Exploiting natural dynamics of nonlinear compliance using adaptive oscillators

Compliance became the essential part of locomotion in robotics. Due to ability of storing and releasing energy, compliance can be used for energy efficiency or reducing impact during ground collision and gaining robustness. On the other side, natural/passive dynamics are important because by exploiting such dynamics, energy efficiency will be assured. Therefore it is crucial to understand how compliance changes natural dynamics of a system. After this inspection, natural dynamics exploitation can be more straightforward through developing tools like adaptive oscillators. Such research to exploits natural dynamics of compliant system are reported in [1],[2] and [3]. Intuitively, it is known that using linear compliance will result in efficiency in only one mode. For instance, in mass-spring system for each spring constant, there is only one frequency where system is energy efficient. Using variable compliance is an attempt to overcome this problem and gain efficiency over a range of different setpoints or tasks. Great achievements reported using variable compliance in robotics application in [4] and [5]. Another way to overcome this problem is using nonlinearity. Natural dynamics and their multi-modality of efficiency will be discussed in this paper. It seems muscle-tendon units in biological systems are taking advantage of such nonlinearity in their compliance [6]. An adaptive oscillator based the one in [7] is presented in this work. This oscillator is able to exploit natural dynamics of system by shaping desired trajectory through frequency and phase lag.