Related papers: Computing Feasible Trajectories for an Articulated…
This paper presents the reachability analysis of curves in $\mathbb{R}^3$ with a prescribed curvature bound. Based on Pontryagin Maximum Principle, we leverage the existing knowledge on the structure of solutions to minimum-time problems,…
Many methods in learning from demonstration assume that the demonstrator has knowledge of the full environment. However, in many scenarios, a demonstrator only sees part of the environment and they continuously replan as they gather…
Maneuvering an articulated vehicle on narrow road stretches is often a challenging task for a human driver. Unless the vehicle is accurately steered, parts of the vehicle's bodies may exceed its assigned drive lane, resulting in an…
Sublinear time complexity is required by the massively parallel computation (MPC) model. Breaking dynamic programs into a set of sparse dynamic programs that can be divided, solved, and merged in sublinear time. The rectangle escape problem…
We study supersolvable line arrangements in ${\mathbb P}^2$ over the reals and over the complex numbers, as the first step toward a combinatorial classification. Our main results show that a nontrivial (i.e., not a pencil or near pencil)…
Motion planning for urban environments with numerous moving agents can be viewed as a combinatorial problem. With passing an obstacle before, after, right or left, there are multiple options an autonomous vehicle could choose to execute.…
An elegant characterization of the complexity of constraint satisfaction problems has emerged in the form of the the algebraic dichotomy conjecture of [BKJ00]. Roughly speaking, the characterization asserts that a CSP {\Lambda} is tractable…
Autonomous terrain traversal of articulated tracked robots can reduce operator cognitive load to enhance task efficiency and facilitate extensive deployment. We present a novel hybrid trajectory optimization method aimed at generating…
In this work, we propose a trajectory optimization approach for robot navigation in cluttered 3D environments. We represent the robot's geometry as a semialgebraic set defined by polynomial inequalities such that robots with general shapes…
We study combinatorial configurations with the associated point and line graphs being strongly regular. Examples not belonging to known classes such as partial geometries and their generalizations or elliptic semiplanes are constructed.…
As fully-actuated systems, omnidirectional multirotor aerial vehicles (OMAVs) have more flexible maneuverability and advantages in aggressive flight in cluttered environments than traditional underactuated MAVs. %Due to the high…
This work develops feasible path trajectories for a coordinated strike with multiple aircraft in a constrained environment. Using direct orthogonal collocation methods, the two-point boundary value optimal control problem is transcribed…
Several tools have been developed to enhance automation of theorem proving in the 2D plane. However, in 3D, only a few approaches have been studied, and to our knowledge, nothing has been done in higher dimensions. In this paper, we present…
We propose a novel exact algorithm for the transportation problem, one of the paradigmatic network optimization problems. The algorithm, denoted Iterated Inside Out, requires in input a basic feasible solution and is composed by two main…
Fixed-parameter tractable (FPT) algorithms have been successfully applied to many intractable problems -- with a focus on decision and optimization problems. Their aim is to confine the exponential explosion to some parameter, while the…
We consider a coordinated complexity-aware 4D trajectory planning problem in this paper. A case study of multiple aircraft traversing through a sector that contains a network of airways and waypoints is utilized to illustrate the model and…
A long standing open problem in extremal graph theory is to describe all graphs that maximize the number of induced copies of a path on four vertices. The character of the problem changes in the setting of oriented graphs, and becomes more…
In this paper we propose a technique that assigns obstacles to clusters used for collision avoidance via Mixed-Integer Programming. This strategy enables a reduction in the number of binary variables used for collision avoidance, thus…
This work studies path planning in two-dimensional space, in the presence of polygonal obstacles. We specifically address the problem of building a roadmap graph, that is, an abstract representation of all the paths that can potentially be…
Performing trajectory design for humanoid robots with high degrees of freedom is computationally challenging. The trajectory design process also often involves carefully selecting various hyperparameters and requires a good initial guess…