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Learning-based approaches have recently shown notable success in legged locomotion. However, these approaches often lack accountability, necessitating empirical tests to determine their effectiveness. In this work, we are interested in…
This article has been written for an educational magazine whose target audience consists of students and teachers of mathematics in universities, colleges and schools. It concerns a notion of duality between rectangles. A proof is given…
Recently, reinforcement learning has become a promising and polular solution for robot legged locomotion. Compared to model-based control, reinforcement learning based controllers can achieve better robustness against uncertainties of…
We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the "separation property": different continuity…
Robot controllers are often optimised for a single robot in a single environment. This approach proves brittle, as such a controller will often fail to produce sensible behavior for a new morphology or environment. In comparison, animal…
This paper presents a real-time gait driven training framework for humanoid robots. First, we introduce a novel gait planner that incorporates dynamics to design the desired joint trajectory. In the gait design process, the 3D robot model…
In this paper, we propose a new method for multirotor planning in dynamic environments. The environment is represented as a temporal occupancy grid which gives the current as well as the future/predicted state of all the obstacles. The…
Motivated by holography, we explore higher derivative corrections to four-dimensional Anti-de Sitter (AdS) gravity. We point out that in such a theory the variational problem is generically not well-posed given only a boundary condition for…
Optimizing gait stability for legged robots is a difficult problem. Even on level surfaces, effectively traversing across different textures (e.g., carpet) rests on dynamically tuning parameters in multidimensional space. Inspired by…
Gait recognition holds the promise of robustly identifying subjects based on walking patterns instead of appearance information. While previous approaches have performed well for curated indoor data, they tend to underperform in…
Analysing human gait has found considerable interest in recent computer vision research. So far, however, contributions to this topic exclusively dealt with the tasks of person identification or activity recognition. In this paper, we…
Robust humanoid stair climbing remains challenging due to geometric discontinuities, sensitivity to step height variations, and perception uncertainty in real-world environments. Existing learning-based locomotion policies often rely on…
We introduce the rotation unfolding of the folding map of a surface in $\mathbb{R}^3$, and investigate its $\mathcal{A}$-vesality. The rotation unfolding is a 2-parameter unfolding and can be considered as a subfamily of the folding family,…
Fefferman and Graham showed some time ago that four dimensional conformal geometries could be analyzed in terms of six dimensional, ambient, Riemannian geometries admitting a closed homothety. Recently it was shown how conformal geometry…
An interface description and numerical simulations of model A kinetics are used for the first time to investigate the intra-surface kinetics of phase ordering on corrugated surfaces. Geometrical dynamical equations are derived for the…
Higher dimensional graphs can be used to colour two-dimensional geometric graphs. If G the boundary of a three dimensional graph H for example, we can refine the interior until it is colourable with 4 colours. The later goal is achieved if…
We study the surface shape of two-dimensional piles using experiments and a continuum theory for surface flows of granular materials (the BCRE equations). We first obtain an analytical solution to the BCRE equations with a simple…
As a unique biometric that can be perceived at a distance, gait has broad applications in person authentication, social security, and so on. Existing gait recognition methods suffer from changes in viewpoint and clothing and barely consider…
In this paper, we construct rotating frames for curves, including plane curves, space curves and curves on surfaces. Hence, the behaviour of an arbitrary moving point on a curve can be seen as the composite of linear motion and rotation.…
This is a survey of the twistor lifts of surfaces in $4$-dimensional spaces. In most part of this survey, the space is Euclidean $4$-space $E^4$. The definitions of the Gauss maps and the twistor lifts of surfaces in $E^4$ are given by…