A structurally flexible humanoid spine based on a tendon-driven elastic continuum

Reinecke, Jens; Deutschmann, Bastian; Fehrenbach, David

doi:10.1109/icra.2016.7487672

Cited by 32 publications

(19 citation statements)

References 11 publications

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“…where p i denotes a certain pose in D, and d(p 1 , p 2 ) = p 1 − p 2 denotes the Euclidean distance between two poses. To solve the maximin-distance optimal design problem, an algorithm is utilized which is similar with the EA: The basic 1 Here, the D-optimality criterion is simplified according to [22] -0. idea is to randomly choose n poses as the initial design set D. Then, a pose p * from the remainder of C is randomly chosen and the algorithms checks, if (9) can be increased by replacing a certain pose p i in D with p * . For details see [28].…”

Section: B Model-free Designmentioning

confidence: 99%

“…1) has been developed. In [1], an elastic continuum mechanism (ECM) is introduced which serves as a neck or spine for David. The ECM consists of a silicone structure which is deformed by a rigid platform at the top end at which the tendon actuation is attached.…”

Section: Introductionmentioning

confidence: 99%

“…1 All Authors are with the Institute of Robotics and Mechatronics of the German Aerospace Center (DLR) bastian.deutschmann@dlr.de [1] and its motion capabilities such as linear, robust controllers [5], impedance controllers [6] or model-based observers for online state estimation such as Kalman Filters. All mentioned alternatives desire the nonlinear stiffness characteristics or the linearized stiffness matrix of the ECM.…”

Section: Introductionmentioning

confidence: 99%

“…Another modelfree technique is task-parametrized Gaussian mixture models which was successfully applied by [15] in the same context. The main drawbacks that hinder the discussed methods to be used in the present application are as follows: On the one hand, the control cycle of the hardware is 1 kHz [1]. Thus the computational costs of continuum mechanical models are to high.…”

Section: Introductionmentioning

confidence: 99%

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A Method to Identify the Nonlinear Stiffness Characteristics of an Elastic Continuum Mechanism

Deutschmann

Liu

Dietrich

et al. 2018

IEEE Robot. Autom. Lett.

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The humanoid robot David is equipped with a novel robotic neck based on an elastic continuum mechanism (ECM). To realize a model-based motion control, the six dimensional stiffness characteristics needs to be known. The paper presents an approach to experimentally identify the stiffness characteristic using a robot manipulator to deflect the ECM and measure the Cartesian wrenches and Cartesian poses with external sensors. A three-step process is proposed to establish Cartesian wrench and pose pairs experimentally. The process consists of a simulation step, to select a good model, a second step that extracts effective poses from workspace which are sampled experimentally and the third step, the pose sampling procedure in which the robot drives the ECM to these effective poses. A full cubic polynomial regression model is adopted based on simulation data to fit the stiffness characteristics. To extract the poses to be sampled in the experiments, two different approaches are evaluated and compared to ensure a well-posed identification. The identification process on the hardware is performed by using Cartesian impedance and inverse kinematics control in combination to comply with the physical constraints imposed by the ECM.

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Section: B Model-free Designmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Method to Identify the Nonlinear Stiffness Characteristics of an Elastic Continuum Mechanism

Deutschmann

Liu

Dietrich

et al. 2018

IEEE Robot. Autom. Lett.

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A nonlinear Timoshenko beam formulation for modeling a tendon‐driven compliant neck mechanism

Eugster

Deutschmann²

2018

Proc Appl Math and Mech

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In this paper, we consider the dynamical behavior of a tendon-driven compliant neck mechanism which is used to actuate the head of a humanoid robot as proposed by [1,2]. The neck is realized as a silicone block mounted onto the robot's torso. At the top end of the silicone block an aluminum plate interconnects the compliant neck with the head. At the same plate, tendons are attached whose actuation causes the soft and flexible block to deform thereby inducing a motion of the robot's head. For workspace design and control of the head's trajectory, a mechanical model is required which appropriately describes the entire neck-head system. We present a dynamic model of the system in which the silicone block and the head are modeled as a planar nonlinear Timoshenko beam and a rigid body, respectively. The tendon actuations are included as external configuration-dependent forces.The motion of the system is described in the three-dimensional Euclidean vector space E 3 with origin O and right-handed orthonormal coordinate frame e I i ∈ E 3 , i = {x, y, z} and takes place exclusively in the e I x -e I z -plane, see Fig. 1b. The cartesian coordinate representation of a vector a ∈ E 3 in an arbitrary orthonormal B-system rotated against the I-system is denotedThe neck made out of silicone is modeled as a planar nonlinear Timoshenko beam. According to the Timoshenko beam assumptions, the motion of the three-dimensional continuum can be described merely by the motion of a centerline and the rotations of plane rigid cross-sections attached to every point of the centerline. The centerline r = r(s, t) ∈ E 3 is a plane curve at time t parameterized by s = [0, L] ⊂ R being the arclength of the undeformed beam with length L. The cross-sections of the beam are represented by the cross-section-fixed frames e C i = e C i (s, t) ∈ E 3 , i = {x, y, z} continuously varying along the centerline and in time. The beam is fixed to the ground such that r(0, t) = 0 and e C i (0, t) = e I i , i = {x, y, z}. The inertia properties of the beam ρA and ρJ yy are the mass and moment of inertia density per unit arclength s, respectively. On top of the beam at s = L a rigid and massless plate with a width of 2b is attached as depicted in Fig. 1c. In P and R two massless tendons are connected to the plate. Both tendons are redirected by a pulley and subjected at their ends to the tensile forces λ l ≥ 0 and λ r ≥ 0, respectively. The head is modeled as a rigid body with center of mass (CoM) S, mass m, moment of inertia J and is rigidly connected to the beam in r(L, t) such that the head-fixed frame e H i (t) := e C i (L, t), i = {x, y, z}. The centerline r and the orthogonal transformation matrix A IC relating the respective coordinates according to I a = A IC C a are determined by the real-valued generalized position functions x = x(s, t), z = z(s, t) and θ = θ(s, t), i.e. I r(s, t) =   x(s, t) 0 z(s, t)   , A IC (s, t) =   cos θ(s, t) 0 sin θ(s, t) 0 1 0 − sin θ(s, t) 0 cos θ(s, t)   .(1)

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Pfanne

2022

Springer Tracts in Advanced Robotics

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A structurally flexible humanoid spine based on a tendon-driven elastic continuum

Cited by 32 publications

References 11 publications

A Method to Identify the Nonlinear Stiffness Characteristics of an Elastic Continuum Mechanism

A Method to Identify the Nonlinear Stiffness Characteristics of an Elastic Continuum Mechanism

A nonlinear Timoshenko beam formulation for modeling a tendon‐driven compliant neck mechanism

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