Cartesian Impedance Control of Redundant and Flexible-Joint by Christian Ott

By Christian Ott

This monograph is dedicated to the classical subject of impedance keep an eye on, which has lately noticeable renewed curiosity following advances within the mechanical layout of light-weight robot platforms with better actuation and sensing services. After a basic creation into the themes of impedance keep an eye on, the ebook makes a speciality of key concerns, specifically the therapy of joint flexibility and kinematic redundancy. a number of keep watch over legislation are built in response to mature techniques similar to the singular perturbation thought, cascaded regulate conception, and passivity. The controllers are in comparison in line with their conceptual strength in addition to useful implementation concerns. The assessment was once played via a number of experiments with the DLR hands and the humanoid manipulator 'Justin'.

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Extra resources for Cartesian Impedance Control of Redundant and Flexible-Joint Robots

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From a control point of view, also the following two well known properties are important. 5. The inertia matrix18 M (q) ∈ Rn×n is symmetric and positive definite: M (q) = M (q)T , y T M (q)y > 0 ∀q, y = 0 ∈ Rn . 6. 30): C(q, q) ˙ (q) − 2C(q, q))y ˙ =0 y T (M ∀y, q, q˙ ∈ Rn . , [SS96]) and will therefore be omitted here. 6 is strongly related to the passivity property of the ˙ via the Christoffel symbols. system and depends on the special choice of C(q, q) In case that the robot contains not only revolute but also prismatic joints, it is useful to consider a subset Qp ⊆ Q in which all20 the prismatic joints i ∈ P keep bounded by some lower and upper bounds qi,min and qi,max , respectively.

K c = 0. 25) corresponds to a vector from the origin of the desired frame D to the origin of the tool frame T , represented in frame D. From this one can get an appropriate set of translational end-effector coordinates by rotating this vector into the base frame S pdt (q, t) = Rsd (t)d pdt (q, t) = pst (q) − psd (t) . 26) Then, one can choose xt = pst (q) as translational coordinates and psd (t) as their corresponding virtual equilibrium position. By this choice the translational part of the stiffness matrix corresponds to a stiffness, which is represented in the base frame S, and consequently the eigenvectors of K t , corresponding to the principal axes of the stiffness matrix, are constant vectors expressed in the base frame.

When approaching such a singular configuration the controller splits up into two parts. One part in the controller is used to control the distance of the joint configuration from the next singular configuration via the relevant term in the factorization. The other part basically controls the movement orthogonally 12 to the singular direction by the classical operational space formulation [Kha87]. While this is a quite effective approach, especially (but not only) for the use in a position controller, in case of an impedance controller one sometimes13 prefers simply to avoid the singular configurations.

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