Full paper Minimizing Energy Consumption in Hexapod Robots

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690 P. Gonzalez de Santos et al. / Advanced Robotics 23 (2009) 681–704Step 7. Compute joint speed ωi ∗ with (22).Step 8. Compute the total energy during half a locomotion cycle with (25), whereT = T cycle /2.4.2. Kinematic Model of the HexapodSection 1 mentioned that the main aim of this work is to configure an energyefficientwalking robot for humanitarian demining activities. This robot model isconsidered herein for simulation purposes. The mechanical and geometric parametersof SILO-6 [15, 16] are defined in Fig. 4 and summarized in Table 1. With thoseparameters, a wire model of the robot can be obtained as illustrated in Fig. 5. Theasterisk represents the location of the COG L of each link. The COG of the body,COG B , is assumed to be at the geometric center of the body. With this model, wecompute the position of the overall COG of the robot, COG R , as well as the forcesand moments acting on it, which depend on the motion of the feet.The foot positions have been designed to minimize the accelerations and, thus,to reduce the dynamic effects. The foot trajectory for each foot in an external referenceframe will consists of a straight trajectory for the foot in its support phase anda transfer trajectory composed of three subtrajectories: a circular trajectory to risethe foot, a straight trajectory to move the foot forward and a circular trajectory toTable 1.Main SILO-6 featuresBodydimensions (m)length L B 0.88front/rear width D 0.38middle width 0.63height 0.26stroke pitch P x 0.365mass (kg) 28.2speed (m/s) 0.05Leglinklength(m)a 1 0.084a 2 0.250a 3 0.250stroke (R x ) (m) 0.25mass (kg) 4.3foot speed (m/s)transfer phase 0.140support phase 0.05Robottotal mass (kg) 54See Fig. 4 for parameter definitions.
P. Gonzalez de Santos et al. / Advanced Robotics 23 (2009) 681–704 691Figure 5. Wire model of the hexapod. Foot positions are indicated in dark circles. The COG of everylink is indicated with an asterisk.place the foot on the ground (Fig. 6b). With these trajectories, we guarantee that footaccelerations at foot takeoff and landing are minimized. Figure 6 plots the foot trajectoryin both the body reference frame (Fig. 6a) and the external reference frame(Fig. 6b). Note that the foot trajectory in the body reference frame is transformedto joint trajectories by using the leg kinematic model described in the Appendix.Applying these joint trajectories into the hexapod’s controller (see a superpositionof robot poses in Fig. 7), the inertial forces and moments acting in the COG R arecomputed.It is worth clarifying that of the energy expended in the walking mechanism(stand, traction, leg swing and head loss), the contribution of the leg swing is insignificant.Every leg in its stand phase must support about one-third of the robot’sweight, while a leg in the swing phase does not support any load. That means thelegs in the swing phase do not expend energy in comparison to the legs in the standphase. Moreover, all the legs in the swing phase expend quite the same energy;therefore, the difference between two foothold solutions is basically the differencebetween their support phases. From the theoretical standpoint, there is, of course,a slight difference in the energy consumed for placing a foot in different points atthe end of the swing phase, but they are quite close to each other and a swing phaseis an unload motion, so this energy can be neglected. Additionally, the algorithmrelies on an optimization method and the model must be kept significant enough,but yet small to be computationally efficient. This is the reason that in our modelwe discard the energy consumed in the swing legs.
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