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Humans can perform parkour by traversing obstacles in a highly dynamic fashion requiring precise eye-muscle coordination and movement. Getting robots to do the same task requires overcoming similar challenges. Classically, this is done by…
Jumping has been an important mechanic since its introduction in Donkey Kong. It has taken a variety of forms and shown up in numerous games, with each jump having a different feel. In this paper, we use a modified Nintendo Entertainment…
An elastic rod, straight in its undeformed state, has a mass attached at one end and a variable length, due to a constraint at the other end by a frictionless sliding sleeve. The constraint is arranged with the sliding direction parallel to…
In the present paper we focus our attention on the design of the feedback-based feed-forward controller asymptotically stabilizing the double-pendulum-type crane system with the time-varying rope length in the desired end position of…
In this paper we deal with the care one must have in adopting approximations in regard with terms he chooses to leave behind in the particular case of the expression valid for the maximum period of a long pendulum oscillating near Earth's…
Rotation distance measures the difference in shape between binary trees of the same size by counting the minimum number of rotations needed to transform one tree to the other. We describe several types of rotation distance where…
During certain times of the year at middle and low latitudes, winds in the upper stratosphere move in nearly the opposite direction than the wind in the lower stratosphere. Here we present a method for maintaining a high-altitude balloon…
The statistics of self-avoiding random walks have been used to model polymer physics for decades. A self-avoiding walk that grows one step at a time on a lattice will eventually trap itself, which occurs after an average of 71 steps on a…
The spontaneous spinning of a rattleback placed on a vibrating platform is investigated. The rattleback is a toy with some curious properties. When placed on a surface with reasonable friction, the rattleback has a preferred direction of…
During the pull-out maneuver, Peregrine falcons were observed to adopt specific flight configurations which are thought to offer an aerodynamic advantage over aerial prey. Analysis of the flight trajectory of a falcon in a controlled…
The forces that act internally in a trebuchet as it delivers a shot depend on the motions of throwing arm, counterweight and sling. These motions are considered known experimentally or theoretically and given in the form of time-dependent…
The logarithmic spiral is observed as a common pattern in several living beings across kingdoms and species. Some examples include fern shoots, prehensile tails, and soft limbs like octopus arms and elephant trunks. In the latter cases,…
Uniform attachment with freezing is an extension of the classical model of random recursive trees, in which trees are recursively built by attaching new vertices to old ones. In the model of uniform attachment with freezing, vertices are…
Handling oversized, variable-shaped, or delicate objects in transportation, grasping tasks is extremely challenging, mainly due to the limitations of the gripper's shape and size. This paper proposes a novel gripper, Lasso Gripper. Inspired…
Jumping is essential for legged robots to traverse through difficult terrains. In this work, we propose a hierarchical framework that combines optimal control and reinforcement learning to learn continuous jumping motions for quadrupedal…
Splay trees are a simple and efficient dynamic data structure, invented by Sleator and Tarjan. The basic primitive for transforming a binary tree in this scheme is a rotation. Sleator, Tarjan, and Thurston proved that the maximum rotation…
A distinctive feature of quadrupeds that is integral to their locomotion is the tail. Tails serve many purposes in biological systems including propulsion, counterbalance, and stabilization while walking, running, climbing, or jumping.…
Interesting phenomena occur when an eccentric rigid body rolls on an inclined or horizontal plane. For example, a variety of motions between rolling and sliding are exhibited until suddenly a jump occurs. We provide a detailed theoretical…
We discuss the equation of motion of the driven pendulum and generalize it to arbitrary driving angle. The pendulum will oscillate about a stable angle other than straight down if the drive amplitude and frequency are large enough for a…
The field of robotics, and more especially humanoid robotics, has several established competitions with research oriented goals in mind. Challenging the robots in a handful of tasks, these competitions provide a way to gauge the state of…