arXiv subjects

Ruijia Zhang

Publications and source records attributed to Ruijia Zhang.

22 records · Page 2Linked to original sources

arXiv2024

Design of a Double-joint Robotic Fish Using a Composite Linkage

Robotic fish is one of the most promising directions of the new generation of underwater vehicles. Traditional biomimetic fish often mimic fish joints using tandem components like servos, which leads to increased volume, weight and control complexity. In this paper, a new double-joint robotic fish using a composite linkage was designed, where the propulsion mechanism transforms the single-degree-of-freedom rotation of the motor into a double-degree-of-freedom coupled motion, namely caudal peduncle translation and caudal fin rotation. Motion analysis of the propulsion mechanism demonstrates its ability to closely emulate the undulating movement observed in carangiform fish. Experimental results further validate the feasibility of the proposed propulsion mechanism. To improve propulsion efficiency, an analysis is conducted to explore the influence of swing angle amplitude and swing frequency on the swimming speed of the robotic fish. This examination establishes a practical foundation for future research on such robotic fish systems.

cs.RO↗

arXiv2023

A unified flow approach to smooth $L^p$ Christoffel-Minkowski problem for $p>1$

In this paper we study an anisotropic expanding flow of smooth, closed, uniformly convex hypersurfaces in $\mathbb{R}^{n+1}$ with speed $ψσ_k(λ)^α$, where $α$ is a positive constant, $σ_k(λ)$ is the $k$-th elementary symmetric polynomial of the principal radii of curvature and $ψ$ is a preassigned positive smooth function defined on $\mathbb{S}^n$. We prove that under some assumptions of $ψ$, the solution to the flow after normalisation exists for all time and converges smoothly to a solution of the well-known $L^p$ Christoffel-Minkowski problem $u^{1-p}( x ) σ_k \left( \nabla^2u+uI\right)=cψ(x)$ for $p>1$.

math.DG↗

arXiv2022

A flow approach to the prescribed Gaussian curvature problem in $\mathbb{H}^{n+1}$

In this paper, we study the following prescribed Gaussian curvature problem $$K=\frac{\tilde{f}(θ)}{ϕ(ρ)^{α-2}\sqrt{ϕ(ρ)^2+|\bar{\nabla}ρ|^2}},$$ a generalization of the Alexandrov problem ($α=n+1$) in hyperbolic space, where $\tilde{f}$ is a smooth positive function on $\mathbb{S}^{n}$, $ρ$ is the radial function of the hypersurface, $ϕ(ρ)=\sinhρ$ and $K$ is the Gauss curvature. By a flow approach, we obtain the existence and uniqueness of solutions to the above equations when $α\geq n+1$. Our argument provides a parabolic proof in smooth category for the Alexandrov problem in $\mathbb{H}^{n+1}$. We also consider the cases $2<α\leq n+1$ under the evenness assumption of $\tilde{f}$ and prove the existence of solutions to the above equations.

math.DG↗

arXiv2021

Asymptotic convergence for a class of anisotropic curvature flows

In this paper, by using new auxiliary functions, we study a class of contracting flows of closed, star-shaped hypersurfaces in $\mathbb{R}^{n+1}$ with speed $r^{\fracαβ}σ_k^{\frac{1}β}$, where $σ_k$ is the $k$-th elementary symmetric polynomial of the principal curvatures, $α$, $β$ are positive constants and $r$ is the distance from points on the hypersurface to the origin. We obtain convergence results under some assumptions of $k$, $α$, $β$. When $k\geq2$, $0<β\leq 1$, $α\geq β+k$, we prove that the $k$-convex solution to the flow exists for all time and converges smoothly to a sphere after normalization, in particular, we generalize Li-Sheng-Wang's result from uniformly convex to $k$-convex. When $k \geq 2$, $β=k$, $α\geq 2k$, we prove that the $k$-convex solution to the flow exists for all time and converges smoothly to a sphere after normalization, in particular, we generalize Ling Xiao's result from $k=2$ to $k \geq 2$.

math.DG↗