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Research Papers

Empirical Potential Functions for Driving Bioinspired Joint Design

[+] Author and Article Information
Matthew Bender

Department of Mechanical Engineering,
Virginia Tech,
Blacksburg, VA 24060
e-mail: mattjb8@vt.edu

Aishwarya George

Department of Electrical and
Computer Engineering,
Virginia Tech,
Blacksburg, VA 24060
e-mail: aishwa2@vt.edu

Nathan Powell

Department of Mechanical Engineering,
Virginia Tech,
Blacksburg, VA 24060
e-mail: nrpowell@vt.edu

Andrew Kurdila

W. Martin Johnson Professor
Fellow ASME
Department of Mechanical Engineering,
Virginia Tech,
Blacksburg, VA 24060
e-mail: kurdila@vt.edu

Rolf Müller

Professor
Department of Mechanical Engineering,
Virginia Tech,
Blacksburg, VA 24060;
SDU-VT International Lab,
Shandong University,
Jinan, Shandong 250100, China
e-mail: rolf.mueller@vt.edu

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received February 13, 2018; final manuscript received September 6, 2018; published online October 31, 2018. Assoc. Editor: Jongeun Choi.

J. Dyn. Sys., Meas., Control 141(3), 031004 (Oct 31, 2018) (11 pages) Paper No: DS-18-1075; doi: 10.1115/1.4041446 History: Received February 13, 2018; Revised September 06, 2018

Bioinspired design of robotic systems can offer many potential advantages in comparison to traditional architectures including improved adaptability, maneuverability, or efficiency. Substantial progress has been made in the design and fabrication of bioinspired systems. While many of these systems are bioinspired at a system architecture level, the design of linkage connections often assumes that motion is well approximated by ideal joints subject to designer-specified box constraints. However, such constraints can allow a robot to achieve unnatural and potentially unstable configurations. In contrast, this paper develops a methodology, which identifies the set of admissible configurations from experimental observations and optimizes a compliant structure around the joint such that motions evolve on or close to the observed configuration set. This approach formulates an analytical-empirical (AE) potential energy field, which “pushes” system trajectories toward the set of observations. Then, the strain energy of a compliant structure is optimized to approximate this energy field. While our approach requires that kinematics of a joint be specified by a designer, the optimized compliant structure enforces constraints on joint motion without requiring an explicit definition of box-constraints. To validate our approach, we construct a single degree-of-freedom elbow joint, which closely matches the AE and optimal potential energy functions and admissible motions remain within the observation set.

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Figures

Grahic Jump Location
Fig. 1

Estimated skeleton reprojected into a Camera View. White lines and points are the skeletal reprojections. Yellow + marks are the original image features.

Grahic Jump Location
Fig. 2

Experimental image (right) and example compliant joint (left). We isolate the elbow motion from our kinematics data and optimize the geometry of the compliant joint.

Grahic Jump Location
Fig. 3

Empirical potential constructed over samples on the unit circle. Configurations associated with low potential energy (blue) occur near the sampled data (magenta dots) while configurations associated with high potential energy (yellow) occur away from the samples: (a) top view and (b) isometric view.

Grahic Jump Location
Fig. 4

Wrist motion is observed from the humerus frame. Dark blue points are the original data, light blue points are the data projected onto SO(2) which is the Lie group of proper rotations that, roughly speaking, are parameterized by one angle. The data on SO(2) are used to identify joint angles, which are used to learn the empirical potential.

Grahic Jump Location
Fig. 5

Compliant joint design. Link 0 is the articulated link and links 1 to L are the beam elements which approximate the empirical potential function.

Grahic Jump Location
Fig. 6

Three compliant articulated mechanisms designed from synthetic or experimental data. Left: two beam specimen generated from synthetic data. Middle: 3 beam specimen generated from synthetic data. Right: three beam specimen generated from motion capture data of the elbow shown with articulated link attached. The articulated link is removable and can be installed on each of the test pieces. All parts were 3D printed using a Monoprice Maker Select V2 printer with a layer resolution of 0.2 mm.

Grahic Jump Location
Fig. 7

Loading condition for beam 1. When the articulated link contacts beam 1, the load applied to beam 1, PB1 acts perpendicular to the articulated link.

Grahic Jump Location
Fig. 8

Modulus of elasticity test. The computer controls the dynamixel. The Arduino and Keyes234 are reads the load cell. The height gauge measures the beam deflection.

Grahic Jump Location
Fig. 9

Force–displacement functions for linear beam testing. Five different thickness beams were tested to generate load displacement functions. Beam thicknesses tested were: 0.068 in (blue), 0.085 in (red), 0.104 in (gray), 0.124 in (yellow), and 0.144 in (green). As shown in the figure, all of the force–deflection curves are strongly linear. Therefore, we can assume linear beam bending through these ranges of deflection.

Grahic Jump Location
Fig. 10

Load–deflection and energy–deflection functions for the compliant mechanism designed using synthetic data and 3 beam elements. The AE energy function (black line) fits over the range of sample points. The optimized load and energy (blue) are close to the experimental load and energy (red with “+” markers). The experimental values are within the confidence bounds (gray dashed), which are computed assuming ±100 μm tolerance on the optimized beam height and offsets: (a) two beam synthetic data, (b) three beam synthetic data, and (c) three beam experimental data.

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