Nonlinear Dynamics

, Volume 83, Issue 3, pp 1275–1301 | Cite as

Optimization of energy efficiency of walking bipedal robots by use of elastic couplings in the form of mechanical springs

  • Fabian Bauer
  • Ulrich Römer
  • Alexander Fidlin
  • Wolfgang Seemann
Original Paper


This paper presents a method to optimize the energy efficiency of walking bipedal robots by more than 50 % in a speed range from 0.3 to \(2.3\,\,\hbox {m}/\hbox {s}\) using elastic couplings—mechanical springs with movement speed independent parameters. The considered robot consists of a trunk, two stiff legs and two actuators in the hip joints. It is modeled as underactuated system to make use of its natural dynamics and feedback controlled with input–output linearization. A numerical optimization of the joint angle trajectories as well as the elastic couplings is performed to minimize the average energy expenditure over the whole speed range. The elastic couplings increase the swing leg motion’s natural frequency, thus making smaller steps more efficient which reduce the impact loss at the touchdown of the swing leg. The process of energy turnover is investigated for the robot with and without elastic couplings. Furthermore, the influence of the elastic couplings’ topology, its degree of nonlinearity, the mass distribution, the joint friction, the coefficient of static friction and the selected actuator is analyzed. It is shown that the optimization of the robot’s motion and elastic coupling toward energy efficiency leads to a slightly slower convergence rate of the controller, yet no loss of stability and a lower sensitivity with respect to disturbances. The optimal elastic coupling discovered by the numerical optimization is a linear torsion spring between the legs.


Bipedal robot Dynamic walking Nonlinear feedback control Optimization Energy efficiency Elastic coupling Mechanical spring 


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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Fabian Bauer
    • 1
  • Ulrich Römer
    • 1
  • Alexander Fidlin
    • 1
  • Wolfgang Seemann
    • 1
  1. 1.Institute of Engineering MechanicsKarlsruhe Institute of TechnologyKarlsruheGermany

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