Related papers: The Cost of Bounded Curvature
Markov-Dubins path is the shortest planar curve joining two points with prescribed tangents, with a specified bound on its curvature. Its structure, as proved by Dubins in 1957 nearly 70 years after Markov posed the problem of finding it,…
Consider a region that requires to be protected from unauthorized penetrations. The border of the region, modeled as a unit line segment, consists of high priority segments that require the highest level of protection separated by low…
Hybrid locomotion, which combines multiple modalities of locomotion within a single robot, enables robots to carry out complex tasks in diverse environments. This paper presents a novel method for planning multi-modal locomotion…
Thanks to the rapid evolvement of robotic technologies, robot mowing is emerging to liberate humans from the tedious and time-consuming landscape work. Traditionally, robot mowing is perceived as a "Coverage Path Planning" problem, with a…
In the semi-discrete version of Monge's problem one tries to find a transport map $T$ with minimum cost from an absolutely continuous measure $\mu$ on $\mathbb{R}^d$ to a discrete measure $\nu$ that is supported on a finite set in…
Consider a set of $n$ simple autonomous mobile robots (asynchronous, no common coordinate system, no identities, no central coordination, no direct communication, no memory of the past, non-rigid, deterministic) initially in distinct…
We study the problem of searching for a target at some unknown location in $\mathbb{R}^d$ when additional information regarding the position of the target is available in the form of predictions. In our setting, predictions come as…
The design (shape) of a robot is usually decided before the control is implemented. This might limit how well the design is adapted to a task, as the suitability of the design is given by how well the robot performs in the task, which…
Computing collision-free trajectories is of prime importance for safe navigation. We present an approach for computing the collision probability under Gaussian distributed motion and sensing uncertainty with the robot and static obstacle…
Most of the quadrupeds developed are highly actuated, and their control is hence quite cumbersome. They need advanced electronics equipment to solve convoluted inverse kinematic equations continuously. In addition, they demand special and…
In this paper, we consider the following query problem: given two weighted point sets $A$ and $B$ in the Euclidean space $\mathbb{R}^d$, we want to quickly determine that whether their earth mover's distance (EMD) is larger or smaller than…
We study the problem of planning paths for $p$ distinguishable pebbles (robots) residing on the vertices of an $n$-vertex connected graph with $p \le n$. A pebble may move from a vertex to an adjacent one in a time step provided that it…
We present a path planning problem for a pursuer to intercept a target traveling on a circle. The pursuer considered here has limited yaw rate, and therefore its path should satisfy the kinematic constraints. We assume that the distance…
Navigating a collision-free and optimal trajectory for a robot is a challenging task, particularly in environments with moving obstacles such as humans. We formulate this problem as a stochastic optimal control problem. Since solving the…
Legged robots are able to navigate complex terrains by continuously interacting with the environment through careful selection of contact sequences and timings. However, the combinatorial nature behind contact planning hinders the…
In the pattern formation problem, robots in a system must self-coordinate to form a given pattern, regardless of translation, rotation, uniform-scaling, and/or reflection. In other words, a valid final configuration of the system is a…
This research investigates the efficiency of Floyd algorithm for obstacle-free path planning for autonomous aerial vehicles (UAVs) or drones. Floyd algorithm is used to generate the shortest paths for UAVs to fly from any place to the…
This paper focuses on the energy-time optimal control of wheeled mobile robots undergoing point-to-point transitions in an obstacles free space. Two interchangeable models are used to arrive at the necessary conditions for optimality. The…
The costs incurred in a mobile robot (MR) change due to change in physical and environmental factors. Usually, there are two approaches to consider these costs, either explicitly modelling these different factors to calculate the cost or…
We consider the problem of robot motion planning in an oriented Riemannian manifold as a topological motion planning problem in its oriented frame bundle. For this purpose, we study the topological complexity of oriented frame bundles,…