By Sadao Kawamura; Mikhail Svinin

ISBN-10: 3540373462

ISBN-13: 9783540373469

ISBN-10: 3540373470

ISBN-13: 9783540373476

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Friction in the joints etc. Making use of the singularity-consistent notation (21), the equation of motion can be rewritten as ˙ (q) + bA(¯ (23) bM q ) n(¯ q ) + g(q) = τ + τ e , Natural Motion and Singularity-Consistent Inversion 17 where ∂n(¯ q) ˙ + C(q, q). ∂¯ q Two remarks are due. First, the above form of the equation of motion incorporates the imposed end-eﬀector constraint. When compared to similar formulations, Eq. (23) has the advantage that it can be applied in the vicinity of any kinematic singularity and at all regular point singularities.

ASME Journal of Dynamic Systems, Measurment and Control 108:163–171 9. Wampler C (1986) Manipulator inverse kinematic solutions based on vector formulations and damped least-squares methods. IEEE Transactions on Systems, Man, and Cybernetics 16(1):93–101 10. Chiaverini S, Siciliano B, Egeland O (1994) Review of damped least-squares inverse kinematics with experiments on an industrial robot manipulator,” IEEE Transactions on Control Systems Technology 2(2):123–134 32 Dragomir N. Nenchev 11. Kir´canski M et al.

Section 2 formulates the robot dynamic equations and kinematics; Section 3 presents the approximate Jacobian setpoint controllers; Section 4 presents the adaptive Jacobian tracking controller; Section 5 oﬀers brief concluding remarks. 2 Robot Kinematics and Dynamics The equations of motion of robot with n degrees of freedom can be expressed in joint coordinates q = [q1 , · · · , qn ]T ∈ Rn as [19, 23, 24]: 1 M (q)¨ q + ( M˙ (q) + S(q, q)) ˙ q˙ + g(q) = τ 2 (1) Approximate Jacobian Control for Robot Manipulators 37 where M (q) ∈ Rn×n is the inertia matrix, τ ∈ Rn is the applied joint torque to the robot, S(q, q) ˙ q˙ = 1 ∂ 1 ˙ M (q)q˙ − { q˙T M (q)q} ˙ T 2 2 ∂q and g(q) ∈ Rn is the gravitational force.

### Advances in Robot Control by Sadao Kawamura; Mikhail Svinin

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