Rigid haptic devices enable humans to physically interact with virtual environments, and the range of impedances that can be safely rendered using these rigid devices is quantified by the Z-Width metric. Series elastic actuators (SEAs) similarly modulate the impedance felt by the human operator when interacting with a robotic device, and, in particular, the robot's perceived stiffness can be controlled by changing the elastic element's equilibrium position.

Many robots are composed of interchangeable modular components, each of which can be independently controlled, and collectively can be disassembled and reassembled into new configurations. When assembling these modules into an open kinematic chain, there are some discrete choices dictated by the module geometry; for example, the order in which the modules are placed, the axis of rotation of each module with respect to the previous module, and/or the overall shape of the assembled robot.

There has been significant research aimed at leveraging programmable robotic devices to provide haptic assistance or augmentation to a human user so that new motor skills can be trained efficiently and retained long after training has concluded. The success of these approaches has been varied, and retention of skill is typically not significantly better for groups exposed to these controllers during training. These findings point to a need to incorporate a more complete understanding of human motor learning principles when designing haptic interactions with the trainee.

Robots are increasingly designed to physically interact with humans in unstructured environments, and as such must operate both accurately and safely. Leveraging compliant actuation, typically in the form of series elastic actuators (SEAs), can guarantee this required level of safety. To date, a number of frequency domain techniques have been proposed which yield effective SEA torque and impedance control; however, these methods are accompanied by undesirable stability constraints.