Optimizing snake locomotion in the plane

Alben, Silas

doi:10.1098/rspa.2013.0236

Cited by 25 publications

(74 citation statements)

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“…Examples of these three classes of optima are shown in the snapshots on the right side of figure 1. In this study, one possible local optimum was observed with isotropic friction µ b /µ f = µ t /µ f = 1, but the efficiency gradient norm was only reduced by about two orders of magnitude from the random initial kinematics [47]. Usually computations did not converge to local optima in the vicinity of isotropic friction (orange box in figure 1).…”

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confidence: 69%

“…Similar models were used in [32,37,38,47,51,53,54], and the same model was found to agree well with the motions of biological snakes in [37]. three different choices of friction coefficients.…”

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confidence: 72%

“…We then proposed a class of concertina-like motions that saturate the upper bound for efficiency for any choice of friction coefficients. The optimal smooth motions of section VI require short wavelengths ∼ (and large frequencies ∼ 1/ to travel an O(1) distance), which explains why the numerical optimization using 45 or 190 modes in [47] did not converge to such motions. It is interesting, however, that in the optimal time-harmonic motions with only three links, concertina-like motions can be seen.…”

Section: Discussionmentioning

confidence: 99%

“…In previous work [47], we computed solutions to equations (11) using quasi-Newton methods. Two major challenges of such methods are finding an initial guess that is sufficiently close for convergence, and choosing a step size in the line search that moves the solution towards convergence.…”

Section: Methodsmentioning

confidence: 99%

“…Wagner and Lauga studied the locomotion of a two-mass system moving in one dimension with isotropic friction (equal in the forward and backward directions) and found that locomotion is possible if the two masses have different friction coefficients and the length of the link connecting them has an asymmetric stroke cycle [45]. For the swimming of microorganisms in a viscous fluid (at zero Reynolds number), the drag anisotropy of long slender bodies and appendages is known to be essential for locomotion [46].In a previous theoretical/computational study we optimized smooth snake body kinematics for efficiency, starting from random initial ensembles [47]. The kinematics were described by the coefficients of a double series, Fourier in time (with unit period) and Chebyshev (polynomials) in arc length along the body axis, truncated at 45 modes (9 temporal by 5 spatial) and in some cases 190 modes (19 temporal by 10 spatial).…”

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confidence: 99%

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Efficient sliding locomotion with isotropic friction

Alben

2019

Phys. Rev. E

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Snakes' bodies are covered in scales that make it easier to slide in some directions than in others.This frictional anisotropy allows for sliding locomotion with an undulatory gait, one of the most common for snakes. Isotropic friction is a simpler situation (that arises with snake robots for example) but is less understood. In this work we regularize a model for sliding locomotion to allow for static friction. We then propose a robust iterative numerical method to study the efficiency of a wide range of motions under isotropic Coulomb friction. We find that simple undulatory motions give little net locomotion in the isotropic regime. We compute general time-harmonic motions of three-link bodies and find three local optima for efficiency. The top two involve static friction to some extent. We then propose a class of smooth body motions that have similarities to concertina locomotion (including the involvement of static friction) and can achieve optimal efficiency for both isotropic and anisotropic friction. I. INTRODUCTIONSnake locomotion has attracted the interest of biologists and engineers for several decades [1][2][3][4][5][6]. Many locomoting animals use appendages such as legs, wings, or fins to exert a force on the substrate or surrounding fluid, and propel the rest of the body forward [7]. Snakes lack appendages, and thus it is less clear which parts of the snake body should exert propulsive forces, and at which instants during the motion, to move forward efficiently.A typical way to understand how organisms move is to study physical or computational models and compare their motions with those of the actual organisms [7][8][9][10][11]. One can take a step further and pose and solve optimization problems for the models. This can suggest locomotion strategies that are effective for man-made vehicles [12][13][14]. It can also help understand why organisms have evolved in particular ways under a multitude of constraints [15][16][17].Often what is optimized is a measure of the efficiency of locomotion. For example, one can maximize the average speed for a given time-averaged power expended by the organism. One can study the effects of physical parameters and constraints by varying them and studying how the optimal solutions change. Well-known examples are optimization studies of organisms moving in low-[18-24] and high-Reynolds-number fluid flows [25][26][27][28][29][30][31]. For locomotion in frictional (terrestrial or granular) media, frictional forces can result in distinctive modes of efficient (or optimal) locomotion [32,33].Snakes are limbless reptiles with elongated bodies, supported by a backbone with 100-500 bony segments (vertebrae) * Electronic address: alben@umich.edu arXiv:1902.03163v1 [physics.bio-ph] 8 Feb 2019 [34]. The vertebrae allow for high flexibility particularly in the lateral (side-to-side) direction, with less flexibility for vertical (dorso-ventral) bending or for torsion. Running along the backbone are muscles that attach to the sides of the vertebrae and cause bending. The snake bod...

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confidence: 69%