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

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

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

This paper presents a method to optimize the en- ergy efficiency of walking bipedal robots by more than 50 % in a speed range from 0.3 to 2.3 m/s using elastic couplings – mechanical springs with movement speed independent pa- rameters. The considered robot consists of a trunk, two stiff legs and two actuators in the hip joints. It is modeled as un- deractuated system to make use of its natural dynamics and feedback controlled with input-output linearization. A nu- merical 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 pro- cess 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 towards energy efficiency leads to a slightly slower conver- gence 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

Optimierung der Energieeffizienz zweibeiniger Roboter durch elastische Kopplungen

In dieser Arbeit wird die Optimierung der Energieeffizienz zweibeiniger Roboter durch den Einsatz elastischer Kopplungen untersucht. Die betrachteten Roboter werden als unteraktuierte Systeme modelliert und mittels Ein-Ausgangs-Linearisierung geregelt. Zur Untersuchung des Einflusses der elastischen Kopplungen auf Energieeffizienz sowie Stabilität und Robustheit werden parallel die Bewegungen der Roboter als auch deren elastische Kopplungen unter Anwendung numerischer Algorithmen optimiert