Download e-book for iPad: 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 visible renewed curiosity following advances within the mechanical layout of light-weight robot structures with stronger actuation and sensing services. After a basic creation into the themes of impedance keep watch over, the e-book makes a speciality of key matters, particularly the therapy of joint flexibility and kinematic redundancy. numerous keep watch over legislation are built in keeping with mature techniques similar to the singular perturbation idea, cascaded keep an eye on concept, and passivity. The controllers are in comparison in line with their conceptual strength in addition to functional implementation concerns. The overview used to be played via numerous experiments with the DLR hands and the humanoid manipulator 'Justin'.

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

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In case of the Cartesian impedance control problem, this relationship is specified in terms of coordinates which describe the motion of the end-effector. e. 3). For the purpose of controller design, instead, a minimal representation in terms of m end-effector coordinates x ∈ Rm is often preferred. In case that all degrees-of-freedom of the end-effector motion are considered in the task, one has m = 6. e. x = f (q). 5 some more details about possible choices for the Cartesian coordinates x are given.

Replaced by q = f −1 (x) and q˙ = J (f −1 (x))x, In analogy to the external torques also the gravity torques g(q) and the joint torques τ can be rewritten in form of the equivalent task space gravity forces F g (x) = J (q)−T g(q) and the new input vector F τ , which is related to τ via τ = J (q)T F τ . Therefore, the system equations finally have the form ˙ x˙ + F g (x) = F τ + F ext . 12) ˙ are the inertia matrix and the Coriolis/centrifugal The matrices Λ(x) and μ(x, x) matrix with respect to the coordinates x.

Then the analysis of this chapter is restricted to an area Q the invertibility is ensured. 5) In the robotics literature this matrix is sometimes called analytical Jacobian, in contrast to the geometrical Jacobian, or the body Jacobian, respectively. 36), describes a subset of the configuration space Q in which the prismatic joint variables keep bounded. 4. Complete Decoupling 31 must be bigger than some value σ0 > 0. Moreover, it is assumed that the mapping ¯ p . e. 6) Q ¯ pc := f (Q ¯ p ) = {x ∈ Rn | ∃q ∈ Q ¯ p , f (q) = x} .

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