Related papers: A "Piano Movers" Problem Reformulated
We study an important practical aspect of the route planning problem in real-world road networks -- maneuvers. Informally, maneuvers represent various irregularities of the road network graph such as turn-prohibitions, traffic light delays,…
This paper presents several new tractability results for planning based on macros. We describe an algorithm that optimally solves planning problems in a class that we call inverted tree reducible, and is provably tractable for several…
In this paper we introduce the notion of an Open Non-uniform Cylindrical Algebraic Decomposition (NuCAD), and present an efficient model-based algorithm for constructing an Open NuCAD from an input formula. A NuCAD is a generalization of…
In this paper, a novel method for path planning of mobile robots is proposed, taking into account the non-holonomic turn radius constraints and finite dimensions of the robot. The approach involves rasterizing the environment to generate a…
In this paper, we propose a new method for path planning to a point for robot in environment with obstacles. The resulting algorithm is implemented as a simple variation of Dijkstra's algorithm. By adding a constraint to the shortest-path,…
Linear projection schemes like Proper Orthogonal Decomposition can efficiently reduce the dimensions of dynamical systems but are naturally limited, e.g., for convection-dominated problems. Nonlinear approaches have shown to outperform…
We present a new algorithm for determining the satisfiability of conjunctions of non-linear polynomial constraints over the reals, which can be used as a theory solver for satisfiability modulo theory (SMT) solving for non-linear real…
This paper proposes a new set of conditions for exactly representing collision avoidance constraints within optimization-based motion planning algorithms. The conditions are continuously differentiable and therefore suitable for use with…
Solid modeling is a technique underlying CAD software as we see it today, and its theories and algorithms are among the most fundamental milestones in the historical development of CAD. Basically, it has answered the question of what…
To increase the speed of operation and reduce operator burden, humanoid robots must be able to function autonomously, even in complex, cluttered environments. For this to be possible, they must be able to quickly and efficiently compute…
Autonomous systems, including robots and drones, face significant challenges when navigating through dynamic environments, particularly within urban settings where obstacles, fluctuating traffic, and pedestrian activity are constantly…
If we give a robot the task of moving an object from its current position to another location in an unknown environment, the robot must explore the map, identify all types of obstacles, and then determine the best route to complete the…
This project aimed to develop an automated cinematography platform using an unmanned aerial vehicle. Quadcopters are a great platform for shooting aerial scenes but are difficult to maneuver smoothly and can require expertise to pilot. We…
Last two decades, the problem of robotic mapping has made a lot of progress in the research community. However, since the data provided by the sensor still contains noise, how to obtain an accurate map is still an open problem. In this…
In this article we consider a linearized Calder\'on problem for polyharmonic operators of order $2m\ (m\ge 2)$ in the spirit of Calder\'on's original work [Cal80]. We give a uniqueness result for determining coefficients of order $\leq…
We consider the speed planning problem for a robotic manipulator. In particular, we present an algorithm for finding the time-optimal speed law along an assigned path that satisfies velocity and acceleration constraints and respects the…
This article describes use of Mathcad mathematical package to solve problem of the motion of two, three and four material points under the influence of gravitational forces on the planar motion and in three-dimensional space. The limits of…
This paper proposes a novel inverse kinematics (IK) solver of articulated robotic systems for path planning. IK is a traditional but essential problem for robot manipulation. Recently, data-driven methods have been proposed to quickly solve…
Modern CAD tools represent 3D designs not only as geometry, but also as a program composed of geometric operations, each of which depends on a set of parameters. Program representations enable meaningful and controlled shape variations via…
Solving real-world optimization problems with quantum computing requires choosing between a large number of options concerning formulation, encoding, algorithm and hardware. Finding good solution paths is challenging for end users and…