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Article | REF: S7730 V1

Modeling and control of robot manipulators

Author: Alain LIÉGEOIS

Publication date: June 10, 2000

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4. Using Jacobian matrices

The Jacobian matrix J and its inverse G or J – 1 have fundamental applications in mechanism analysis and control.

4.1 Calculating static forces

From the kinematic model, we can write the differential model :

dX = J (Q)dQ

Let's assume that the variables q i are directly the variables associated with the relative displacements of the rotary or linear motors. Each of these exerts a force or torque noted γ i , hence for all degrees of freedom a vector of forces

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