Full paper Minimizing Energy Consumption in Hexapod Robots

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700 P. Gonzalez de Santos et al. / Advanced Robotics 23 (2009) 681–704project. Nevertheless, the most important result is to quantify the range of energyconsumption we can save by applying minimization methods.7. ConclusionsEnergy optimization is an important topic for autonomous robots, because it is theway of increasing duty time for missions without modifying the power supply onboard the robot.This paper studies the energy required for six-legged robots using alternatingtripodgaits, the fastest gait for hexapods, and derives a method to minimize theenergy for one tripod. Minimization of consecutive tripods minimizes the energythroughout an entire trajectory. The method works on any kind of irregular terrain,although some simple models for irregular terrain have been used in the examplespresented above.The method requires some advance knowledge of the terrain; therefore, it isapplicable to robots capable of obtaining an elevation map of the terrain. Energyexpenditure was computed by using the SILO-6 walking robot as a model. This robotis designed for humanitarian demining missions and uses a system to obtain anelevation map of the terrain in front of the robot.This paper provides some figures for the energy saved in such a robot and researchis ongoing on the computation of the method for real-time applications.Energy consumed by electronics (computers, drivers, analog I/O, etc.) constitutes alarge source of energy loss. Diminishing this energy loss is a technical concern thatmust always be taken into account.AcknowledgementsThis work was supported by the Spanish Ministry of Education and Science throughCICYT grant DPI2004-05824.References1. Q. Huang, T. Hase and K. Ono, Optimal trajectory planning method using inequality state constraintfor biped walking robot with upper body mass, Special Issue on New Trends of Motion andVibration Control, J. Syst. Des. Dyn. (JSME Dyn. Meas. Control Div.) 1, 168–179 (2007).2. V. V. Lapshin, Energy consumption of a walking machine. Model estimations and optimization,in: Proc. 7th Conf. on Advanced Robotics, San Feliu de Guixols, pp. 420–425 (1995).3. D. E. Orin and S. Y. Oh, Control of force distribution in robotic mechanisms containing closekinematic chains, J. Dyn. Syst. Meas. Control 103, 134–141 (1981).4. M. A. Nahon and J. Angeles, Minimization of power losses in cooperating manipulators, J. Dyn.Syst. Meas. Control 114, 213–219 (1992).5. D. W. Marhefka, Gait planning for power minimization in walking machines, Master’s Thesis,Ohio State University (1996).6. D. W. Marhefka and D. E. Orin, Gait planning for energy efficiency in walking machines, in: Proc.IEEE Int. Conf. on Robotics and Automation, Alburquerque, NM, pp. 474–480 (1997).
P. Gonzalez de Santos et al. / Advanced Robotics 23 (2009) 681–704 7017. M. F. Silva, J. A. Tenreiro Machado and A. M. Endes Lopes, Energy analysis of multi-leggedlocomotion systems, in: Proc. 4th Conf. on Climbing and Walking Robots, Karlsruhe, pp. 143–150(2001).8. T. Zelinska, Efficiency analysis in the design of walking machines, J. Theor. Appl. Mech. 38,693–708 (2000).9. V. V. Zhoga, Computation of walking robots movement energy expenditure, in: Proc. IEEE Int.Conf. on Robotics and Automation, Leuven, pp. 163–168 (1998).10. J. E. Bares and D. S. Wettergreen, Dante II: technical description, results and lesson learned, Int.J. Robotics Res. 18, 621–649 (1999).11. J. Bares and W. Whittaker, Configuration of autonomous walkers for extreme terrain, Int. J. RoboticsRes. 12, 535–559 (1993).12. Nomad: Lunar Rover Navigation, http://www.cs.cmu.edu/∼lri/nav97.html (1997).13. C. Ye and J. Borenstein, A new terrain mapping method for mobile robot obstacle negotiation, in:Proc. UGV Technology Conf. at the 2003 SPIE AeroSense Symp., San Jose, CA, pp. 2561–2562(2003).14. P. Pfaff and W. Burgard, An efficient extension of elevation maps for outdoor terrain mapping, in:Proc. 5th Int. Conf. on Field and Service Robotics, Port Douglas, QLD, pp. 165–176 (2005).15. P. Gonzalez de Santos, J. A. Cobano, E. Garcia, J. Estremera and M. A. Armada, A six-leggedrobot-based system for humanitarian demining missions, Mechatronics 17, 417–430 (2007).16. SILO-6 website, http://www.iai.csic.es/users/silo617. S. M. Song and K. J. Waldron, Machines that Walk: the Adaptive Suspension Vehicle. MIT Press,Cambridge, MA (1989).18. M. Kaneko, S. Tachi, K. Tanie and M. Abe, Basic study on similarity in walking machines from apoint of energetic efficiency, IEEE J. Robotics Automat. 3, 19–30 (1987).19. J. Nishii, K. Ogawa and R. Suzuki, The optimal gait pattern in hexapods based on energetic efficiency,in: Proc. 3rd Int. Symp. on Artificial Life and Robotics, Beppu, Vol. 1, pp. 106–109 (1998).20. S. Ma, Time optimal control of manipulators with limit heat characteristics of actuator, Adv. Robotics16, 309–324 (2002).21. P. Gonzalez de Santos, E. Garcia and J. Estremera, Improving walking-robot performances byoptimizing leg distribution, Autonomous Robots 23, 247–258 (2007).22. W. Y. Jiang, A. M. Liu and D. Howard, Foot-force distribution in legged robots, in: Proc. 4th Int.Conf. on Climbing and Walking Robots, Karlsruhe, pp. 331–338 (2001).23. P. Gonzalez de Santos, J. Estremera and E. Garcia, Optimizing leg distribution around the body inwalking robots, in: Proc. IEEE Int. Conf. on Robotics and Automation, Barcelona, pp. 3218–3223(2005).24. R. Kurame, K. Yoneda and S. Hirose, Feedforward and feedback trot gait control for quadrupedwalking vehicle, Autonomous Robots 12, 157–172 (2002).25. J. C. Lagarias, J. A. Reeds, M. H. Wright and P. E. Wright, Convergence properties of the Nelder–Mead simplex method in low dimensions, SIAM J. Optimizat. 9, 112–147 (1998).AppendixThis Appendix presents the leg kinematics used for simulation and control purposes(Fig. A.1). The direct kinematic relationships consist in envisioning the position(x i ,y i ,z i ) T of foot i as a function of the joint components (θ i1 ,θ i2 ,θ i3 ) T :(x i ,y i ,z i ) T = T DIR (θ i1 ,θ i2 ,θ i3 ), (A.1)
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