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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
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