Exploiting sensorimotor stochasticity for learning control of variable impedance actuators

Abstract

Abstract-Novel anthropomorphic robotic systems increasingly employ variable impedance actuation in order to achieve robustness to uncertainty, superior agility and efficiency that are hallmarks of biological systems. Controlling and modulating impedance profiles such that it is optimally tuned to the controlled plant is crucial to realise these benefits. In this work, we propose a methodology to generate optimal control commands for variable impedance actuators under a prescribed tradeoff of task accuracy and energy cost. In contrast to classical optimal control methods that typically require an accurate analytical plant dynamics model, we employ a supervised learning paradigm to acquire both the process dynamics as well as the stochastic properties. This enables us to prescribe an optimal impedance and command profile (i) tuned to the hardto-model stochastic characteristics of a plant and (ii) adapt to the systematic changes such as a change in load.

Transferring impedance control strategies between heterogeneous systems via apprenticeship learning

“…8). While full details about this actuator can be found in [9], here we briefly discuss the salient features. Inspired by human antagonistic muscles, the Edinburgh SEA uses two motors, connected to a pair of springs to adjust equilibrium position and stiffness (and therefore torque) around the joint.…”

“…8(b)), and s 1 and s 2 their respective lengths. Note that, there is a non-linear relationship between the latter and the commanded servomotor positions (see [9] for details). Finally, we represent the state of the joint as e x = (q,q) ∈ R 2 , i.e., the instantaneous joint angle and velocity.…”

“…In the first two experiments, we conduct simulation studies into behaviour transfer from (i) 1-link and (ii) 2-link systems with antagonistic actuation, to VIA systems with decoupled control of impedance. We then report experiments in learning from human demonstrations for behaviour transfer to the Edinburgh series elastic actuator (SEA) [9].…”

BLUE: A bipedal robot with variable stiffness and damping

“…It can easily be shown that for co-contraction to change stiffness, non-linear springs must be used, and so most designs for antagonistic variable stiffness focus on creating a suitable non-linear spring (e.g. [18] [11] [19]) or arranging linear springs in such a way as to create non-linearity [20].…”

Exploiting variable physical damping in rapid movement tasks

“…For example, optimal control approaches have been shown to be highly effective in exploiting the elastic properties of variable stiffness actuators in explosive tasks such as throwing and hitting [4], [7] as well as in periodic tasks [8], [9], [10]. In addition, stochastic optimal control with model adaptation has also been exploited in order to cope with model uncertainty and perturbations [11], [12], [13]. This is also consistent with observations regarding the way in which humans adapt their impedance under similar conditions [14].…”