walking styles shown in Figure 7, the energy consumption increases at a higher rate as the gain increases. This indicates that this group of spinal movements leads to inefficient walking when the spinal joints are allowed to bend more. Interestingly, when we compare Figure 5 with Figure 7, we observe the tendency that for the walking 100 0 400 Style 12 200 100 0 100 400 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Gain (h) Style 16 100 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Gain (c) Style 11 300 200 100 0 Style 13 200 200 400 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Gain (e) 300 0 Energy (J) Energy (J) 100 400 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Gain (g) Style 8 200 300 0 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Gain (b) 300 0 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Gain (d) 300 100 400 Energy (J) Energy (J) Style 7 200 200 0 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Gain (a) 300 300 Style 4 400 Energy (J) 100 Style 2 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Gain (f) Style 15 400 Energy (J) 200 400 400 Energy (J) 300 0 Energy (J) Style 1 Energy (J) Energy (J) 400 styles that correspond to a high level of upper torso swinging motion [see, e.g., Figure 7(b)-(e), (i), and (j)], relatively more energy (more than 220 J) is required to complete the walking task than when the robot is walking with other styles of spinal movements. This indicates that it is inefficient to walk with too much swinging of the upper torso. 300 200 100 0 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Gain (i) 300 200 100 0 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Gain (j) Figure 7. The effect of spine curvature gain on mechanical energy consumption of a humanoid robot (the ten energy-inefficient styles). For comparison, the energy consumption of its rigid-torso counterpart (when the gain is zero) is shown as a solid horizontal line. june 2013 * IEEE ROBOTICS & AUTOMATION MAGAZINE * 77