Soft actuation in cyclic motions: Stiffness profile optimization for energy efficiency

Abstract

In this paper, we investigate the role of variable stiffness in the reduction of the energy cost for mechanical systems that perform desired tasks. The objective is to assess the use of Variable Stiffness Actuation (VSA) by determining an optimal stiffness profile and the associated energy cost of performing a desired task. For the analysis we consider mechanical systems of n-Degrees of Freedom (DoF), using VSA. We find an analytical solution that expresses the optimal stiffness profile during the task as a function of joint trajectories. This stiffness profile can be either constant or variable in time, and it minimizes a cost function, when performing a desired task. We calculate the cost related to the torque of the system and the additional cost of changing or keeping a stiffness actively constant. Additionally, we discuss some cases for which it is worth to change the stiffness during a task and cases for which a constant stiffness may be better solution. Furthermore, from simulations and experiments we show cases in which using a variable stiffness profile allows cost savings w.r.t. constant stiffness. The use of variable stiffness depends on the task, i.e. on the joint trajectories and their frequency, as well as on the mechanical implementation of the actuator used

Series and Parallel Elastic Actuation: Influence of Operating Positions on Design and Control

“…Elastic robots can provide human safety in working environments [1], [3] and be beneficial in motion assistance [5], [6] and rehabilitation [7]. Elastic actuators can furthermore improve robot efficiency by adapting their own characteristics to the operating state [8], [9], [10], e. g., by matching natural system behavior to cyclic trajectories [11]. Various concepts for actuators incorporating fixed or variable elasticity have been proposed [12] of which most comprise a serial elastic element to couple drive and link compliantly for safe human-robot interaction.…”

Advances in Mechanical Systems Dynamics 2020

“…The serial configuration (adopted for example in References [42,50,79]) provides the actuator with a compliance that can be employed to decrease contact shocks and to reduce force peaks due to impacts, for example, In human-robot interaction [46]. On the other hand, the parallel configuration [65,[80][81][82] results in simpler mechanism and mathematics formulation [78].…”

Natural Motion for Energy Saving in Robotic and Mechatronic Systems

“…The serial configuration (adopted for example in References [42,50,79]) provides the actuator with a compliance that can be employed to decrease contact shocks and to reduce force peaks due to impacts, for example, In human-robot interaction [46]. On the other hand, the parallel configuration [65,[80][81][82] results in simpler mechanism and mathematics formulation [78].…”

“…Another control-based approach to employ stiffness variability for energy efficiency during a task is proposed by A. Velasco et al in Reference [79]. The method aims at determining the optimal stiffness profile of serial springs that minimizes the energy consumption of the mechanical system, performing a given task.…”

“…In some cases, an analytical solution is found to the optimal design problem, avoiding the cost of setting up and solving numerical optimization problems. These papers include References [79,86,96,98,99]. An alternative approach is to tackle the problem with an optimal control theory approach.…”