Research Description:

Biological Locomotion

Biological snakes supposedly lost their limbs to move effectively in cluttered and highly convoluted environments such as underground chasms and in and between cracks and crevices. However, when snakes returned to the surface with open flat terrains, they developed new modes of locomotion without the need to re-grow legs. Snakes exhibit four main modes of locomotion:

·        Lateral undulation: Fish move forward by shaping their bodies in an “S-shaped” curve that travels tailwards [Gans 1980] [Elwood and Cundall 1994]. Almost all limbless vertebrates, including snakes, mimic their ancestors by using this kind of locomotion for traversing the ground, however they have to induce higher torques and forces in order to deal with the loss of buoyancy in water. Snakes propel themselves on the ground by summing the longitudinal resultants of posterolateral forces (Figure 1b). Biologists do not agree on the energetic cost of snakes using lateral undulation. [Chodrow and Taylor 1973] claim that lateral undulation requires half the metabolic cost compared to tetra-pod of equivalent mass, while [Walton, Jayne, Bennett 1990] claims that energetic cost is comparable between undulating snakes and locomoting tetra-pods of the same size and mass.

Robotics researchers have already implemented lateral undulation in robotic snakes. Hirose with his 1972 pioneering work in snake robots was able to implement this kind of motion on simple planar snake robots [Hirose 1993]. Miller, Ostrowski, and others have been experimenting with this kind of locomotion as well [Ostrowski and Burdick 1998]. All of these efforts use passive wheels under the snake body. These passive wheels theoretically provide infinite lateral friction and null axial friction, which is essential in propelling the snake robot forward. All of these methods propel the robot on very flat terrains and use more energy than a conventional wheeled robot of comparable size.

  ·        Concertina: When a snake is placed in narrow surroundings, it automatically “elbows out” regions of its body to establish static points of contact. Using the static points as fixtures, the body moves forward and then elbows out to form static points of contact, as if it were climbing a rope, but from the inside. Due to the stop and go movement of the body of the snake, momentum is not conserved and thus the mode of motion is energetically expensive and slow. Jayne claims that concertina is 7 times more inefficient when compared to other kinds of locomotion in real snakes [Walton, Jayne, Bennett 1990]. However, snakes use concertina only when other options of locomotion are ineffective such as traversing tight spaces with high friction, and more importantly, climbing.

Nobody has yet implemented this mode of locomotion on robotic snakes. Hirose has made some preliminary observations on biological snakes trying to understand their biomechanics of movement in concertina [Hirose 1993]. The proposed work will be the first to investigate using concertina as a mode of locomotion for robotic snakes for the purpose of climbing through complicated three-dimensional environments.

·        Linear Progression: In this mode of locomotion, the snake anchors its body at certain sites that seem to continuously move tailwards. Some critical aspects of this kind of locomotion are that the snake ribs operate in parallel, the skin must possess appreciable anteroposterior flexibility and, most of the snake’s mass moves forward at a constant speed. Linear progression is energy efficient due to conservation of momentum.

Chirikjian and Burdick implemented this mode of locomotion on the planar Caltech hyper-redundant mechanism and Yim at Xerox has done some similar experiments with his modular polybots. The proposed effort will implement linear progression on non-flat surfaces, i.e., three-dimensional terrains.

·        Side Winding: This mode of locomotion is a special case of concertina using static friction, but was previously believed to be a form of lateral undulation. At any given instant, at least two portions of the snake are in static contact with the ground. The rest of the snake body is lifted and moves forward. The snake uses small irregularities in the surface against which it pushes sideways. Side winding conserves momentum and is claimed to be the most efficient mode of locomotion. This was verified by measuring how fast and how long a snake can maintain this motion. Chirikjian and Burdick did some basic research on side winding for snake robots [Chirikjian and Burdick, 1994]. We are not interested in this mode of locomotion, however, because it does not lend itself to covert and minimally invasive operations.

Mentioned above is a description of classical snake locomotion modes in their usual habitats. Here, we are going to take a biomimetic approach in that we will look at biology for inspiration, but not a blueprint, for designing locomotion algorithms. The goal here is to identify the fundamental principles that describe the snakes’ motion and how they switch from one locomotion mode to another.  Observing the snakes’ behaviors and video taping them will motivate engineering advancement in developing our locomotion algorithm.

Howie Choset
Elie Shammas

· Chodrow, R. E., and C. R. Taylor. "Energetic cost of limbless locomotion in snakes." Federation Proc. 32:422. 1973.
· Elwood, J. R. L. and Cundall, D. "Morphology and behavior of the feeding apparatus in Cryptobranchus alleganiensis (Amphibia: Caudata)." Journal of Morphology 220: 47-70, 1994
· Gans, C. Biomechanics Approach to Vertebrate Biology, [Reissue]. The University of Michigan Press, Ann Arbor, 1980.
· Hirose, S. Biologically Inspired Robots: Snake-like Locomotors and Manipulators. Oxford University Press: Oxford 1993.
· Walton, M. Jayne, B.C. & Bennett, A.F. "The energetic cost of limbless locomotion." Science 249:524-527, 1990.