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In this article we present the discrete-time isoholonomic problem of theplanar Purcell's swimmer and solve it using the Discrete-time Pontryaginmaximum principle. The 3-link Purcell's swimmer is a locomotion system movingin a low Reynolds number environment. The kinematics of the system evolves on aprincipal fiber bundle. A structure preserving discrete-time kinematic model ofthe system is obtained in terms of the local form of a discrete connection. Anadapted version of the Discrete Maximum Principle on matrix Lie groups is thenemployed to come up with the necessary optimality conditions for an optimalstate transfer while minimizing the control effort. These necessary conditionsappear as a two-point boundary value problem and are solved using a numericaltechnique. Results from numerical experiments are presented to illustrate thealgorithm.

Exact isoholonomic motion of the planar Purcell's swimmer