Planar Formation Control of a School of Robotic Fish: Theory and Experiments

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.

Nonholonomic Systems With Redundant Degrees of Freedom Can Exploit Nonlinear Frequency Response to Improve Speed and Efficiency of Locomotion

Rigid body nonholonomic systems serve as models for locomotion of several terrestrial animals such as snakes as well as for fish-like swimming motion. Several well known nonholonomic systems have also found applications in the field of mobile robotics in everything from wheeled vehicles to articulated snake like robots. However, one aspect of their dynamics has remained unexplored. This is to do with the effects of increasing the degrees of freedom by adding additional ‘segments’ such as in a chain, with the joints between segments having a nonzero torsional stiffness. Such nonholonomic systems when subjected to periodic actuation or inputs have additional modes of oscillation. The interplay of the nonholonomic constraints, linear elastic potentials and additional degrees of freedom can produce rich frequency-amplitude response in the dynamics of the system and can lead to significantly higher speed and efficiency. In this paper we explore such dynamics with the example of a well known nonholonomic system, the Chaplygin sleigh and a variant of it with an additional degree of freedom. Such models can be expected to better match the dynamics of biological swimmers and have widespread applications for soft and under-actuated robots.

Locomotion of a Compliant Mechanism With Nonholonomic Constraints

Compliant mechanisms have been studied extensively as an alternative to traditional rigid body design with advantages like part number reduction, compliance, and multistable configurations. Most of the past research on compliant mechanisms has been restricted to the case where they are subject to holonomic constraints. In this paper, we develop a model of a planar compliant mechanism with nonholonomic constraints as a mobile robot that can move on the ground. The only actuation that is assumed is a torque on the system. It is shown that the dynamics of this system is similar to that of a well-known nonholonomic system, called the Chaplygin sleigh, but with an added degree-of-freedom and an additional quartic potential. The interaction of compliance and the nonholonomic constraint lead to multiple stable limit cycle oscillations in a reduced velocity space that correspond to oscillations about different stable physical configurations. These limit cycle oscillations produce motion of the compliant mechanism in the plane with differing characteristics. The modeling framework in this paper can form the basis for the design of underacted mobile compliant nonholonomic robots or mobile robots that incorporate compliant mechanisms as mechanical switches.