Adaptive Natural Oscillator to exploit natural dynamics for energy efficiency

Abstract

We present a novel adaptive oscillator, called Adaptive Natural Oscillator (ANO), to exploit the natural dynamics of a given robotic system. This tool is built upon the Adaptive Frequency Oscillator (AFO), and it can be used as a pattern generator in robotic applications such as locomotion systems. In contrast to AFO, that adapts to the frequency of an external signal, ANO adapts the frequency of reference trajectory to the natural dynamics of the given system. In this work, we prove that, in linear systems, ANO converges to the system's natural frequency. Furthermore, we show that this tool exploits the natural dynamics for energy efficiency through minimization of actuator effort. This property makes ANO an appealing tool for energy consumption reduction in cyclic tasks; especially in legged systems. We also extend the proposed adaptation mechanism to high dimensional and general cases; such as n-DOF manipulators. In addition, by investigating a hopper leg in simulation, we show the efficacy of ANO in face of dynamical discontinuities; such as those inherent in legged locomotion. Furthermore, we apply ANO to a simulated compliant robotic manipulator performing a periodic task where the energy consumption is drastically reduced. Finally, the experimental results on a 1-DOF compliant joint show that our adaptive oscillator, despite all practical uncertainties and deviations from theoretical models, exploits the natural dynamics and reduces the energy consumption.

Natural Motion for Energy Saving in Robotic and Mechatronic Systems

“…M. Khoramshahi et al and R. Nasiri et al present in References [83,105] a linear and a non-linear adaptive natural oscillator, ANO and NANO, respectively. These tools are capable of tuning the frequency and the shape of cyclic motions for energy efficiency and ensure optimality and convergence.…”

“…Moreover, they are built upon the adaptive frequency oscillators but, in contrast to AFO that adapts to the frequency of an external signal, ANO adapts the frequency of reference trajectory to the natural dynamics of the system (Figure 8). In Reference [105], the efficiency of ANO is shown in the simulations of a hopper leg and of a compliant robotic manipulator performing a cyclic task. Furthermore, experimental results of a 1-DOF joint with variable compliance (Figure 9) show the feasibility of the approach, exploiting the natural dynamics and reducing the consumed energy.…”

“…Three robotic models are investigated in simulation: the pendulum, the adaptive toy and the hopper-leg, showing the feasibility of the proposed approach to achieve energy efficiency. [105]. The linear spring acts as a parallel rotational spring at the joint and its stiffness can be tuned by controlling the ball screw mechanism.…”

Untethered quadrupedal hopping and bounding on a trampoline

“…(11) with Eq. (12) indicates that the common negative-feedback control law can increase the amplitude of the oscillation, a scenario that hinders the stabilization of the robot. Equation 10can then be used to reduce the amplitude of the oscillation by neutralizing the item -2k s ðy c Lþ L 2 b -L 2 Þ; in this manner, the amplitude of the oscillation can be contained.…”

“…Apart from model-based methods, biologically inspired methods can offer other perspectives on efficient jumping. Khoramshahi et al [12,13] and Buchli et al [14,15] proposed different frequency adaptive oscillators to automatically converge to the resonance frequency of a hopping system with springy legs, and their proposed scheme resulted in reduced energy cost. However, majority of existing proposed controllers are designed for torquecontrolled robots, which are unsuitable for small-sized prototype tests.…”