Computing roadmaps in unbounded smooth real algebraic sets I: Connectivity results

Article Computer Science, Theory & Methods

Positive dimensional parametric polynomial systems, connectivity queries and applications in robotics

Jose Capco et al.

Summary: This paper introduces methods and algorithms for solving connectivity queries of parameterized semi-algebraic sets. These queries are applied in the design of robotic structures with similar kinematic properties. The algorithms provide solutions to connectivity queries of a specific parameter, which is related to kinematic-singularity free path-planning of a specific manipulator. The paper proves how to reduce the problems related to connectivity queries of parameterized semi-algebraic sets to closed and bounded semi-algebraic sets. The algorithm designed in this paper uses computer-algebra methods and has a complexity of singly exponential in the dimension of the ambient space. The algorithm is scalable enough to analyze the family of UR-series robots. The paper also provides a manual analysis of the UR-series robots, proving the number of connected components.

JOURNAL OF SYMBOLIC COMPUTATION (2023)

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Article Robotics