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Table 3 Estimated parameter values (desired image of string shape:d)

From: Dynamic manipulation of unknown string by robot arm: realizing momentary string shapes

Each parameter

Initial parameter

1st time estimation

2nd time estimation

Spring constant \(k_{s}\) (N/m/kg)

\(9.0 \times 10^{3}\)

\(1.0\times 10^{5}\)

\(5.2\times 10^{4}\)

Damping coefficient \(c_{s}\) (Ns/m/kg)

0.13

0.45

6.2

Hinge spring constant \(k_{h}\) (Nm/rad/kg)

\(8 .0\times 10^{-3}\)

\(6.7\times 10^{-2}\)

\(4.10\times ^{-2}\)

Hinge damping coefficient \(c_{h}\) (Nms/rad/kg)

\(3.0 \times 10^{-7}\)

\(8.6\times 10^{-3}\)

\(6.8\times 10^{-3}\)

Air resistance proportional coefficient \(C_{c1}\) (Nms/rad/kg)

\(1.0 \times 10^{-4}\)

1.3

0.75

Air resistance squared proportional coefficient \(C_{c2}\) (Nms/rad/kg)

\(1.0 \times 10^{-4}\)

0.28

\(3.2\times 10^{-4}\)

Hinge spring constant of grasp point \(k_{ph}\) (Nm/rad/kg)

\(1.0 \times 10^{-3}\)

5.0

5.0

Hinge damping coefficient of grasp point \(c_{ph}\) (Nms/rad/kg)

\(1.1 \times 10^{-6}\)

\(3.0\times 10^{-4}\)

\(7.5\times 10^{-5}\)

Matching rate E

0.52

0.62