Abstract
This paper presents a nonlinear control design for the stabilization of parallel and circular motion in a school of robotic fish actuated with internal reaction wheels. The closed-loop swimming dynamics of the fish robots are represented by the canonical Chaplygin sleigh. They exchange relative state information according to a connected, undirected communication graph to form a system of coupled, nonlinear, second-order oscillators. Prior work on collective motion of constant-speed, self-propelled particles serves as the foundation of our approach. However, unlike a self-propelled particle, the fish robots follow limit-cycle dynamics to sustain periodic flapping for forward motion with time-varying speed. Parallel and circular motions are achieved in an average sense without feedback linearization of the agents’ dynamics. Implementation of the proposed parallel formation control law on an actual school of soft robotic fish is described, including system identification experiments to identify motor dynamics and the design of a motor torque-tracking controller to follow the formation torque control. Experimental results demonstrate a school of four robotic fish achieving parallel formations starting from random initial conditions.
Highlights
Collective behavior of mobile agents has received significant interest recently in fields such as biology, physics, computer science, and control engineering (Reynolds, 1987; Vicsek et al, 1995; Ren et al, 2007)
Our approach bridges collective motion of self-propelled particles (Paley, 2007) and feedback control of a fish robot modeled by Chaplygin sleigh dynamics (Lee et al, 2019)
The control law Eq 17 is illustrated by numerical simulation using control Eq 17 and the full dynamics Eq 8
Summary
Collective behavior of mobile agents has received significant interest recently in fields such as biology, physics, computer science, and control engineering (Reynolds, 1987; Vicsek et al, 1995; Ren et al, 2007). Second-order consensus of coupled oscillators with double-integrator dynamics (Napora and Paley, 2013) uses the gradient of a phase potential Another class of collective behaviors of multi-agent systems are circular formations. The contributions of this paper are 1) a control design that achieves parallel motion for a school of robotic fish, represented by a system of coupled, nonlinear, second-order oscillators with Chaplygin sleigh dynamics using only relative state information; 2) a control design that achieves circular motion for the same system; 3) system identification of the reaction-wheel motor dynamics and the design of an optimal estimation and tracking controller that follows the torque commands of the formation control; and 4) experimental validation of the parallel formation control law on a school of bio-inspired robotic fish (Figure 1).
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