Related papers: A "Piano Movers" Problem Reformulated
Many real-world applications need path planning algorithms to solve tasks in different areas, such as social applications, autonomous cars, and tracking activities. And most importantly motion planning. Although the use of path planning is…
Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, particularly for quantifier elimination over real-closed fields. However, it can be expensive, with worst case complexity doubly exponential in the…
Cylindrical Algebraic Decomposition (CAD) is an important tool within computational real algebraic geometry, capable of solving many problems for polynomial systems over the reals. It has long been studied by the Symbolic Computation…
A new algorithm to compute cylindrical algebraic decompositions (CADs) is presented, building on two recent advances. Firstly, the output is truth table invariant (a TTICAD) meaning given formulae have constant truth value on each cell of…
We present an algorithm for non-holonomic motion planning (or 'parking a car') that is as computationally efficient as a simple approach to solving the famous Piano-mover's problem, where the non-holonomic constraints are ignored. The core…
A Cylindrical Algebraic Decomposition (CAD) is a decomposition of R^n into a finite collection of semialgebraic cells. A CAD satisfies the "frontier condition" if, for every cell C, there is a collection of cells of the decomposition whose…
The Cylindrical Algebraic Decomposition (CAD) algorithm is a comprehensive tool to perform quantifier elimination over real closed fields. CAD has doubly exponential running time, making it infeasible for practical purposes. We propose to…
Cylindrical Algebraic Decompositions (CADs) endowed with additional topological properties have found applications beyond their original logical setting, including algorithmic optimizations in CAD construction, robot motion planning, and…
In order for a bimanual robot to manipulate an object that is held by both hands, it must construct motion plans such that the transformation between its end effectors remains fixed. This amounts to complicated nonlinear equality…
Motion planning techniques for quadrotors have advanced significantly over the past decade. Most successful planners have two stages: a front-end that determines a path that incorporates geometric (or kinematic or input) constraints and…
This paper explores an eclectic range of path-planning methodologies engineered for rolling surfaces. Our focus is on the kinematic intricacies of rolling contact systems, which are investigated through a motion planning lens. Beyond…
Cylindrical Algebraic Decomposition (CAD) was the first practical means for doing real quantifier elimination (QE), and is still a major method, with many improvements since Collins' original method. Nevertheless, its complexity is…
Cylindrical algebraic decomposition (CAD) is an important tool for working with polynomial systems, particularly quantifier elimination. However, it has complexity doubly exponential in the number of variables. The base algorithm can be…
Recent advancements in robotics have transformed industries such as manufacturing, logistics, surgery, and planetary exploration. A key challenge is developing efficient motion planning algorithms that allow robots to navigate complex…
Cylindrical algebraic decomposition (CAD) plays an important role in the field of real algebraic geometry and many other areas. As is well-known, the choice of variable ordering while computing CAD has a great effect on the time and memory…
Planning in robotics is often split into task and motion planning. The high-level, symbolic task planner decides what needs to be done, while the motion planner checks feasibility and fills up geometric detail. It is known however that such…
We consider cylindrical algebraic decomposition (CAD) and the key concept of delineability which underpins CAD theory. We introduce the novel concept of projective delineability which is easier to guarantee computationally. We prove results…
Learning motion planners to move robot from one point to another within an obstacle-occupied space in a collision-free manner requires either an extensive amount of data or high-quality demonstrations. This requirement is caused by the fact…
We present a decoupled algorithm for motion planning for a collection of unit-balls moving among polyhedral obstacles in $\mathbb{R}^d$, for any $d \ge 2$. We assume that the robots have revolving areas in the vicinity of their start and…
We present a new certified and complete algorithm to compute arrangements of real planar algebraic curves. Our algorithm provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic…