Process for Calibrating the Position of a Multiply Articulated System Such as a Robot

• US 20110046925A1
• Filed: 06/12/2008
• Published: 02/24/2011
• Est. Priority Date: 06/15/2007
• Status: Abandoned Application

• Current Assignee: Commissariat a L'Energie Atomique (French Alternative Energies and Atomic Energy Commission)
• Original Assignee: Commissariat a L'Energie Atomique (French Alternative Energies and Atomic Energy Commission)
• Inventors: Bidard, Catherine, Keller, Delphine, Perrot, Yann, Chalfoun, Joe
• Application Number:
  US12/664,515
• Publication Number:
  US 20110046925A1
• Time in Patent Office: Days
• US Class Current: 703/2
• CPC Class Codes: B25J 9/1653 parameters identification, estimation, stiffness, accuracy, error analysis
• CPC Class Codes: B25J 9/1692 Calibration of manipulator

Abstract

The present invention relates to a method of calibrating the position of a multiply-articulated system, notably a robot. The multiply-articulated system consisting of a chain of N segments interlinked by an articulated link, the calibration minimizing the difference between the measured position X_m of a member linked to the last segment of the chain and its calculated position X_C, X_C being equal to the product A₁.A₂ . . . A_i . . . A_N.X_N, a homogeneous transformation matrix A_i being associated with each segment of order i, this matrix being a function of configuration parameters of the system and of given generalized parameters characterizing the flexibility of the segment, the method comprises: a first step of calculating a flexible model of the system consisting of the matrices A₁, A₂ . . . A_i . . . A_N; a second step of calibrating the flexible model by obtaining a set of generalized parameters minimizing the difference between X_m and X_C; a third step of generalized polynomial calibration of the flexible model by the introduction of generalized error matrices E_i between the homogeneous transformation matrices in the flexible model, the calculated position X_C being equal to the product A₁.E₁.A₂.E₂ . . . A_N.E_N.X_N, a generalized error matrix Ei being associated with each segment of order i, each matrix E_i of a segment being a polynomial function of the configuration parameters linked to the segment.

Claims

1. A method of calibrating the position of a multiply-articulated system consisting of a chain of N segments interlinked by an articulated link, the calibration minimizing the difference between the measured position X_m of a member linked to the last segment of the chain and its calculated position X_C, X_C being equal to the product A₁.A₂ . . . A_i . . . A_N.X_N, a homogeneous transformation matrix A_i being associated with each segment of order i, this matrix being a function of configuration parameters of the system and of given generalized parameters characterizing the flexibility of the segment, said method comprising:

a first step of calculating a flexible model of the system consisting of the matrices A₁, A₂ . . . A_i . . . A_N;

a second step of calibrating the flexible model by obtaining a set of generalized parameters (p_opt) minimizing the difference between X_m and X_C;

a third step of generalized polynomial calibration of the flexible model by the introduction of generalized error matrices E_i between the homogeneous transformation matrices in the flexible model, the calculated position X_C being equal to the product A₁.E₁.A₂.E₂ . . . A_N.E_N.X_N, a generalized error matrix E_i being associated with each segment of order i, each matrix E_i of a segment being a polynomial function of the configuration parameters linked to the segment.

2. The method as claimed in claim 1, wherein in the first step the flexible model of the system is obtained by the determination of new generalized parameters from the rigid parameters of the system according to an iterative process:

a geometrical model is calculated as a function of configuration parameters, of original generalized parameters and of geometrical properties of the system;

deformations of the system are calculated as a function of the geometrical model and of mechanical stresses;

new generalized parameters are calculated as a function of the deformations;

the new generalized parameters are compared to the original parameters;

if the difference Δ

P between the new parameters and the original parameters is less than a given threshold ε

, the flexible model is obtained from the new generalized parameters;

otherwise, a new iteration is executed, this iteration rectifying the model by using the new generalized parameters.

3. The method as claimed in claim 2, wherein the mechanical stresses include flexibility stresses belonging to the generalized parameters.

4. The method as claimed in claim 1, wherein the configuration parameters include the angles of the rotation axes and of elevation relative to a given reference.

5. The method as claimed in claim 1, wherein a segment is modeled by a parallelogram and a rotation axis being articulated between two joints, a first joint belonging to the segment and the second joint belonging to the next segment in the chain, the parallelogram modeling an elevation movement about an axis passing through a peak of the parallelogram, the segment being subject to torsion, compression and traction stresses.

6. The method as claimed in claim 5, wherein each segment is modeled by the following flexibility parameters:

a spring of stiffness k_t1 which represents the torsion of the joint (26) upstream of the rotation axis;

a spring of stiffness k_f1 which represents the deflection of the rotation axis;

a spring of stiffness k_r which represents the elasticity of a rotation movement transmission element;

a spring of stiffness k_t2 which represents the torsion of the joint downstream of the rotation axis;

a spring of stiffness k_tp which represents the torsion of the parallelogram;

springs of stiffness k_b1 representing the flexibility of a side of the parallelogram, of stiffness k_tube representing the flexibility of the opposite side and of stiffness k_j1 representing the flexibility of a branch linking a point (J) of the adjacent side to an end of this side;

a rotation model being obtained as a function of the generalized flexibility parameters φ

_t1, φ

_f1, θ

, φ

_t2, α

, φ

_tb respectively representing the rotation angles of the springs of stiffnesses k_t1, k_f1, the rotation angle about the rotation axis, the rotation angles of the springs of stiffnesses k_r, k_t2, the rotation angle about the elevation axis, and the rotation angle of the spring of stiffness k_tp.

7. The method as claimed in claim 5, wherein a segment comprising a tube fitted with a connecting rod and provided at each end with a joint, a first joint being articulated about the joint of the next segment through the intermediary of the rotation axis, the rotation movements being obtained by means of rotation pulleys driving a rotation cable, one side of the segment models the tube, the opposite side models the connecting rod, the branch models a balancing element and the rotation movement transmission element models the rotation cable.

8. The method as claimed in claim 1, wherein a generalized error matrix E_i associated with a segment is a nonlinear function of six parameters ε

₁, ε

₂, ε

₃, ε

₄, ε

₄, ε

₆, three of these parameters ε

₁, ε

₂, ε

₃ representing the Euler angles corresponding to the rotation movement of a system of coordinates linked to the segment, the other three parameters ε

₄, ε

₄, ε

₆ representing a translation in the space of the center O_i of the system of coordinates, each generalized parameter is a polynomial function of the components of the configuration vector.

9. The method as claimed in claim 8, wherein the matrix E_i is written in the following form: