相关论文: The Integrable Snake Model

Snake graphs and their perfect matchings play a key role in the description of cluster variables of cluster algebras associated to surfaces. In this paper, we introduce triangular snake graphs and establish a bijection between their routes…

Limbless terrestrial animals exhibit exceptional locomotor versatility and control, currently unmatched by engineered counterparts. Here, we introduce a computational framework that enables soft synthetic snakes to navigate unstructured,…

We examine the problem of snake-like locomotion by studying a system consisting of a planar inextensible elastic rod that is able to control its spontaneous curvature. Using a Cosserat model we derive, through variational principles, the…

In this theoretical study, we present an analytical framework to investigate the slithering motion of snakes on flat surfaces. While previous studies have predominantly relied on numerical methods to identify optimal locomotion kinematics,…

We introduce a multi-species generalization of the symmetric simple exclusion process with open boundaries. This model possesses the property of being integrable and appears as physically relevant because the boundary conditions can be…

Contact-rich problems, such as snake robot locomotion, offer unexplored yet rich opportunities for optimization-based trajectory and acyclic contact planning. So far, a substantial body of control research has focused on emulating snake…

Continuous neural field models with inhomogeneous synaptic connectivities are known to support traveling fronts as well as stable bumps of localized activity. We analyze stationary localized structures in a neural field model with periodic…

Snakes are a remarkable evolutionary success story. Many snake-inspired robots have been proposed over the years. Soft robotic snakes (SRS) with their continuous and smooth bending capability better mimic their biological counterparts'…

Snake graphs appear naturally in the theory of cluster algebras. For cluster algebras from surfaces, each cluster variable is given by a formula which is parametrized by the perfect matchings of a snake graph. In this paper, we continue our…

We study the parameterized complexity of a variant of the classic video game Snake that models real-world problems of motion planning. Given a snake-like robot with an initial position and a final position in an environment (modeled by a…

We construct a direct natural bijection between descending plane partitions without any special part and permutations. The directness is in the sense that the bijection avoids any reference to nonintersecting lattice paths. The advantage of…

Studying snake robot locomotion in a cluttered environment has been a complicated task because the motion model is discontinuous due to the physical contact with obstacles, and the contact force cannot be determined solely by contact…

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…

Snake robots have the potential to maneuver through tightly packed and complex environments. One challenge in enabling them to do so is the complexity in determining how to coordinate their many degrees-of-freedom to create purposeful…

We introduce several commutative rings, the snake rings, that have strong connections to cluster algebras. The elements of these rings are residue classes of unions of certain labeled graphs that were used to construct canonical bases in…

Geodesic tracking on the projective line bundle $\R^2 \times P^1 $ has many uses, including the segmentation of objects in images. However, global tracking requires expensive distance map computations. We provide a practical solution to…

Soft robotic snakes made of compliant materials can continuously deform their bodies and, therefore, mimic the biological snakes' flexible and agile locomotion gaits better than their rigid-bodied counterparts. Without wheel support, to…

This paper presents the design and performance of a screw-propelled redundant serpentine robot. This robot comprises serially linked, identical modules, each incorporating an Archimedes' screw for propulsion and a universal joint (U-Joint)…

Using the generalized normally ordered form of words in a locally-free group of $n$ generators, we show that in the limit $n\to\infty$, the partition function of weighted directed lattice animals on a semi-infinite strip coincides with the…

This paper presents a convexity analysis for the dynamic snake model based on the Potential Energy functional and the Hamiltonian formulation of the classical mechanics. First we see the snake model as a dynamical system whose singular…