Fig. 2: Schematic depiction of the elasticity and plasticity framework.
From: Learning plastic matching of robot dynamics in closed-loop central pattern generators
a, Short-term elastic feedback (top) and long-term plasticity (bottom). Elastic feedback (green) mitigates stochastic short-term perturbations (red), such as pot holes, that disturb the system (spring) from its desired state (dashed line). Elastic activity is reversible and only active when a perturbation is present, just as a spring only deflects as long as an external force is active and then returns to its initial state. Plasticity (yellow) changes the system behaviour permanently to adapt to long-term active stimuli from the environment. If the same perturbation is frequently present, the system adapts to the perturbation. In our example the spring adapts its set point (spring length, dashed line) and stiffness (spring thickness). In this way, an initial desired system state that might be encoded in the initial control design can be adapted to better deal with perturbations throughout its life span, as well as changing environments. After plastic adaptation the spring deflects less (green, bottom right). b, Control structure of Morti. kp, kd and ki are the joint controller gains; G(s) is the plant transfer function in Laplace space s. c, Flowchart of the matching approach. The elastic feedback activity mitigates short-term perturbations through sparse contact feedback from the FootTile contact sensors. We measured the amount of elastic feedback activity as a proxy for the mismatching of dynamics. Over a longer time window, the optimizer minimizes the elastic feedback activity to plastically match the control pattern of the CPG to Morti’s natural dynamics. F, front; L, left; H, hind; R, right. Colour representations are similar to those in Fig. 5b. d, Diagram of a step cycle in phase space (ϕ). The segments are colour-coded by feedback mechanism: late touchdown (red) later than the desired touchdown time (δoverSwing), late toeoff (yellow) later than the desired toeoff time (δϕ,knee), early toeoff (green) and early touchdown (purple). The stance phase from touchdown to toeoff is shaded blue.
