Skip to main content

View full-text article in PMC

. Author manuscript; available in PMC: 2016 Feb 3.

Published in final edited form as: IEEE Trans Robot. 2015 Jan 23;31(1):67–84. doi: 10.1109/TRO.2014.2378431

TABLE IV.

Workspace Boundary Curves for Fig. 3.

Boundary Curve

Section Variables

Boundary Curvature

AB

ϕ_p = 0

0 ≤ ϕ_d ≤ Φ_d

u_{d} = {\hat{u}}_{d}

u_{p} = {\hat{u}}_{p}

{\hat{u}}_{d}

BC

0 ≤ ϕ_p ≤ Φ_p

ϕ_d = Φ_d

u_{d} = {\hat{u}}_{d}

u_{p} = {\hat{u}}_{p}

{\hat{u}}_{p}

CD

ϕ_p = Φ_p

ϕ_d = Φ_d

0 \leq u_{d} \leq {\hat{u}}_{d}

0 \leq u_{p} \leq {\hat{u}}_{p}

- -

DE

0 ≤ ϕ_p ≤ Φ_p

ϕ_d = Φ_d

u_{d} = {\hat{u}}_{d}

0 \leq u_{p} \leq {\hat{u}}_{p}

{\hat{u}}_{p}

EA

0 ≤ ϕ_p ≤ Φ_p

0 ≤ ϕ_d ≤ Φ_d

0 \leq u_{d} \leq {\hat{u}}_{d}

0 \leq u_{p} \leq {\hat{u}}_{p}

0