Intermittent locomotion as an optimal control strategy

P Paoletti; L Mahadevan

doi:10.1098/rspa.2013.0535

Intermittent locomotion as an optimal control strategy

Proc Math Phys Eng Sci. 2014 Apr 8;470(2164):20130535. doi: 10.1098/rspa.2013.0535.

Authors

P Paoletti¹, L Mahadevan²

Affiliations

¹ School of Engineering and Applied Sciences , Harvard University , 29 Oxford Street, Cambridge, MA 02138, USA.
² School of Engineering and Applied Sciences , Harvard University , 29 Oxford Street, Cambridge, MA 02138, USA ; Department of Organismic and Evolutionary Biology , Harvard University , 29 Oxford Street, Cambridge, MA 02138, USA ; Department of Physics , Harvard University , 29 Oxford Street, Cambridge, MA 02138, USA.

Abstract

Birds, fish and other animals routinely use unsteady effects to save energy by alternating between phases of active propulsion and passive coasting. Here, we construct a minimal model for such behaviour that can be couched as an optimal control problem via an analogy to travelling with a rechargeable battery. An analytical solution of the optimal control problem proves that intermittent locomotion has lower energy requirements relative to steady-state strategies. Additional realistic hypotheses, such as the assumption that metabolic cost at a given power should be minimal (the fixed gear hypothesis), a nonlinear dependence of the energy storage rate on propulsion and/or a preferred average speed, allow us to generalize the model and demonstrate the flexibility of intermittent locomotion with implications for biological and artificial systems.

Keywords: flight; intermittent locomotion; optimal control; swimming.