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Table 4 Reproducibility of estimated parameters (desired image of string: J)

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

Each parameter Trial no.0 Trial no.1 Trial no.2 Trial no.3 Trial no.4
Spring constant \(k_{s}\) (N/m/kg) \(9.0 \times 10^{5}\) \(4.9 \times 10^{5}\) \(4.2\times 10^{5}\) \(5.2\times 10^{4}\) \(2.5\times 10^{5}\)
Damping coefficient \(c_{s}\) (Ns/m/kg) 57 19.1 3.3 4.3 4.1
Hinge spring constant \(k_{h}\) (Nm/rad/kg) 0.57 7.0 2.7 \(8.0\times 10^{-3}\) \(1.3\times 10^{-2}\)
Hinge damping coefficient \(c_{h}\) (Nms/rad/kg) \(2.5 \times 10^{-2}\) \(2.8 \times 10^{-2}\) \(5.5\times 10^{-2}\) \(8.5\times 10^{-4}\) \(9.8\times 10^{-7}\)
Air resistance proportional coefficient \(C_{c1}\) (Nms/rad/kg) 0.52 \(1.2 \times 10^{-4}\) \(1.0 \times 10^{-4}\) \(1.8 \times 10^{-4}\) \(1.8 \times 10^{-4}\)
Air resistance squared proportional coefficient \(C_{c2}\) (Nms/rad/kg) 0.26 0.51 \(6.9\times 10^{-4}\) 1.1 \(1.7\times 10^{-4}\)
Hinge spring constant of grasp point \(k_{ph}\) (Nm/rad/kg) 0.27 \(6.4 \times 10^{-3}\) \(8.1 \times 10^{-3}\) 5.0 \(7.5 \times 10^{-3}\)
Hinge damping coefficient of grasp point \(c_{ph}\) (Nms/rad/kg) \(7.3\times 10^{-3}\) \(9.6\times 10^{-5}\) \(1.4\times 10^{-2}\) \(7.7\times 10^{-5}\) \(4.6\times 10^{-3}\)
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