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The dynamics and the steady states of a point-like tracer particle immersed in a confined critical fluid are studied. The fluid is modeled field-theoretically in terms of an order parameter (concentration or density field) obeying…
The shallow shelf approximation is a better ``sliding law'' for ice sheet modeling than those sliding laws in which basal velocity is a function of driving stress. The shallow shelf approximation as formulated by \emph{Schoof} [2006a] is…
The non-thermal nature of self-propelling colloids offers new insights into non-equilibrium physics. The central mathematical model to describe their trajectories is active Brownian motion, where a particle moves with a constant speed,…
This paper considers a scenario of pursuing a moving target that may switch behaviors due to external factors in a dynamic environment by motion estimation using visual sensors. First, we present an improved Visual Motion Observer with…
The paper is concerned with mechanical systems which are controlled by implementing a number of time-dependent, frictionless holonomic constraints. The main novelty is due to the presence of additional non-holonomic constraints. We develop…
Tracking of individual particle and studying their motion serves as a direct means to understand the dynamics in crowded and complex environments. In this study, the dynamics of tracer particles in the matrix of dense soft-colloidal…
Compensating for slip and skid is crucial for mobile robots navigating outdoor terrains. In these challenging environments, slipping and skidding introduce uncertainties into trajectory tracking systems, potentially compromising the safety…
The problem of sequentially transferring from a source object track and a model to another Bayesian filter has become ubiquitous. Due to the lack of a structural model that can capture the dependence among different models, the transfer may…
We study the tracking of a trajectory for a nonholonomic system by recasting the problem as an optimal control problem. The cost function is chosen to minimize the error in positions and velocities between the trajectory of a nonholonomic…
Underwater gliders are increasingly deployed in challenging missions - such as hurricane-season observations and long-endurance environmental monitoring - where strong currents and turbulence pose significant risks to navigation safety. To…
We present a new stability proof for cascaded geometric control used by aerial vehicles tracking time-varying position trajectories. Our approach uses sliding variables and a recently proposed quaternion-based sliding controller to…
A complete model of the motion of a quadcopter along a smooth spatial trajectory is presented. Based on the model, a robust algorithm is proposed for controlling a quadcopter using measurements of linear coordinates and yaw angle. By…
The article addresses the mathematical modeling of the folding of a thin elastic sheet along a prescribed curved arc. A rigorous model reduction from a general hyperelastic material description is carried out under appropriate scaling…
We propose a computational framework to learn stylisation patterns from example drawings or writings, and then generate new trajectories that possess similar stylistic qualities. We particularly focus on the generation and stylisation of…
A coupled map lattice for convection is proposed, which consists of Eulerian and Lagrangian procedures. Simulations of the model not only reproduce a wide-range of phenomena in Rayleigh-B\'{e}nard convection experiments but also lead to…
Experimental analysis of the motion in a system of two coupled oscillators with arbitrary initial conditions was performed and the normal coordinates were obtained directly. The system consisted of two gliders moving on an air track, joined…
Skateboarders perform a reciprocating motion on a curved ramp, called pumping, by moving their bodies up and down perpendicular to the ramp's surface. We propose a simple mechanical model for this pumping motion and solve the equation of…
The work presented in this report introduces a framework aimed towards learning to imitate human gaits. Humans exhibit movements like walking, running, and jumping in the most efficient manner, which served as the source of motivation for…
Autonomous underwater gliders use buoyancy control to achieve forward propulsion via a sawtooth-like, rise-and-fall trajectory. Because gliders are slow-moving relative to ocean currents, glider control must consider the effect of oceanic…
This paper presents an analytical framework to study the geometry arising when a soft continuum arm grasps a planar object. Both the arm centerline and the object boundary are modeled as smooth curves. The grasping problem is formulated as…