Optimal elastic coupling in form of one mechanical spring to improve energy efficiency of walking bipedal robots

Abstract

This paper presents a method to optimize the energy efficiency of walking bipedal robots by more than 80 % in a speed range from 0.3 to 2.3 m/s using elastic couplings-mechanical springs with movement speed independent parameters. The considered planar robot consists of a trunk, two two-segmented legs, two actuators in the hip joints, two actuators in the knee joints and an elastic coupling between the shanks. It is modeled as underactuated system to make use of its natural dynamics and feedback controlled via 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 in detail for the robot with and without elastic coupling between the shanks. Furthermore, the influences of the elastic couplings' topology and of joint friction are analyzed. It is shown that the optimization of the robot's motion and elastic coupling towards energy efficiency leads to a slightly slower convergence rate of the controller, yet no loss of stability but a lower sensitivity with respect to disturbances. The optimal elastic coupling discovered via numerical optimization is a linear torsion spring with transmissions between the shanks. A design proposal for this elastic coupling-which does not affect the robot's trunk and parallel shank motion and can be used to enhance an existing robot-is given for planar as well as spatial robots.

Hybrid Zero Dynamics Control for Bipedal Walking with a Non-Instantaneous Double Support Phase

“…The necessary condition for the asymptotic stability of the limit cycle's periodic solution is 0 < Λ < 1, which is fulfilled in all but one of the investigated scenarios. In comparison to our extended HZD control concepts, the gait with an instantaneous DSP mostly results in a Floquet multiplier 0.8 < Λ < 1, according to the study in [29]. The improved stability property is in fact one of the most important advantages of including a non-instantaneous DSP into the periodic gait.…”

“…After solving these low dimensional dynamics for the periodic orbits, the full system states can be reconstructed using the predefined reference trajectories. A major advantage is that the passive dynamics in the controlled system can be utilized to create highly efficient gaits [28][29][30] via a priori numerical optimization. The objective is to minimize the energy consumption of locomotion which is evaluated by the dimensionless cost of transport := supp /(ℓ step • ), i. e. the supplied energy supp during one total step divided by the step length ℓ step and the weight force .…”

Energy Consumption Minimizing for Electro-HydraulicServo Driving Planar Parallel Mechanism by Optimizing the Structure Based on Genetic Algorithm

“…The experiment shows that the robot with elastic load suspension mechanism consumed up to 24% less power than with a rigidly attached load. Bauer et al [11], [12] proposed elastic couplings mechanical springs to optimize the energy efficiency of walking bipedal robots by more than 80 % in a speed range from 0.3 to 2.3m/s. In the study of energy consumption of quadruped robots [13], the reasonable gait parameters are determined to reduce energy consumption significantly.…”