Intermittent locomotion as an optimal control strategy

Rolling of stimuli-bent cylindrical robots using contact finite element simulations

Curved cylinders, if rigid, cannot roll on a surface like straight cylinders, but soft cylinders bent by specific stimuli can! Studying the autonomous locomotion of these soft robots and their interactions with the environment using finite element analysis is challenging due to the complex multiphysics of stimuli-responsive soft materials and nonlinear contact mechanics. In this pioneering work, we simulate the rolling of stimuli-bent cylinders on a surface using contact finite elements and introduce a simple yet effective pseudo-thermal field method. Our approach successfully reproduces several modes of autonomous locomotion observed experimentally, including phototropic locomotion, phototropic climbing on a slanted surface, steering under partial illumination, and backward rolling under alternating heat-light stimuli. Parametric analysis demonstrates strong agreement between the experiments and our numerical results, validating the effectiveness of our approach. This study reveals the intriguing and highly nonintuitive dynamics of photo- or thermally bent cylindrical soft robots, and serves as a paradigm for modelling and simulating such rolling robots.

Pausing to swarm: locust intermittent motion is instrumental for swarming-related visual processing

Intermittent motion is prevalent in animal locomotion. Of special interest is the case of collective motion, in which social and environmental information must be processed in order to establish coordinated movement. We explored this nexus in locust, focusing on how intermittent motion interacts with swarming-related visual-based decision-making. Using a novel approach, we compared individual locust behaviour in response to continuously moving stimuli, with their response in semi-closed-loop conditions, in which the stimuli moved either in phase with the locust walking, or out of phase, i.e. only during the locust's pauses. Our findings clearly indicate the greater tendency of a locust to respond and 'join the swarming motion' when the visual stimuli were presented during its pauses. Hence, the current study strongly confirms previous indications of the dominant role of pauses in the collective motion-related decision-making of locusts. The presented insights contribute to a deeper general understanding of how intermittent motion contributes to group cohesion and coordination in animal swarms.

Using neuronal models to capture burst-and-glide motion and leadership in fish

While mathematical models, in particular self-propelled particle models, capture many properties of large fish schools, they do not always capture the interactions of smaller shoals. Nor do these models tend to account for the use of intermittent locomotion, often referred to as burst-and-glide, by many species. In this paper, we propose a model of social burst-and-glide motion by combining a well-studied model of neuronal dynamics, the FitzHugh-Nagumo model, with a model of fish motion. We first show that our model can capture the motion of a single fish swimming down a channel. Extending to a two-fish model, where visual stimulus of a neighbour affects the internal burst or glide state of the fish, we observe a rich set of dynamics found in many species. These include: leader-follower behaviour; periodic changes in leadership; apparently random (i.e. chaotic) leadership change; and tit-for-tat turn taking. Moreover, unlike previous studies where a randomness is required for leadership switching to occur, we show that this can instead be the result of deterministic interactions. We give several empirically testable predictions for how bursting fish interact and discuss our results in light of recently established correlations between fish locomotion and brain activity.

The lost art of mathematical modelling

We provide a critique of mathematical biology in light of rapid developments in modern machine learning. We argue that out of the three modelling activities - (1) formulating models; (2) analysing models; and (3) fitting or comparing models to data - inherent to mathematical biology, researchers currently focus too much on activity (2) at the cost of (1). This trend, we propose, can be reversed by realising that any given biological phenomenon can be modelled in an infinite number of different ways, through the adoption of an pluralistic approach, where we view a system from multiple, different points of view. We explain this pluralistic approach using fish locomotion as a case study and illustrate some of the pitfalls - universalism, creating models of models, etc. - that hinder mathematical biology. We then ask how we might rediscover a lost art: that of creative mathematical modelling.

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

Bedding planes and vertical sections of many sedimentary rock formations reveal bioturbation structures, including burrows, produced by diverse animal taxa at different rates and durations. These variables are not directly measurable in the fossil record, but neoichnological observations and experiments provide informative analogues. Comparable to marine invertebrates from many phyla, a captive beetle larva burrowing over 2 weeks showed high rates of sediment disturbance within the first 100 h but slower rates afterwards. Tunnelling by earthworms and adult dung beetles is also inconstant-displacement of lithic material alternates with organic matter displacement, often driven by food availability with more locomotion when hungry. High rates of bioturbation, as with locomotion generally, result from internal and external drives, slowing down or stopping when needs are filled. Like other processes affecting sediment deposition and erosion, rates can drastically differ based on measured timescale, with short bursts of activity followed by hiatuses, concentrated in various seasons and ontogenetic stages for particular species. Assumptions of constant velocities within movement paths, left as traces afterward, may not apply in many cases. Arguments about energetic efficiency or optimal foraging based on ichnofossils have often overlooked these and related issues. Single bioturbation rates from short-term experiments in captivity may not be comparable to rates measured at an ecosystem level over a year or generalized across multiple time scales where conditions differ even for the same species. Neoichnological work, with an understanding of lifetime variabilities in bioturbation and their drivers, helps connect ichnology with behavioural biology and movement ecology.

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

This paper addresses the physical mechanism of intermittent swimming by considering the burst-and-coast regime of fish swimming at different speeds. The burst-and-coast regime consists of a cycle with two successive phases, i.e., a phase of active undulation powered by the fish muscles followed by a passive gliding phase. Observations of real fish whose swimming gait is forced in a water flume from low to high speed regimes are performed, using a full description of the fish kinematics and mechanics. We first show that fish modulate a unique intrinsic cycle to sustain the demanded speed by modifying the bursting to coasting ratio while maintaining the duration of the cycle nearly constant. Secondly, we show using numerical simulations that the chosen kinematics by correspond to optimized gaits for swimming speeds larger than 1 body length per second.

Li et al. use experimental observations of red-nose tetrafish and mathematical simulations to model the burst-and-coast swimming regime. This study shows that in order to sustain the necessary speed, fish adopt a unique intrinsic cycle by modifying the burst to coast ratio and can implement this pattern at a range of swimming speeds.

Pursuit predation with intermittent locomotion in zebrafish

The control of a predator's locomotion is critical to its ability to capture prey. Flying animals adjust their heading continuously with control similar to guided missiles. However, many animals do not move with rapid continuous motion, but rather interrupt their progress with frequent pauses. To understand how such intermittent locomotion may be controlled during predation, we examined the kinematics of zebrafish (Danio rerio) as they pursued larval prey of the same species. Like many fishes, zebrafish move with discrete burst-and-coast swimming. We found that the change in heading and tail excursion during the burst phase was linearly related to the prey's bearing. These results suggest a strategy, which we call intermittent pure pursuit, that offers advantages in sensing and control. This control strategy is similar to perception and path-planning algorithms required in the design of some autonomous robots and may be common to a diversity of animals.

Toads modulate flight strategy according to distance to refuge

Among antipredator behaviours, escaping and hiding in a refuge are widespread in nature. Frequently, threatened prey flee towards a refuge nearby, if available. Therefore, refuge proximity may affect the fleeing strategy of a prey. In this work, I tested this hypothesis in Epidalea calamita, a cursorial toad that flees by means of intermittent runs. In a linear runway in standardized conditions, toads were recorded while conducting a short-distance (refuge at 70 cm), a medium-distance (refuge at 140 cm, divided in two 70-cm tracks), and a long-distance trial (refuge at 210 cm, divided in three 70-cm tracks), in a random sequence. Video analyses permitted to calculate sprint speed and run rates (number of runs per meter) in each track. Distance to refuge affected toad flight strategy. Toads started flights at a faster speed in the short-distance trials. In the medium- and the long-distance trials, toads accelerated after the first track, seemingly not motivated by refuge proximity. In these trials, run rate was greater in the first tracks. Altogether, these findings suggest that threatened toads respond firstly with slow, intermittent movements, and only shift to less intermittent, faster sprints if the threat persists. However, run rate was lower in the short-distance trial than in the first tracks of the other trials, suggesting straighter (and faster) flight toward the refuge when it is close. The effects of refuge proximity were greater in males, which (jointly with faster sprint speed) could reflect a greater conspicuousness of males to predator resulting in better escape strategies.

Mathematical analysis and validation of an exactly solvable model for upstream migration of fish schools in one-dimensional rivers

Upstream migration of fish schools in 1-D rivers as an optimal control problem is formulated where their swimming velocity and the horizontal oblateness are taken as control variables. The objective function to be maximized through a migration process consists of the biological and ecological profit to be gained at the upstream-end of a river, energetic cost of swimming against the flow, and conceptual cost of forming a school. Under simplified conditions where the flow is uniform in both space and time and the profit to be gained at the goal of migration is sufficiently large, the optimal control variables are determined from a system of algebraic equations that can be solved in a cascading manner. Mathematical analysis of the system reveals that the optimal controls are uniquely found and the model is exactly solvable under certain conditions on the functions and parameters, which turn out to be realistic and actually satisfied in experimental fish migration. Identification results of the functional shapes of the functions and the parameters with experimentally observed data of swimming schools of Plecoglossus altivelis (Ayu) validate the present mathematical model from both qualitative and quantitative viewpoints. The present model thus turns out to be consistent with the reality, showing its potential applicability to assessing fish migration in applications.