Fundamental dynamics based adaptive energy control for cooperative swinging of complex pendulum-like objects

Abstract

Abstract-We present an adaptive energy-based controller for cooperative swinging of complex pendulum-like objects by two agents. The complex pendulum-like object has two oscillation degrees of freedom of which one is to be controlled to a goal energy and the other one has to be damped. The closed-loop fundamental dynamics of a simple pendulum are extended to the two-agent pendulum. Based on the fundamental dynamics, a simple adaptive mechanism identifies the natural frequency of the system. An amplitude factor is adapted such that an agent behaves as a leader or a follower. A leader knows the goal energy and controls the system according to desired reference dynamics. A follower either imitates the leader's energy flow or estimates the leader's goal energy. Properties as stability of both leader-follower structures are analyzed analytically based on the fundamental dynamics assumption. The applicability of the control approaches to a complex pendulum-like object is shown in simulation.

Cooperative Dynamic Manipulation of Unknown Flexible Objects

“…However, there is no analytic solution for ϑ(ϑ E , ϕ) from (14). Therefore, we approximate the system energy ϑ E through the phase space radius ϑ r…”

“…In our initial work, we treated pendulum-like object swinging [13] based on the assumption that all system parameters are known. This assumption was alleviated in [14] by an adaptive approach. The contribution of this work is three-fold: firstly, we experimentally verify the adaptive approach presented in [14].…”

“…This assumption was alleviated in [14] by an adaptive approach. The contribution of this work is three-fold: firstly, we experimentally verify the adaptive approach presented in [14]. Secondly, we combine our results from cooperative swinging of pendulum-like objects and human-human swinging of rigid objects in [15], towards cooperative swinging of flexible objects.…”

“…Normalization with Ω = ω g marked via solid lines and Ω = ω 0 via dashed lines. For energies up to ϑ E = 0.5π and a normalization with Ω = ω g , the phase space is approximately a circle with radius ϑ r ≈ ϑ E and the phase angle ϕ rises approximately linear over time.Figure adaptedfrom[14]…”