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Table 2 Summary of total input energy

From: Energy-efficient control of a screw-drive pipe robot with consideration of actuator’s characteristics

S f (m) t f (s) I: \(\int _0^{{t_{\mathrm{f}}}} {{V_{\mathrm{a}}}{i_{\mathrm{a}}}} \mathrm{d}t\) II: \(\int _0^{{t_{\mathrm{f}}}} {{i_{\mathrm{a}}}^2{R_{\mathrm{a}}}} \mathrm{d}t\) III: \(\int _0^{{t_{\mathrm{f}}}} {{V_{\mathrm{a}}}{i_{\mathrm{a}}}} \mathrm{d}t\)
0.3 m 4 14.79 (14.02) 14.37 15.65
1.2 m 10 76.09 (71.46) 75.28 85.53
2.0 m 15 134.91 (126.50) 132.83 155.18
Figure 8b   3.10 3.31 14.12
Figure 11a   23.30 (19.70) 21.65 23.91
Figure 11b   83.82 N/A 86.40
  1. I refers to the minimum energy control that considers \(R_{\mathrm{a}}\) and \(R_{\mathrm{h}}\), while the numbers in the bracket denote the results that \(R_{\mathrm{h}} \rightarrow \infty\); II refers to the loss minimization control that only considers \(R_{\mathrm{a}}\); III refers to the computed torque control that considers \(R_{\mathrm{a}}\) and \(R_{\mathrm{h}}\)
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