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

Abstract

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 m/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 towards 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.

Energy-efficacy comparisons and multibody dynamics analyses of legged robots with different closed-loop mechanisms

“…In the consideration that increasing the size of the Klann is not beneficial according to our characteristics analysis, it is difficult for the small-sized robot to introduce the regeneration system, similar to that of insects. Therefore, a comparison of closed-loop Conventional actuators without brake [55]; muscles in slow motion 2 Actuators with brake (or geared with a high reduction ratio); muscles of insects [51] 3 Actuators with regeneration brake [6,20,57]; Coupling of muscles with the tendon in high speed movements [4,5,7] linkages is considered to be validated enough. On the other hand, the ideal treadmill condition has the limitation in the dynamic aspect of the movement.…”

Simultaneous optimization of gait and design parameters for bipedal robots

“…Subsequently, the first (34), (31) and second integral (32) are approximated via trapezoidal rule T N at the N grid points. With the solution of the HZD, the velocities (27), (15), accelerations (29), (16) and actuator torques (3), (2) are computed. The cost of transport f (x) is approximated by a third application of the trapezoidal rule.…”

“…The system's natural dynamics can evolve due to the underactuation. Energy efficient gaits can be generated via offline optimization of the reference trajectories [1], [2], [10], [13].…”

“…mass distribution, dimensions, stiffnesses). Changes of design parameters affect the optimal gaits and considerably influence efficiency [1], [2], [12], [24]. While some parameters like stiffnesses [25] may be adjusted after assembly, most parameters are fixed.…”

“…A method which can be used during the design of a robot to increase energy efficiency as well as to identify the most critical parameters is simultaneous optimization of gait and design parameters via numerical simulations. In [1], [2], a bilevel optimization of the robot's parameters (stiffnesses) via a gradient-free upperlevel method in combination with a gradient-based lowerlevel for optimal gait generation is proposed. The upper-level optimizes the average energy efficiency of several gaits in a speed range to counteract specialization for one specific speed.…”