Related papers: The grasshopper problem
We analyze statistical features of the ``optimization landscape'' in a random version of one of the simplest constrained optimization problems of the least-square type: finding the best approximation for the solution of an overcomplete…
We develop a numerical scheme to determine which planar snake motions are optimal for locomotory efficiency, across a wide range of frictional parameter space. For a large coefficient of transverse friction, we find that retrograde…
A new equation is proposed to explain the curvature of spent sparklers. We found the state of a segment of the sparkler to depend strongly on the state of its spent segments. The equation is nearly able to produce the sparkler shape for a…
2D nesting problems rank among the most challenging cutting and packing problems. Yet, despite their practical relevance, research over the past decade has seen remarkably little progress. One reasonable explanation could be that nesting…
We consider the problem of reorienting a rigid object with arbitrary known shape on a table using a two-finger pinch gripper. Reorienting problem is challenging because of its non-smoothness and high dimensionality. In this work, we focus…
Purpose: To present an algorithm for spatially sorting objects into an annular structure. Design/Methodology/Approach: A swarm-based model that requires only stochastic agent behaviour coupled with a pheromone-inspired…
We propose a framework for optimizing a planar parallel-jaw gripper for use with multiple objects. While optimizing general-purpose grippers and contact locations for grasps are both well studied, co-optimizing grasps and the gripper…
We propose a new approach for solving combinatorial optimization problem by utilizing the mechanism of chases and escapes, which has a long history in mathematics. In addition to the well-used steepest descent and neighboring search, we…
This paper presents a novel methodology to model and optimize trajectories of a quadrupedal robot with spinal compliance to improve standing jump performance compared to quadrupeds with a rigid spine. We introduce an elastic model for a…
Motivated by the central limit problem for convex bodies, we study normal approximation of linear functionals of high-dimensional random vectors with various types of symmetries. In particular, we obtain results for distributions which are…
In this paper, we investigate a pursuit-evasion game in which a mobile observer tries to track a target in an environment containing obstacles. We formulate the game as an optimal control problem with state inequality constraint in a simple…
We study systematically the conformal geometry of higher spin bosonic gauge fields in three spacetime dimensions. We recall the definition of the Cotton tensor for higher spins and establish a number of its properties that turn out to be…
The note considers normalized gradient descent (NGD), a natural modification of classical gradient descent (GD) in optimization problems. A serious shortcoming of GD in non-convex problems is that GD may take arbitrarily long to escape from…
This work concerns an alignment problem that has applications in many geospatial problems such as resource allocation and building reliable disease maps. Here, we introduce the problem of optimally aligning $k$ collections of $m$ spatial…
Many theoretical and experimental studies have used heuristic methods to investigate the dynamic behaviour of the passive coupling of adjacent structures. However, few papers have used optimization techniques with guaranteed convergence in…
We study, in d-dimensions, the random walker with geometrically shrinking step sizes at each hop. We emphasize the integrated quantities such as expectation values, cumulants and moments rather than a direct study of the probability…
Grasping is essential in robotic manipulation, yet challenging due to object and gripper diversity and real-world complexities. Traditional analytic approaches often have long optimization times, while data-driven methods struggle with…
Under the spin-position decoupling approximation, a vector with a phase in 3D orientation space endowed with geometric algebra, substitutes the vector-matrix spin model built on the Pauli spin operator. The standard quantum operator-state…
We construct the exact ground state for an antiferromagnetic spin-3/2 model on the two-leg ladder as an optimum ground state. The ground state contains a discrete parameter "sigma"=+/-1 and a continuous parameter "a" which controls z-axis…
We investigate reflected random walks in the quarter plane, with particular emphasis on the time spent along the reflection boundary axes. Assuming the drift of the random walk lies within the cone, the local time converges -- without the…