# Characterization of Control-Dependent Variable Stiffness Behavior in Discrete Muscle-Like Actuators
## 1 Introduction
More recent work in SEA's has led to the development of Variable Stiffness Actuators (VSA), or Variable Impedance Actuators (VIA's). [PERSON] et al. provide a definition for and discussion of the range of VSA's and many of their characteristics in his overview of Variable Stiffness Actuators [5]. These actuators have numerous advantages (some of which have already been mentioned) including: compliance, the ability to reject disturbances due to the nature of their system dynamics, and the ability to be used in unpredictable environments. In his paper, [PERSON] also categorizes the different ways that variable stiffness is achieved in the many designs that have been developed. The three main categories are: active impedance control, inherent compliance and inherent damping, and inertial actuators. The actuator outlined in this work falls under the first and second categories. The actuator itself is defined by inherent variable stiffness and it can be actively controlled to vary this stiffness even more. Discrete actuators have been implemented in the past with platforms seeking to control vibration and antenna shaping, see [6, 7, 8, 9, 10]. The main types of discrete actuators used in those applications  
Figure 1: Modular, discrete muscle-like variable-stiffness actuator. Figure 2: Compliance is necessary for allowing different contraction patterns for parallel motor units. See how in the third figure violation has occurred and is resolved by the addition of a compliant spring element in the fourth figure: (**a**) rigid connection for active units; (**b**) rigid connection for non-active units; (**c**) breaks laws of mechanics of materials; and (**d**) addition of compliant element. were piezoelectric, but the theoretical work done in this paper is able to be applied to many different types of discrete actuators. Discrete actuators are able to emulate human skeletal muscle with several distinctive characteristics. The first is _compliance_, which is a necessary characteristic in designing the actuator for applications where human-robot interaction is needed [11]. The second characteristic is _redundancy_, which is important because it achieves something that is novel and desirable for actuators, keeping the robot operational despite a component failure, which is an important characteristic when considering actuators that will be used in remote areas making repair difficult or impossible. The third characteristic is a _modular construction_; this is significant because the cost for expanding the actuator to new configurations or larger applications is low and the complex nature of redesigning an actuator for larger applications can be simplified if a framework for one of these actuators is already in place. This article seeks to provide such a framework for discrete actuators. A discussion on the actuator design will lead into showing the variable stiffness behavior seen most vividly in simulation, after which the capability of the SEA model will be shown, leading into a discussion on the control law developed through simulation, and finally an experiment with data showing the variable stiffness behavior.