Plane Motion of a Particle Subject to Curvature Constraints

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Abstract

A particle P moves in the plane with constant speed and subject to an upper bound on the curvature of its path. This paper studies the classes of trajectories by which P can reach a given point in a given direction and obtains, for all t, the set R (t) of all possible positions for P at time t, thus extending the results of several recent authors.

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Cite This Study

Cockayne et al. (Wed,) studied this question.

synapsesocial.com/papers/69fca4af8dc9aff719fa481c https://doi.org/https://doi.org/10.1137/0313012

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Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1On Pursuit with Curvature Constraints1972 · 25 citations
2Curvature and Arclength1970 · 5 citations
3A Partial Differential Equation and Parallel Plane Curves1964 · 6 citations
4Differential Games. A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization1966 · 439 citations
5On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents1957 · 3,002 citations

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