Efficient and Goal-Directed Oscillations in Articulated Soft Robots: The Point-To-Point Case

Abstract

Introducing elasticity in the mechanical design can endow robots with the ability of performing efficient and effective periodic motions. Yet, devising controllers that can take advantage of such elasticity is still an open challenge. This letter tackles an instance of this general problem, by proposing a control architecture for executing goal-oriented and efficient point-to-point periodic motions. This is achieved by (i) producing motor torques that excite intrinsic modal oscillations, and simultaneously (ii) adjusting parallel elasticity so to shape the natural modes. Analytical proofs of convergence are provided for the linear approximation. The performance and efficiency (in the sense of low energy expenditure) of the method in the nonlinear case are assessed with extensive simulations and experiments.

Experimental Closed-Loop Excitation of Nonlinear Normal Modes on an Elastic Industrial Robot

“…1 All authors are with the German Aerospace Center (DLR); Institute of Robotics and Mechatronics; Münchener Straße 20, 82234 Weßling, Germany. tasks in an industrial context [7]- [11]. Consequently, many algorithms have been recently proposed that stabilize nonlinear oscillations in mechanical systems.…”

The GummiArm Project: A Replicable and Variable-Stiffness Robot Arm for Experiments on Embodied AI

“…Thus, the system coupled the simple CPGs with the world, through the soft joints of the GummiArm, which drove the error signal used by the learning algorithm. Interestingly, Bonacchi et al ( 2021 ) have recently shown that the elasticity of a joint can be exploited to achieve point to point goal-directed periodic movement, by tuning the elasticity to shape the natural modes of the system. The GummiArm joints could serve well for future experiments in this direction.…”

Exciting Nonlinear Modes of Conservative Mechanical Systems by Operating a Master Variable Decoupling

“…f) E reaches [E − , E + ] asymptotically: The previous step of the proof implies that ā1 (x 1 (t), ẋ1 (t)) = 0, and ( 13) is equal to (7) for all the t > T . The manifold attractiveness follows from H3 and lemma 1, and in turn…”

“…where again we applied the chain rule and plugged in ( 6) and (7). Now, we exploit once more the tangency constraints ( 5), together with the definition of ∆ and the expression of its time derivative (9).…”

“…Inspired by biology, researchers have introduced elastic and soft elements into the mechanical design of robotic systems, leading to soft robots [5]. These systems are thought to be especially suited for performing oscillatory tasks, and their expected practical applications include locomotion [6], periodic pick and place [7], and carrying payloads that exceed the static torque limits [8]. Elastic elements may also be optimized to maximize performance [9], [10].…”