Related papers: How far can Tarzan jump?
We study a model of multi-excited random walk with non-nearest neighbour steps on $\mathbb Z$, in which the walk can jump from a vertex $x$ to either $x+1$ or $x-i$ with $i\in \{1,2,\dots,L\}$, $L\ge 1$. We first point out the multi-type…
We discuss the quenched tail estimates for the random walk in random scenery. The random walk is the symmetric nearest neighbor walk and the random scenery is assumed to be independent and identically distributed, non-negative, and has a…
The dynamics of a rigid, rotating, precessing, massive ring orbiting a point mass within the perimeter of the ring are considered. It is demonstrated that orbits dynamically stable against perturbations in three dimensions exist for a range…
Casting manipulation has been studied to expand the robot's movable range. In this manipulation, the robot throws and reaches the end effector to a distant target. Usually, a special casting manipulator, which consists of rigid arm links…
Consider a vertex-reinforced jump process defined on a regular tree, where each vertex has exactly $b$ children, with $b \ge 3$. We prove the strong law of large numbers and the central limit theorem for the distance of the process from the…
A terrestrial robot that can maneuver rough terrain and scout places is very useful in mapping out unknown areas. It can also be used explore dangerous areas in place of humans. A terrestrial robot modeled after a scorpion will be able to…
The number of free sites next to the end of a self-avoiding walk is known as the atmosphere. The average atmosphere can be related to the number of configurations. Here we study the distribution of atmospheres as a function of length and…
Most engineered pilings require substantially more force to be driven into the ground than they can resist during extraction. This requires relatively heavy equipment for insertion, which is problematic for anchoring in hard-to-access…
Cables are ubiquitous in many settings and it is often useful to untangle them. However, cables are prone to self-occlusions and knots, making them difficult to perceive and manipulate. The challenge increases with cable length: long cables…
Motivated by a winged seed, which takes advantage of a wing with high angles of attack and its associated leading-edge vortex to boost lift, we propose a powered 13.8-gram aerial robot with the maximum take-off weight of 310 mN (31.6 gram)…
The class of self-nested trees presents remarkable compression properties because of the systematic repetition of subtrees in their structure. In this paper, we provide a better combinatorial characterization of this specific family of…
We present an analysis of the motion of a simple torsion pendulum and we describe how, with straightforward extensions to the usual basic dynamical model, we succeed in explaining some unexpected features we found in our data, like the…
This paper presents a general formulation of equations of motion of a pendulum with n point mass by use of two different methods. The first one is obtained by using Lagrange Mechanics and mathematical induction(inspection), and the second…
Non-autonomous dynamical systems help us to understand the implications of real systems which are in contact with their environment as it actually occurs in nature. Here, we focus on systems where a parameter changes with time at small but…
Robust grasping represents an essential task in robotics, necessitating tactile feedback and reactive grasping adjustments for robust grasping of objects. Previous research has extensively combined tactile sensing with grasping, primarily…
We prove that the speed of a biased random walk on a supercritical Galton-Watson tree conditioned to survive is analytic within the ballistic regime. This extends the previous work arXiv:1906.07913 in which it was shown that the speed is…
Autonomous navigation in extreme mountainous terrains poses challenges due to the presence of mobility-stressing elements and undulating surfaces, making it particularly difficult compared to conventional off-road driving scenarios. In such…
Many snakes live in deserts, forests, and river valleys and traverse challenging 3-D terrain like rocks, felled trees, and rubble, with obstacles as large as themselves and variable surface properties. By contrast, apart from branch…
Tasks in outdoor open world environments are now ripe for automation with mobile manipulators. The dynamic, unstructured and unknown environments associated with such tasks -- a prime example would be collecting roadside trash -- makes them…
Rigid grippers used in existing aerial manipulators require precise positioning to achieve successful grasps and transmit large contact forces that may destabilize the drone. This limits the speed during grasping and prevents "dynamic…