Δφ2, . . . , Δφn, wherein n is a natural number larger than a value obtained by dividing the number of unknown parameters by 6), respectively, each of the errors being an error between a position of the arm tip measured by a measurement device and a position commanded by control at each of the plurality of positions;
• an inter-error difference calculating unit that calculates an inter-error difference (Δφy (1≦y≦n−1)) between a given reference error (Δφm (1≦m≦n)) arbitrarily selected from the n-piece errors (Δφ) and other errors (Δφx (x≦n, except for m)) other than the given reference error (Δφm) among the n-piece errors;
• and
• a converging unit that makes a parameter, which is a basis for calibrating the inter-error differences (Δεy), converge until a sum of absolute values of the respective inter-error differences (Δεy) becomes equal to or less than a given threshold (ε0 (ε0>0)),
• wherein the converging unit comprises
• a Jacobian determinant calculating unit that calculates a Jacobian determinant (J) for parameter matrices (q, θ), wherein (q) is a matrix of the parameters and θ is a matrix of angles of respective axes of the arm,
• an error matrix calculating unit that calculates an error matrix (Δq) of the parameter matrix q based on a product of an inter-error difference (Δεy) and a simulated inverse matrix of the Jacobian determinant (J),
• an updating unit that updates the parameter matrix (q) by adding the error matrix (Δq) to the parameter matrix (q), and
• a re-calculating unit that re-calculates the position of the arm tip depending on the updated parameter matrix (q), so that the parameter matrix (q) is made to converge so as to calibrate the position of the arm tip,
• wherein the position of the arm tip includes a spatial position and an attitude of the arm tip, and
• the plurality of positions (n) includes a plurality of spatial positions and attitudes (n).