All Outputs (4)

Efficient and Scalable Inverse Kinematics for Continuum Robots (2023)
Journal Article
Wild, S., Zeng, T., Mohammad, A., Billingham, J., Axinte, D., & Dong, X. (2024). Efficient and Scalable Inverse Kinematics for Continuum Robots. IEEE Robotics and Automation Letters, 9(1), 375 - 381. https://doi.org/10.1109/lra.2023.3331291

With their flexible nature, continuum robots offer hyper-redundancy regarding their workspace; their backbone can take many shapes upon a single tip position and orientation. Deciphering which backbone shape to use under certain conditions is crucial... Read More about Efficient and Scalable Inverse Kinematics for Continuum Robots.

The non-local Lotka-Volterra system with a top hat kernel - Part 1: dynamics and steady states with small diffusivity (2023)
Journal Article
Billingham, J., & Needham, D. J. (2023). The non-local Lotka-Volterra system with a top hat kernel - Part 1: dynamics and steady states with small diffusivity. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 479(2277), Article 20230381. https://doi.org/10.1098/rspa.2023.0381

We study the dynamics of the non-local Lotka-Volterra system ut=Duuxx+u(1-φ - u-αv), vt=Dvvxx+v(1-φ - v-βu), where a star denotes the spatial convolution and the kernel φ is a top hat function. We initially focus on the case of small, equal diffusivi... Read More about The non-local Lotka-Volterra system with a top hat kernel - Part 1: dynamics and steady states with small diffusivity.

A rational approach to beam path planning in additive manufacturing: the inverse heat placement problem (2023)
Journal Article
Yang, Y., Billingham, J., Axinte, D., & Liao, Z. (2023). A rational approach to beam path planning in additive manufacturing: the inverse heat placement problem. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 479(2270), Article 20220386. https://doi.org/10.1098/rspa.2022.0386

High demand for components with complex geometries at macro and micro levels drives the development of additive manufacturing (AM). However, the scientific basis for designing energy beam scanning strategies (e.g. beam scanning speed, beam path, beam... Read More about A rational approach to beam path planning in additive manufacturing: the inverse heat placement problem.

The Riemann problem for a generalized Burgers equation with spatially decaying sound speed. I Large‐time asymptotics (2023)
Journal Article
Needham, D. J., Meyer, J. C., Billingham, J., & Drysdale, C. (2023). The Riemann problem for a generalized Burgers equation with spatially decaying sound speed. I Large‐time asymptotics. Studies in Applied Mathematics, https://doi.org/10.1111/sapm.12561

In this paper, we consider the classical Riemann problem for a generalized Burgers equation, u t + h α ( x ) u u x = u x x , $$\begin{equation*} u_t + h_{\alpha }(x) u u_x = u_{xx}, \end{equation*}$$ with a spatially dependent, nonlinear sound speed,... Read More about The Riemann problem for a generalized Burgers equation with spatially decaying sound speed. I Large‐time asymptotics.