Intermittent locomotion as an optimal control strategy

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.

Burst-and-coast swimmers optimize gait by adapting unique intrinsic cycle

“…This behavior is observed either permanently as part of the strategy of an animal to move and explore its environnement, or during short periods as part of high-speed swimming regimes. Burst and coast has been addressed extensively by the biomechanics community in the past decades [1][2][3][4][5][6][7][8][9][10], often associated with locomotion cost optimization. Starting from the early studies of Weihs [1], these works have essentially investigated the relationship between the construction of the burst-and-coast cycle and the global swimming efficiency, when compared to continuous undulatory mechanisms.…”

Burst-and-coast swimmers optimize gait by adapting unique intrinsic cycle

“…This behavior is observed either permanently as part of the strategy of an animal to move and explore its environment, or during short periods as part of high-speed swimming regimes. Burst and coast have been addressed extensively by the biomechanics community in the past decades [1][2][3][4][5][6][7][8][9][10] , often associated with locomotion cost optimization. Starting from the early studies of Weihs 1 , these works have essentially investigated the relationship between the construction of the burst-and-coast cycle and the global swimming efficiency, when compared to continuous undulatory mechanisms.…”

Intermittent and temporally variable bioturbation by some terrestrial invertebrates: implications for ichnology

“…Sediment-disturbing locomotion can be considered a subset of locomotion in general, where intermittency has been noted to be common by biologists (Kramer and McLaughlin 2001;Bartumeus and Levin 2008;Bazazi et al 2012;Paoletti and Mahadevan 2014). Kramer and McLaughlin's (2001) survey found that animals exhibiting intermittent locomotion paused nearly 50% of their locomotion time, considering that, in contrast to previous steady-state assumptions of constant speed or the treatment of variable speed as unimportant in research, these breaks are too widespread to be ignored.…”