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Method for positioning a tool of a multi-joint robot

  • US 4,894,788 A
  • Filed: 04/21/1988
  • Issued: 01/16/1990
  • Est. Priority Date: 05/04/1987
  • Status: Expired due to Fees
First Claim
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1. A method for positioning a tool of a multi-joint robot having a plurality of rotatable joints (Gi-1, Gi, Gi+1 ) defining robot joint axes, with one of the joints being connected to the tool and the location and the orientation of the tool being represented in a reference coordinate system and the respective position of the tool relative to the reference coordinate system and the angular positions of the robot joint axes being linked by a coordinate-transformation equation system having parameters which are determined by the desired distances and desired directions of the robot joints representing the ideal kinematic of the robot, comprising the following steps:

  • (a) determining a preliminary desired angular position (θ

    i-1, θ

    i, θ

    i+1) for each of the joints, respectively, for a desired position in space (x) of the tool based upon reference distances (ai-1, ai, ai+1 di-1, di, di+1) and directions of the joint axes required to position the tool in the desired position;

    (b) determining the positioning error (Δ

    x) of the tool due to the difference between the reference distance (ai-1, ai, ai+1, di-1, di, di+1) and the desired directions and the actual spacings and actual direction of the joints (Gi-1, Gi, Gi+1);

    (c) transforming the determined positioning error (Δ

    x) into corresponding angular correction values (Δ

    θ

    ) for the preliminary desired angular positions (θ

    i-1

    i, θ

    i+1) of the joints (Gi-1, Gi, Gi+1) by means of the inverse Jacobi matrix (Fθ



    v,Fref)-1) of the ideal kinematic of the robot of the coordinate-transformation equation system;

    (d) calculating the error-corrected angular position (θ

    f) for each of the joints (Gi-1, Gi, G+1) by addition of the angular correction values (Δ

    θ

    ) determined in step c) to the preliminary desired angular positions (θ

    i-1

    i, θ

    i+1) determined in step a); and

    (e) moving the tool to the desired position by rotating the joints in accordance with the error-corrected angular position (θ

    f) calculated in step (d).

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